https://ntrs.nasa.gov/search.jsp?R=19770014078 2020-03-22T11:21:52+00:00Z NASA SP-415 The proceedings of a conference held a t the Dryden Flight Research Center in Edwards, California , on October 9-1 0, 1915 Prepared by Langley Research Center Scientific and Technical Ijzfoymatzon Ofice 1976 N A T I O N A L A E R O N A U T I C S A N D SPACE A D M I N I S T R A T I O N 1K7ashington, D.C. For sale by the National Technical Information Service Springfield, Virginia 22 16 1 Price - $1 2.50 FOREWORD This document is a compilation of 19 t e c h n i c a l papers and comments from a panel d i scuss ion presented during a symposium on F l u t t e r Tes t ing Techniques t h a t w a s held a t t h e NASA Hugh L. Dryden F l i g h t Research Center, Edwards, Ca l i fo rn ia , October 9-10, 1975. Sponsored j o i n t l y by t h e NASA Hugh L. Dryden F l i g h t Research Center and t h e NASA Langley Research Center i n conjunct ion wi th t h e U.S . A i r Force Wright Aeronautical Laboratory, t h e U.S. N a v y A i r Systems Command, and t h e Aerospace F l u t t e r and Dynamics Council, t h e symposium focused on recent developments i n f l u t t e r t e s t i n g i n f l i g h t and on t h e ground and on new methods and techniques f o r improving f l u t t e r t e s t i n g and d a t a ana lys i s . The idea f o r t h i s symposium germinated during t h e 1974 f a l l meeting of t h e Aerospace F l u t t e r and Dynamics Council. There were several reasons f o r holding a symposium on f l u t t e r t e s t i n g ; among them was t h e l a c k of a compre- hensive forum on f l u t t e r t e s t i n g s i n c e t h e F l i g h t F l u t t e r Test ing Symposium he ld May 15-16, 1958. I n add i t ion , major advances have been made i n equipment and f a c i l i t i e s s i n c e t h a t da t e . These advances have l e d t o t h e c r e a t i o n of new techniques f o r t e s t i n g and a n a l y s i s t h a t have been evaluated during t h e develop- ment of new a i r c r a f t from t h e t e s t i n g of models during des ign t o t h e f l u t t e r c learance of t h e f l i g h t veh ic l e s . Thus, t h i s symposium provided an opportuni ty t o d i scuss and eva lua te the s ta te of t h e art f o r f l u t t e r t e s t i n g . sium should a l s o s e r v e t o encourage research i n t h e f i e l d , r e s u l t i n g i n f u r t h e r improvements i n t h e methods used and s a f e r and less c o s t l y t e s t i n g techniques. The sympo- On behalf of t h e symposium committee, I would l i k e t o thank t h e au thors f o r t h e i r f i n e papers , t h e se s s ion chairmen f o r t h e i r inva luable assistance, and t h e panel members f o r sha r ing t h e i r experience and i n s i g h t i n t o f l u t t e r technology. The papers contained i n t h i s compilation have been e d i t e d only f o r c l a r i t y and format. opinions of t h e ind iv idua l au thors . Technical conten ts and views expressed are t h e r e s p o n s i b i l i t y and Eldon E. Kordes Chairman iii COMMITTEES SYMPOSIUM COMMITTEE: Eldon E. Kordes, General Chairman Wilmer H. Reed 111 Walter J. Mykytow George P. Maggos Clarence H. Perisho NASA Flight Research Center NASA Langley Research Center Air Force Wright Aeronautical Laboratory Naval Systems Command Aerospace Flutter and Dynamics Council TECHNICAL PROGRAM COMMITTEE: Clarence H. Perisho, Chairman Mike H. Abla Jack B. Bartley William F. Grosser McDonnell Douglas Corporation Gates Learjet Company Boeing Commercial Airplane Company Lockheed Georgia Company U. S. Army Mobility R&D Laboratory Robert A. Ormiston Raymond P. Peloubet Wilmer H. Reed I11 Convair Aerospace Division, General Dynamics Corporation NASA Langley Research Center Bell Helicopter Company Jing G. Yen PUBLICATION: Wilmer H. Reed 111 NASA Langley Research Center LOCAL ARRANGEMENTS AND GENERAL ASSISTANCE: Trudy Tiedemann B. Lyle Schofield NASA Flight Research Center Air Force Flight Test Center V CONTENTS FOREWORD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iii COMMITTEES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . V SESSION I - THEORY, METHODOLOGY, AND TECHNIQUES Chairman: John C. Houbolt Aeronautical Research Associates of Princeton, Inc. 1. ON IDENTIFYING FREQUENCIES AND DAMPING IN SUBCRITICAL FLUTTER TESTING . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 John C. Houbolt 2. CURVE FITTING OF AEROELASTIC TRANSIENT RESPONSE DATA WITH EXPONENTIAL FUNCTIONS . . . . . . . . . . . . . . . . . . . . . . . 43 Robert M. Bennett and Robert N. Desmarais 3 . DETERMINATION OF SUBCRITICAL DAMPING BY MOVINGBLOCK/RANDOEC APPLICATIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 Charles E. Hammond and Robert V. Doggett, Jr. 4 . TRANSIENT EXCITATION AND DATA PROCESSING TECHNIQUES EMPLOYING THE FAST FOURIER TRANSFORM FOR AEROELASTIC TESTING . . . . . . . . . . . 77 W. P. Jennings, N. L. Olsen, and M. J. Walter 5. TURBULENCE EXCITED FREQUENCY DOMAIN DAMPING MEASUREMENT AND TRUNCATION EFFECTS . . . . . . . . . . . . . . . . . . . . . . . . . 115 Jaak Soovere SESSION I1 - WIND-TUNNEL TECHNIQUES AND APPLICATIONS Chairman: Dale E. Cooley Air Force Flight Dynamics Laboratory 6 . SPECIFICATION OF INPUTS AND INSTRUMENTATION FOR =UTTER TESTING OF MULTIVARIABLE SYSTEMS . . . . . . . . . . . . . . . . . . . . . . . 1 4 3 Narendra K. Gupta and W. Earl Hall, Jr. 7. SOME EXPERIENCE USING SUBCRITICAL RESPONSE METHODS IN WIND-TUNNEL FLUTTER MODEL STUDIES . . . . . . . . . . . . . . . . . . . . . . . 181 Jerome T. Foughner , Jr . 8. WIND TUNNEL INVESTIGATION OF SUPERSONIC WING-TAIL FLUTTER . . . . . . 1 9 3 Lawrence J. Huttsell, Thomas E. Noll, and Donald E. Holsapple vii 9. THE DESIGN, ANALYSIS, AND TESTING OF A LOW-BUDGET WIND-TUNNEL FLUTTER MODEL WITH ACTIVE AERODYNAMIC CONTROLS a . e .) . e I) e e 213 R. Bolding and Re Stearman 10. CORRELATION WITH FLIGHT OF SOME AEROELASTIC MODEL STUDIES IN THE NASA LANGLEY TRANSONIC DYNAMICS TUNNEL . . . . . . . . . . . . . . . 243 Wilmer H. Reed I11 11. PANEL DISCUSSION THEORETICAL ANALYSIS VERSUS TESTING - A TRADE-OFF . . . . . . . . . 263 SESSION I11 - FLIGHT TEST TECHNIQUES AND APPLICATIONS Chairman: Robert F. O'Connell Lockheed-Calif ornia Company 12. TIME SERIES ANALYSIS IN FLIGHT FLUTTER TESTING AT THE AIR FORCE FLIGHT TEST CENTER: CONCEPTS AND RESULTS . . . . . . . . . . . . . 287 Russell W. Lenz and Bruce McKeever 13. FLIGHT FLUTTER TESTING TECHNOLOGY AT GRUMMAN . . . . . . . . . . . . . 319 H. J. Perangelo and F. W. Milordi 14. THE APPLICATION OF DIGITAL COMPUTERS TO NEAR-REAL-TIME PROCESSING OF FLUTTER TEST DATA . . . . . . . . . . . . . . . . . . . . . . . . 377 S . R. Hurley 15. THE APPLICATION OF RECENT TECHNIQUES IN FLIGHT FLUTTER TESTING . . . . 395 M. A. Abla 16. F-15 FLIGHT FLUTTER TEST PROGRAM . . . . . . . . . . . . . . . . . . . . 413 Henry Katz, Francis G. Foppe, and Daniel T. Grossman 17. YF-16 FLIGHT FLUTTER TEST PROCEDURES . . . . . . . . . . . . . . . . . 433 Warren J. Brignac, Halvor B. Ness, Maynard K. Johnson, and Larz M. Smith SESSION IV - FLIGHT TEST TECHNIQUES AND APPLICATIONS - ROTARY WING Chairman: George P. Maggos Naval Air Systems Command 18. INFLIGHT ROTOR STABILITY MONITOR . . . . . . . . . . . . . . . . . . . 457 William A. Kuczynski viii 19. INVESTIGATION OF AEROELASTIC STABILITY PHENOMENA OF A HELICOPTER Wen-Liu Miao, W. Thomas Edwards, and David E. Brandt BY IN-FLIGHT SHAKE TEST . . e e a e e . e 473 20. FLIGHT FLUTTER TESTING OF ROTARY WING AIRCRAFT USING A CONTROL SYSTEM OSCILLATION TECHNIQUE . e . . . . . . . . . e . . . . . . 501 Jing G. Yen, Sathy Viswanathan, and Carl G. Matthys ix ON IDENTIFYING FREQUENCIES AND DAMPING I N SUBCRITICAL FLUTTER TESTING John C. Houbolt Aeronaut ica l Research Assoc ia tes of P r ince ton , I n c . SUMMARY A review i s given of var ious procedures t ha t might be used i n e v a l u a t i n g system response c h a r a c t e r i s t i c s as involved i n sub- c r i t i c a l f l i g h t and wind-tunnel f l u t t e r t e s t i n g o f a i r c r a f t . Emphasis i s given t o the means f o r e l i m i n a t i n g o r minimizing the contamination e f f e c t s produced by an unknown n o i s e i n the inpu t . Resu l t s o f a newly developed procedure f o r i d e n t i f y i n g modal fre- quency and damping va lues , and a p o s s i b l e way f o r making a de- t a i l e d e v a l u a t i o n of system parameters , a r e a l s o given. INTRODUCTION The purpose of t h i s r e p o r t i s t o g ive a review of va r ious procedures tha t might be used i n e v a l u a t i n g system response c h a r a c t e r i s t i c s as involved i n s u b c r i t i c a l f l i g h t and wind t u n n e l f l u t t e r t e s t i n g o f a i rc raf t . The a i m i n such t e s t i n g i s g e n e r a l l y t o e v a l u a t e modal damping and f requencies as a func t ion o f f l i g h t speed. I n some cases , s t u d i e s a i m t o i d e n t i f y t h e s y s t e m para- meters i n g r e a t e r d e t a i l , such as i d e n t i f y i n g t h e c o e f f i c i e n t s o f a modelled d i f f e r e n t i a l equa t ion o f motion. In p r a c t i c a l s u b c r i t i c a l f l u t t e r t e s t i n g three main problems a r i s e : (1) the re u s u a l l y i s an unknown n o i s e i n p u t , such as that due to t u rbu lence , and t h i s contamination makes t h e s y s t e m response eva lua t ion very d i f f i c u l t , u n c e r t a i n , o r impossibxe; ( 2 ) t i m e f o r a t e s t run must o f t e n be kept s h o r t , such as l e s s than 1 0 seconds ( f o r example, t o achieve a given speed t h e a i r p l a n e may have t o be put i n a sha l low d ive and t h e i n t e r v a l o f t ime over which t e s t cond i t ions are reasonably cons t an t i s t h e r e f o r e l i m i t e d ) , sho r t - ness o f r eco rds i n t u r n aggrava tes t h e n o i s e problem; and ( 3 ) an under ly ing desire i s t o be able t o perform rap id ana lyses of t h e r eco rds so t h a t t h e t e s t s may proceed almost immediately to the next t es t run. The procedures p re sen ted h e r e i n r e p r e s e n t va r ious a t tempts t o cope w i t h these problems, w i t h emphasis be ing given t o means f o r minimizing o r o b v i a t i n g the n o i s e problem. Much o f t h e mater ia l i n t h i s r e p o r t i s covered i n r e f e r e n c e 1, which c o n t a i n s a number o f r e f e r e n c e s t o o t h e r work; no o t h e r r e f e r e n c e i s t h e r e f o r e c i t e d . Some new f i n d i n g s are i n c l u d e d , RELEVANT EQUATIONS L e t t h e g e n e r a l govern ing d i f f e r e n t i a l e q u a t i o n f o r r e sponse f o r t he a i r p l a n e s u b c r i t i c a l f l u t t e r sys tem b e g iven by Dly = D2P where D1 and D2 are d i f f e r e n t i a l o p e r a t o r s , and y i s t h e r e sponse t o t h e f o r c i n g f u n c t i o n P . The f o r c e P may be a p r e s c r i b e d f o r c e , as o b t a i n e d from a shaker , o r i t may be some unknown q u a n t i t y , such as due t o a tmospher ic t u r b u l e n c e , and these f o r c e s may be a c t i n g s i n g l y or i n combinat ion. I f t h e i n p u t f o r c e i s a Di rac f u n c t i o n 6(0) a t t = 0 , e q u a t i o n (1) d e f i n e s t h e impulse r e sponse f u n c t i o n h as fo l lows Dlh = D 2 6 ( 0 ) Fo r a u n i t s i n u s o i d a l i n p u t , P = e iwt , and w i t h i w t y = H e e q u a t i o n (1) y i e l d s t h e f requency r e sponse f u n c t i o n acco rd ing t o t h e e q u a t i o n ( A , + i A 2 ) ( A + i B ) = N 1 + i N 2 (4) where Al,N1 and A 2 , N 2 are t h e r e a l and imaginary p a r t s t h a t are a s s o c i a t e d w i t h t h e o p e r a t o r s D1 and D2 . The A com- ponent o f H i s symmetr ical w i t h r e s p e c t t o t h e f requency w , the B component i s a n t i s y m m e t r i c a l . The h and H f u n c t i o n s are re la ted b y t h e F o u r i e r t r a n s - form p a i r Ro ( 5 ) H = h e - i w t d t 0 2 h = - 1 HeiWt dw 2lT By t he sup f o r any g e n e r a l r p o s i t i o n theorem, the s o l u t i o n o f eq a t i o n (l), f o r c i n g f u n c t i o n P , i s g iven by 00 Y = P ( T ) h ( t - T ) d T -00 ( 7 ) The F o u r i e r t r a n s f o r m o f t h i s e q u a t i o n i s from which H fo l lows as F H = X ( 9 1 FP Equat ion ( 8 ) a l s o leads t o t h e well-known spectral result I f P i s e q u a l t o P + Q , where P i s a known f o r c e , and Q i s an unknown "noise" f o r c e , e q u a t i o n ( 8 ) would appear F = H(Fp + FQ) Y - The m u l t i p l i c a t i o n th rough the complex con juga te Fp leads i n t u r n to t h e s p e c t r a l e q u a t i o n i s the c r o s s spectrum between P and y , @ p i s t h e i s the c r o s s spectrum between P and @PY where = 0 , and t h u s spectrum o f P , and Q . I f P and Q are u n c o r r e l a t e d , @pQ e q u a t i o n (11) y i e l d s t he impor t an t c ross -spec t rum e q u a t i o n @PQ I which appears as a comple te ly n o i s e - f r e e r e s u l t . 3 Reference 1 g i v e s some s i g n i f i c a n t s p e c i a l s o l u t i o n s to e q u a t i o n (I), as f o l l o w s . DIRh = D2h(-t) where 00 Thus, t h e a u t o c o r r e l a t i o n f u n c t i o n o f h i s t h e r e sponse o f s y s t e m to a f o r c e i n p u t o f h ( - t ) 11: _I where Qn i s white n o i s e . For t h i s s i t u a t i o n , it can b e shown tha t = Rh ; t h u s , t h e c o r r e l a t i o n f u n c t i o n o f t h e r e s p o n s e to white n o i s e i s t h e same as t h e a u t o c o r r e l a t i o n f u n c t i o n o f t h e impulse f u n c t i o n h . Ry n 111: - D R = D2Rp I Py Thus, i f the a u t o c o r r e l a t i o n f u n c t i o n o f an i n p u t P i s a p p l i e d to the s y s t e m as an i n p u t f o r c e , t he r e sponse i s the c ross -co r re - l a t i o n f u n c t i o n between P and t h e r e sponse y due to P e CLASSIFICATION OF THE SWEPT SINE F U N C T I O N Forc ing i n p u t s are ach ieved by s e v e r a l means, such as i n - e r t i a l shakers or aerodynamic vane e x c i t e r s , e x p l o s i v e c h a r g e s , s t i c k raps, and the n a t u r a l t u r b u l e n c e o f t h e atmosphere. O f a l l these means, vane e x c i t e r s or shakers a r e most commonly used . For the f o r c i n g f u n c t i o n , t h e swept s i n e wave has become a p o p u l a r c h o i c e , mainly because i t cove r s a s i z a b l e f r equency band i n a s h o r t p e r i o d o f t i m e and because t h e s p e c t r a l c o n t e n t o f t h i s f u n c t i o n resembles whi te n o i s e . The r a t e o f sweep and t o t a l d u r a t i o n are prime v a r i a b l e s ; w i t h some t e s t s t h e sweep r a t e i s fas t , i n o t h e r s t h e ra te i s q u i t e s low, For d i s c u s s i o n and t e s t i n g pu rposes , i t a p p e a r s d e s i r a b l e to make a c l a s s i f i c a t i o n o f t h e d u r a t i o n of sweep. The ra te o f change o f f requency depends o f c o u r s e on t h e f requency range covered and t h e d u r a t i o n r e q u i r e d to make t h e sweep, For t h e t e s t i n g o f most a i r c r a f t sys t ems , however, 4 i t appea r s tha t c l a s s i f i c a t i o n can be based mainly on d u r a t i o n a l o n e The f o l l o w i n g c l a s s i f i c a t i o n i s sugges t ed : 1) F a s t sweep - one made w i t h a d u r a t i o n o f about 5 t o 1 0 seconds 2 ) Moderate sweep - d u r a t i o n o f around 1 minute 3) Slow sweep - d u r a t i o n of a round 5 minutes Each of these sweeps has c e r t a i n advantages and c e r t a i n de- f i c i e n c i e s , depending on the a p p l i c a t i o n . The s low sweep i s t h e b e s t f o r minimiz ing n o i s e , b u t t h e drawback i s l o n g t e s t i n g and r e c o r d a n a l y s i s times. I n many i n s t a n c e s , though, t e s t c o n d i t i o n s d i c t a t e t h e u s e o f f a s t sweeps. DAMPING AND FREQUENCY EVALUATION FOR THE IDEAL CASE F i g u r e 1 i n d i c a t e s three b a s i c ways f o r e v a l u a t i n g the damping and f requency o f a mode. It i s assumed t h a t a t e s t has been made, such as th rough a p p l i c a t i o n o f a swept s i n e wave f o r c i n g f u n c t i o n , and tha t t h e r e sponse has been ana lyzed to ob- t a i n H ( e q u a t i o n ( g ) ) , which y i e l d s B and A , C = IHI = A + B2 , and h ( e q u a t i o n ( 6 ) ) . The s i t u a t i o n d e p i c t e d by t h i s f i g u r e i s ideal ; t ha t i s , t h e r e i s no n o i s e p r e s e n t i n the i n p u t and only a s i n g l e mode i s invo lved . The t o p s k e t c h d e p i c t s t h e t r a n s f e r l o c i or admi t t ance p l o t i n v o l v i n g A and B . The r e s o n a n t f requency f o i s i d e n t i f i e d a t t h e p o i n t where t h e r e i s the g r e a t e s t ra te o f change o f a r c l e n g t h with r e s p e c t to a change i n t h e f r equency . The damping r a t i o - i s g i v e n by t h e e q u a t i o n shown. I n the second scheme i n v o l v i n g C 2 = A + B p l o t t e d a g a i n s t f , t h e modal f r equency i s i d e n t i f i e d by t h e l o c a t i o n o f t he peak, t h e damping by t he width a t 1 / 2 power. I n t he t h i r d scheme, i n v o l v i n g damped unforced motion a f t e r some e x c i t a t i o n , f requency i s i d e n t i f i e d by t h e p e r i o d T , damping by t h e l o g decrement e q u a t i o n . 2 2 2 @ c r 2 2 Note, the o f fhand appearance o f a peak ( second s k e t c h o f f i g u r e 1) may a t f irst cause a m i s i n t e r p r e t a t i o n of damping. I n f i g u r e 2 , f o r example, t h e peaks on t h e r i g h t v i s u a l l y seem to i n d i c a t e more damping t h a n the peaks on t h e l e f t ; a l l peaks on the same l i n e have t h e same damping, however, as measured i n terms o f p e r c e n t o f c r i t i c a l damping. Likewise, t h e th ree peaks on t h e r i g h t o f t h e middle s k e t c h have t h e same damping, even though t h e s h o r t e s t peak seems to s u g g e s t a l a r g e r damping t h a n the t a l l e s t peak e 5 Other means f o r deducing frequency and damping i n v o l v e curve- f i t t i n g p rocedures , such as f i t t i n g t h e expe r imen ta l ly d e r i v e d frequency r e sponse f u n c t i o n H , or f i t t i n g t h e impulse r e sponse f u n c t i o n h and then deducing the roots from t h e f i t t e d cu rves . When modes are c l o s e t o g e t h e r , or when n o i s e i s p r e s e n t i n the i n p u t , t h e t echn iques o f f i g u r e 1 break down. It i s towards h a n d l i n g t h e s i t u a t i o n of t h e presence o f a number of modes and the contaminat ion due to an unknown n o i s e source t h a t t he re- mainder o f t h i s r e p o r t i s devoted. THE USE OF EXCITERS AND TRANSDUCERS I N COMBINATION It i s odd t h a t l i t t l e i n g e n e r a l has been done i n u s i n g t r a n s d u c e r s i n p a i r s as a way of h e l p i n g t o s o l v e t h e c l o s e l y spaced mode s i t u a t i o n , p a r t i c u l a r l y i n s e p a r a t i n g the symmetr ica l and an t i symmet r i ca l modes which have f r e q u e n c i e s c l o s e t o g e t h e r . F i g u r e 3 s e r v e s as a reminder o f what p r a c t i c e s should b e fo l lowed i n g e n e r a l . With one shaker, s a y on t h e r i g h t , t h e use o f on ly t h e s i g n a l from p o i n t 1 makes i t very d i f f i c u l t to d i s - t i n g u i s h t h e symmetric mode from the an t i symmetr ic mode. The a d d i t i o n o f t h e s i g n a l s from p o i n t 1 and p o i n t 2 , however, i d e n t i f i e s t h e symmetric mode and v i r t u a l l y e l i m i n a t e s t h e a n t i - symmetric mode. The s u b t r a c t i o n o f t h e s i g n a l s , on t h e o t h e r hand, i d e n t i f i e s t h e an t i symmetr ic mode t o t h e e x c l u s i o n o f t h e symmetric mode. Th i s s u b t r a c t i o n scheme a l s o p rov ides f o r good r e j e c t i o n o f symmetric e x c i t a t i o n due to n o i s e . F o r two shakers, one on t h e l e f t and one on the r i g h t , use o f y1 o r y1 i- y2 f o r in-phase e x c i t a t i o n g i v e s s y m m e t r i c mode i s o l a t i o n . or c a s e , due to n o i s e . If t h e two shakers are 180' out o f phase , g i v e s good an t i symmetr ic mode i s o l a t i o n . Agaig: i n t h i s a l s o g i v e s good r e j e c t i o n o f symmetric e x c i t a t i o n y 1 - y2 y1 - y2 The use of two pick-ups i n a d i f f e r e n t chordwise p o s i t i o n , such as at p o i n t s 3 and 4, a l s o shou ld be cons ide red a s a way of h e l p i n g t o i s o l a t e c l o s e l y spaced modes;. t he idea h e r e i s t h a t e x c i t a t i o n o f d i f f e r e n t modes appears i n a d i f f e r e n t r e l a t i v e s e n s e acco rd ing to the c l o s e n e s s to t h e nodal l i n e s , F igure 4 d e p i c t s r e s u l t s o b t a i n e d f o r a three-mode system, w i t h two symmetric modes o f 3 Hz and 10 Hz and one ai i t isymmetr ic mode of 9 . 8 Hz; t h u s , the an t i symmetr ic mode had a frequency only 2 pe rcen t d i f f e r e n t from one of t h e symmetric modes. With one shaker, a swept s i n e wave e x c i t a t i o n , and only one pick-up, t h e deduced r e s u l t s f o r A , B , C 2 , B vs A , and h , i n d i c a t e tha t o n l y two modes a r e p r e s e n t , one around 3 Hz and one around 1 0 Hz. 6 Figure 5 a p p l i e s to one-shaker e x c i t a t i o n of t h e same s y s t e m , b u t t h e s i g n a l s from a r i g h t and a l e f t t r a n s d u c e r are s u b t r a c t e d . The marked change i n t h e r e s u l t s i s a c l e a r i n d i c a t i o n tha t two modes a r e p r e s e n t n e a r 1 0 Hz. F o r f i g u r e 6, t he s i t u a t i o n i s t h e same as f o r f i g u r e 5 , excep t t h a t a s t r o n g symmetric e x c i t a t i o n due to n o i s e i s a l s o p r e s e n t . The r e s u l t s , i n s p i t e o f the n o i s e , g i v e s a t i p - o f f t h a t there a r e two c l o s e l y spaced modes around 1 0 Hz. Thus, w i t h one s h a k e r o p e r a t i o n , t he t echn ique o f adding t h e s i g n a l s from two o p p o s i t e t r a n s d u c e r s and o f s u b t r a c t i n g the s i g n a l s and comparing t h e deduced r e s u l t s appea r s as a good way to es t ab l i sh whether two modes with f r e q u e n c i e s c l o s e t o g e t h e r - one symmetric, one an t i symmetr ic - are p r e s e n t . Two s h a k e r s , first used symmetr ica l ly t h e n a n t i s y m m e t r i c a l l y , p rovide an even b e t t e r way t o i s o l a t e symmetric and an t i symmetr ic modes. I N I T I A L SEQUENCE OF DATA A N A L Y S I S Some o f the f i r s t data a n a l y s i s checks tha t should be made a r e o f t e n over looked i n a t e s t i n g sequence. A review of c e r t a i n i n i t i a l s t e p s t h a t should b e performed i s t h u s cons ide red worth- wh i l e . It i s assumed tha t tes ts a r e b e i n g made w i t h a swept s i n e f o r c e i n p u t , The f i r s t a n a l y s i s t h a t should be made i s to make an a t tempt to i d e n t i f y modal f r e q u e n c i e s roughly , to c l a s s i f y t he modes as to whether t h e y are symmetr ical o r a n t i s y m m e t r i c a l , and to see i f t h e apparent modes can be i d e n t i f i e d w i t h ground v i - b r a t i o n modes. Suggested f i r s t s t e p s a r e a s fo l lows : 1) Combine s i g n a l s as i n d i c a t e d i n t h e p r e v i o u s s e c t i o n . 2 ) Scan t h e combined t i m e h i s t o r y s i g n a l s and look f o r " b u r s t s " i n t h e response ; t he o b j e c t here i s t o o b t a i n a rough i d e a o f t h e modal f r e q u e n c i e s and to e s t a b l i s h whether t h e mode i s symmetric o r an t i symmetr ic and whether p r i m a r i l y bending or t o r s i o n . 3) From the s i g n a l s , e s t a b l i s h raw H v a l u e s ( e q u a t i o n ( 9 ) ) and i n t u r n h v a l u e s ( e q u a t i o n ( 6 ) ) . Clear h , accord ing to the c l e a r e d h procedure d i s c u s s e d sub- s e q u e n t l y , t r a n s f o r m back to first improved H , and form C2 = 1 H I 2 = A2 + B2 . Examine the C 2 f u n c t i o n to ob- t a i n a second check on the modal f r e q u e n c i e s ( v e r i f y t h o s e es tab l i shed by scann ing t h e t i m e h i s t o r y s i g n a l s , p i c k up o t h e r s t ha t may have been missed) and to o b t a i n a f i rs t e s t i m a t i o n of modal damping where p o s s i b l e . o f t h e n o i s e problem can be made, and a judgment can be 4 ) From t h e appearance of t h e C2 f u n c t i o n s , an assessment 7 r e n d e r e d as to what t y p e p rocedures s h o u l d be used subsequen t ly to minimize the n o i s e problem, E s s e n t i a l l y , the idea behind these s t e p s i s to do something q u i t e s imple a t f i rs t s o as to o b t a i n a qu ick i n s i g h t as to what t h e f r e q u e n c i e s might b e and to o b t a i n a qu ick appraisal o f the s e v e r i t y and n a t u r e o f t he n o i s e problem. TECHNIQUES FOR M I N I M I Z I N G OR ELIMINATING INPUT NOISE EFFECTS Use o f Both I n p u t and Output I n f o r m a t i o n S i x schemes f o r cop ing w i t h t h e problem o f hav ing n o i s e i n t he i n p u t are p r e s e n t e d i n b r i e f f a s h i o n i n t h i s s e c t i o n . (See r e f e r e n c e 1 f o r more d e t a i l . ) It i s assumed t h a t one or more s h a k e r s are used to d r i v e t h e system, such as by a swept s i n e wave, and t h a t an unknown e x c l t a t i o n n o i s e f o r c e , such as due to b u f f e t i n g or a tmospher i c t u r b u l e n c e , i s a l s o p r e s e n t . C l e a r i n g h .- F i g u r e 7 i s t y p i c a l o f t h e r e s u l t s t h a t are o b t a i n e d for H and h , by means o f e q u a t i o n s (9) and ( 6 ) , when a l a r g e i n p u t n o i s e i s p r e s e n t a l o n g w i t h t h e swept s i n e wave e x c i t a t i o n . One way to e l i m i n a t e much o f the n o i s e con tamina t ion i s s i m p l y to c l e a r or erase the r e s u l t s f o r h beyond a p o i n t where u s e f u l i n f o r m a t i o n no l o n g e r seems to a p p e a r , such as p o i n t a i n f i g u r e 7, and t h e n to t r a n s f o r m t h i s t r u n c a t e d h back to H ( eqe ( 5 ) ) . Example r e s u l t s are g i v e n i n f i g u r e 8. The remarkable improvement t h a t i s o b t a i n e d for t h e A and B v a l u e s by d o i n g t h i s s imple exped ien t is seen , Weight ing h .- Another t e c h n i q u e i s shown i n f i g u r e 9. Here t h e raw h i s weighted by an e x p o n e n t i a l f u n c t i o n ; t h e weighted r e s u l t i s t h e n t r a n s f o r m e d back to g i v e r e f i n e d A and B v a l u e s . T h i s t e c h n i q u e , as w i t h f i g u r e 8 , r e d u c e s n o i s e e f f e c t s g r e a t l y . With t h i s w e i g h t i n g t e c h n i q u e , a c o r r e c t i o n to t h e deduced v a l u e s o f damping must be made to c o r r e c t f o r t h e a p p a r e n t damping t h a t i s added by t h e w e i g h t i n g f u n c t i o n used . Use o f cross c o r r e l a t i o n between i n p u t and o u t p u t . - F i g u r e lO(a) a p p l i e s to t h e raw r e s u l t s as o b t a i n e d by use o f e q u a t i o n ( 9 ) . By c o n t r a s t , the r e s u l t s shown i n f i g u r e 1 0 ( b ) were o b t a i n e d by use of e q u a t i o n (121, which i n v o l v e s the c r o s s spec t rum between the measured o u t p u t and t h e known shaker f o r c e i n p u t . T h i s c r o s s - c o r r e l a t i o n t e c h n i q u e i s s e e n to g i v e a marked improvement i n t h e deduced A and B values.. I n g e n e r a l , t h e l o n g e r t h e r e c o r d , the b e t t e r i s t h e n o i s e min imiza t ion by t h i s t echn ique . 8 Peak s h i f t i n g . - F igu re 11 i s used to d e s c r i b e the peak s h i f t i n g t echn ique f o r e l i m i n a t i n g n o i s e e f f e c t s , The t o p s k e t c h d e p i c t s t h e swept s i n e wave i n p u t f o r c e , the bot tom s k e t c h the noise-contaminated r e sponse , F i r s t , s e l e c t a peak such as a Then s e l e c t peak b and s h i f t the e n t i r e r e c o r d s o as t o make peak b f a l l on peak a a Next, take peak c and s h i f t the r e c o r d to make peak c f a l l on a . peaks i n s u c c e s s i o n , and t h e n add a l l composl te i n p u t f o r c e d e s i g n a t e d by Db t h i s f o r a number of the r e s u l t s to form a The ou tpu t r e sponse i s handled i n t he same way, b u t u s i n g t he same s h i f t s as used f o r t he i n p u t ; t he composi te r e sponse i s d e s i g n a t e d as YT = E yn Now deduce H from PT and yT , u s i n g e q u a t i o n ( 9 ) . The concept i n t h i s t echn ique i s tha t a s i n g l e s h o r t record may be used and t ha t the s h i f t i n g and adding o p e r a t i o n s cause t h e meaningful o r i n t e l l i g e n t p a r t o f t he r e c o r d to b e enhanced, ampl i f ied , o r r e i n f o r c e d , whi le t h e n o i s e l e v e l remains t he same ( o r t h e s igna l - to -no i se r a t i o i n c r e a s e s ) e Figure 1 2 g i v e s re- s u l t s o b t a i n e d i n a p a r t i c u l a r case where only 19 s h i f t s were made. I n t h e maln frequency range o f i n t e r e s t , around 1 0 H z , i t i s seen that p r a c t i c a l l y n o i s e - f r e e r e s u l t s are o b t a i n e d . A f e a t u r e of t h e peak s h i f t i n g scheme i s t h a t i t i s p o s s i b l e to c o n c e n t r a t e on v a r i o u s frequency ranges even w i t h t h e use o f a s i n g l e r eco rd . For example, i n f i g u r e 11, two " b u r s t s " i n the o u t p u t response a r e n o t e d , s u g g e s t i n g two f r e q u e n c i e s of p o s s i b l e concern. To c o n c e n t r a t e on t h e lower f requency , peaks i n t h e v i c i n i t y o f peak a are s h i f t e d t o f a l l a t peak a ; t o concen- t r a t e on the h i g h e r f requency , peaks i n t h e v i c i n i t y o f peak p are s h i f t e d , . . Ensemble averaging . - I n ensemble ave rag ing , t h e concept i s to deduce, by r e p e a t r u n s , a number of raw estimates f o r the f u n c t i o n h , and t h e n to add a l l t h e r a w f u n c t i o n s t o g e t h e r . The idea i s t h a t t h i s averaging- type o p e r a t i o n w i l l "average o u t " n o i s e e f f e c t s and l e a v e only t h e meaningful s i g n a l . Example r e s u l t s , i n v o l v i n g an ensemble average o f 20 r a w f u n c t i o n s , are shown i n f i g u r e 13 . It i s seen that v i r t u a l l y n o i s e - f r e e r e s u l t s are ob- t a i n e d . T h i s i s one of t h e best schemes f o r e l i m i n a t i n g n o i s e , b u t t he main drawback i s tha t it r e q u i r e s making a number o f r e p e a t runs . Sweep ove r l i m i t e d frequency band.- F igure 14 i s g iven as a h e l p to d e s c r i b e a l i m i t e d sweep approach. Suppose t h a t t e s t sweeps are made to cover t h e range o f 3 Hz t o 25 Hz i n 1 0 seconds , and c o n s i d e r t ha t t h e a n a l y s i s of t h e r e s u l t s i n d i c a t e some modal 9 i n f o r m a t i o n i n t h e r ange o f 1 0 Hz b u t t h a t t h e r e s u l t s are t o o n o i s y to b e i n t e r p r e t e d w i t h conf idence . A good way t o improve the s i t u a t i o n i s t o sweep o v e r o n l y the f requency range o f con- c e r n , s a y , i n t h i s c a s e , from 8 Hz to 1 2 Hz i n the 1 0 seconds o f sweep t i m e . Generally., a v a s t improvement i n the deduced re- s u l t s w i l l b e no ted . The d i s a d v a n t a g e , o f c o u r s e , i s t h e problem o f r e s e t t i n g t h e sweep r a n g e and o f h a v i n g to make a n o t h e r run . Use o f Output I n f o r m a t i o n Only There are a t l ea s t two ways t o d e r i v e s y s t e m re sponse c h a r a c t e r i s t i c s by c o n s i d e r a t i o n o f t h e o u t p u t r e s p o n s e a l o n e . The p rocedures a p p l y i n g e n e r a l whether t h e r e s p o n s e i s due to a f o r c e d swept e x c i t a t i o n w i t h an unknown n o i s e i n p u t o r whether t h e r e s p o n s e i s due to n o i s e e x c i t a t i o n a l o n e . One p rocedure i n v o l v e s t h e e s t a b l i s h m e n t o f t h e au to - c o r r e l a t i o n f u n c t i o n R o f t h e o u t p u t r e sponse . Each s i d e or h a l f of t h i s symmetric f u n c t i o n has c h a r a c t e r i s t i c s of t h e h f u n c t i o n . The F o u r i e r t r a n s f o r m o f R i s t h e s p e c t r u n t h e r e s p o n s e . Examinat ion o f t h i s spec t rum g i v e s an i n d i c a t i o n o f t h e f r equency and damping of t h e system modes. Ensemble a v e r a g i n g o f the R f u n c t i o n s i s found to b e a powerfu l way to minimize n o i s e by t h i s approach , r e f e r e n c e 1. Othe r ways t o use t h e Ry s equen t s e c t i o n . Y of @ Y Y Y f u n c t i o n and minimize n o i s e w i l l b e i n d i c a t e d i n t h e sub- A second p rocedure f o r d e r i v i n g system r e s p o n s e c h a r a c t e r - i s t i c s u s i n g r e sponse i n f o r m a t i o n a l o n e i s t h e format ion o f t h e "randomdec" s i g n a t u r e . The e s s e n t i a l s o f one t y p e o f c o n s t r u c t i o n f o r t h i s approach are shown i n f i g u r e 15. It can be r easoned t h a t t he sum o f a l l t h e i n d i v i d u a l s i g n a l s should form a pure s i g n a l which resembles or has c h a r a c t e r i s t i c s o f t h e h f u n c t i o n . Damping and f requency f o l l o w from t h e r e s u l t i n g summed s i g n a l . A main d i f f i c u l t y of t h e approach i s that the summation must o f t e n i n v o l v e hundreds o f f u n c t i o n s b e f o r e converged v a l u e s o f t h e sum are ach ieved . Another d i f f i c u l t y i s i n i d e n t i f y i n g c l o s e l y spaced modes. SUCCESSIVE, CORRELATIONS OF CORRELATION RESULTS - A P R O M I S I N G SOLUTION TO THE NOISE PROBLEM Under a c o n t r a c t e f f o r t f o r AFFTC/AFSC, Edwards AFB, t h e a u t h o r has developed a d d i t i o n a l t e c h n i q u e s f o r t r e a t i n g the n o i s e problem - t e c h n i q u e s which a p p e a r remarkable and i n a way u n b e l i e v a b l e . This s e c t i o n summarizes some o f t h e r e s u l t s 10 o b t a i n e d . The p rocedures invo lved are q u i t e v e r s a t i l e and r e p r e - sent subsequent m a n i p u l a t i o n s f o r improving the q u a l i t y o f t he re- sults t ha t are o b t a i n e d by most all t h e p rocedures d e s c r i b e d e a r l i e r i n t h i s r e p o r t . Two f i g u r e s are p r e s e n t e d f i rs t as a way to d e s c r i b e the p rocedures invo lved . I n f i g u r e 1 6 , t h e t o p s k e t c h r e f e r s to a u t o c o r r e l a t i o n o f t h e raw h f u n c t i o n ( s e e eq. (14)) t h a t has been deduced b y any o f the p rocedures d i s c u s s e d p r e v i o u s l y , o r it re fers to t h e a u t o c o r r e l a t i o n R , o b t a i n e d by c o n s i d e r i n g o n l y t h e r e s p o n s e (due to n o i s e a l o n e , due to a swept s i n e wave a l o n e , o r due t o these fcrrcing f u n c t i o n s a c t i n g i n combina t ion ) . Note, t he raw h s h o u l d a lways be c l e a r e d as d i s - cussed i n connec t ion w i t h f i g u r e s 7 and 8. L ikewise , i f the a u t o c o r r e l a t i o n f u n c t i o n i s used, t h e "noisy" t a i l s ( t h e t a i l p o r t i o n s on e i t h e r s ide which appear to be due to n o i s e o n l y ) s h o u l d be erased. Then the fo l lowing s t e p s are performed: Y Make R1 one-sided; c a l l it rl Form R2 , t he a u t o c o r r e l a t i o n o f r1 Form f u n c t i o n f o r improvement ( r e d u c t i o n i n n o i s e c o n t e n t ) and f o r mode i d e n t i f i c a t i o n @ * , t he F o u r i e r t r a n s f o r m o f R2 ; look a t t h i s Go back to R2 Make R2 one-sided; c a l l i t r Repeat t h e s e s t e p s as o f t e n as n e c e s s a r y u n t i l the spec t rum 2 a p p e a r s w i thou t d i s t o r t i o n due t o n o i s e . @n I n t he a p p l i c a t i o n of these s t e p s , t h e f o l l o w i n g w i l l o c c u r : The modes which show up w i t h low power w i l l f i rs t d i s a p p e a r (means for r e c o v e r i n g these modes w i l l be d i s c u s s e d s u b s e q u e n t l y ) . The mode w i t h the n e x t l owes t power ( a c t u a l l y a combi- n a t i o n o f power and damping) w i l l t h e n d i s a p p e a r , and so on, u n t i l f i n a l l y only one mode remains . With each i t e r a t i o n , t h e r e s u l t s become more and more n o i s e - f r e e . Sometimes, depending on modal power and dampfng and on mode c l o s e n e s s , n o i s e - f r e e r e s u l t s w i l l occu r w i t h pe rhaps two o r th ree modes s t i l l remain ing . The r e a d i n g o f t h e f requency and damping of these re- main ing modes, by the second scheme o f f i g u r e 1, w i l l be 11 an a c c u r a t e i n d i c a t i o n of the f requency and damping o f these modes, F i g u r e 1 7 i l l u s t r a t e s a companion t y p e m a n i p u l a t i o n , I n t h i s c a s e , t h e c o r r e l a t i o n f u n c t i o n s are kep t i n t h e i r two-sided form; t h u s , a c o r r e l a t i o n f u n c t i o n o f a c o r r e l a t i o n f u n c t i o n i s found, i n s u c c e s s i o n , I n t h i s c a s e , t h e f o l l o w i n g shou ld b e ob s e r v e d 1) The modes with the lowes t power l o s e more and more power w i t h each i t e r a t i o n and f i n a l l y d i s a p p e a r . 2 ) The peaks become more and more sp iked ; damping i s lost, b u t f requency i s more and more s h a r p l y p i n p o i n t e d . Although t h e t h e o r y i s no t g i v e n h e r e , i t s h o u l d be n o t e d t h a t t h e consequences o f t h e two t y p e s of man ipu la t ion d e s c r i b e d can be e x p l a i n e d on a t h e o r e t i c a l bas i s . Means f o r r e c o v e r i n g any lost mode a r e as f o l l o w s . Go back to t h e o r i g i n a l spec t rum t y p e f u n c t i o n $1 . peak a would probably have remained to t h e end . But , suppose i t was d e s i r e d to i d e n t i f y t h e mode i n i c a t e d by b more pre- c i s e l y . I n t h i s c a s e , s imp ly e r a s e t he 4 , f u n c t i o n above fre- quency w 2 and below w1 ( i n t h i s c a s e , e r a s i n g above w 2 i s a l l t h a t i s r e q u i r e d ) ; a p p l i c a t i o n o f t h e s t e p s d e s c r i b e d e a r l i e r w i l l t h e n b r i n g ou t mode b i n a p u r e form. I n f i g u r e 1 6 , F igu re 1 8 shows r e s u l t s as o b t a i n e d by t h e one-sided proce- d u r e , u s i n g h as e s t a b l i s h e d from a raw o r contaminated H The exper iment i nvo lved use o f an a n a l o g s i m u l a t i o n o f a s y s t e m ; e x c i t a t i o n was by means o f a l i n e a r swept s i n e wave, and an un- known random n o i s e . I n p a r t ( a ) , w e see f r e q u e n c i e s a round 3 Hz and 10 Hz, b u t t h e p r e c i s e l o c a t i o n and damping cannot be e s - t a b l i s h e d . I n pa r t ( b ) , which r e p r e s e n t s t h e f i rs t i t e r a t i o n , mode 1 has j u s t about d i s a p p e a r e d , and t h e r e s t o f t h e f u n c t i o n i s much more n o i s e - f r e e . By 5 i t e r a t i o n s , mode 2 has become very p u r e ; damping and f requency a r e n e a r l y p r e c i s e l y t h e v a l u e s set i n t he a n a l o g s e t up ( i n t h i s c a s e , f o = 10 Hz , - ' - 0 . 0 5 ) . e c r F igu re 19 g i v e s r e s u l t s u s i n g t h e r e sponse o n l y , and i t s a u t o c o r r e l a t i o n , f o r t he same run o f f i g u r e 18. The raw spec t rum i n d i c a t e s t he two modes i n t h e v i c i n i t y o f 3 Hz and 10 Hz, By t h r e e i t e r a t i o n s , t h e 1 0 Hz mode i s i d e n t i f i e d p u r e l y . I n f i g u r e 2 0 , end r e s u l t s are shown f o r convergence to t h e mode n e a r 3 Hz, I n t h i s c a s e , s t r a i n r e sponse r a t h e r t h a n a c c e l e r a t i o n r e sponse was used, and convergence went a u t o m a t i c a l l y to t h e lowes t mode (no spec t rum e r a s i n g had to be pe r fo rmed) . 12 Note, d i sp lacement o r s t r a i n emphasizes t h e lower modes, w h i l e a c c e l e r a t i o n r e s p o n s e , due to t h e u2 we igh t ing , emphasizes t h e h i g h e r modes e Figure 2 1 s e r v e s to show the remarkable power o f t he proce- d u r e to r e g e n e r a t e c o r r e c t f requency and damping i n f o r m a t i o n when s e v e r e t r u n c a t i o n s i n t he f requency p l a n e are made, F i g u r e 21(a) i s the o r i g i n a l spec t rum o f h o b t a i n e d f o r a one- mode s y s t e m and wi thou t n o i s e i n t h e i n p u t , The shaded areas were t h e n erased; arter s e v e r a l i t e r a t i o n s , s t a r t i n g w i t h t h i s t r u n - c a t e d spectrum, t he spec t rum as i n d i c a t e d by f i g u r e 2 1 ( b ) was found. Frequency and damping o f t h e mode i s s t i l l i n t a c t . The experiment was r e p e a t e d , t r u n c a t i n g f i g u r e 21(a) to t h e s e v e r e form shown by f i g u r e 2 1 ( c ) ; here t r u r , c a t i o n i s w i t h i n the Qalf- power l i m i t s . A f t e r s e v e r a l i t e r a t i o n s , t h e r e s u l t s shown i n f i g u r e 2 1 ( d ) were o b t z i n e d . Damping and f r equency a r e s t i l l t h e same as the o r i g i n a l , even thoueh the only i n f o r m a t i o n used was t h a t g iven by f i g u r e 2 1 ( c ) , F igu re 22 shows r e s u l t s t h a t were o b t a i n e d w i t h a sys t em hav ing f r e q u e n c i e s o f 9 and 1 0 Hz, b o t h wi th F i g u r e 2 2 ( a ) r e p r e s e n t s t h e raw o r contaminated spec t rum of h a After s e v e r a l i t e r a t i o n s by t h e one-sided approach , t h e r e s u l t shown i n f i g u r e 2 2 ( b ) was o b t a i n e d ; t h e f requency and damping are i n e x c e l l e n t agreement w i t h the model v a l u e s , F i g u r e 2 2 ( c ) r e p r e - s e n t s the spec t rum as o b t a i n e d by c o n s i d e r i n g t h e r e sponse o n l y . F i g u r e 2 2 ( d ) i s t h e r e s u l t o b t a i n e d by t h e one-s ided approach a f t e r i n f o r m a t i o n beyond f, was e r a s e d ; t h i s e r a s i n g was done to b r i n g out t h e lower mode. The damping and f requency i n d i c a t e d by f i g u r e 2 2 ( d ) f o r t h i s mode i s i n good agreement w i t h t he c o r r e c t v a l u e s , even though the in fo rma t ion c o n t a i n e d i n peak 1 was a l l t h a t was used , F i g u r e 2 2 ( e ) i s t h e r e s u l t o b t a i n e d by a p p l y i n g t h e two-sided approach to t h e Ry s h a r p s p i k e s i s shown by t h i s s k e t c h . - ’ - 0.05 . ‘ Bcr f u n c t i o n ; t h e tendency t o form F i g u r e 2 3 a p p l i e s to a sys tem hav ing modes f a i r l y c l o s e t o g e t h e r as fo l lows : f ,Hz B’Bcr Mode 1 8 0 .05 2 9 0 .05 1 0 0 . 0 2 3 F i g u r e 2 3 ( a ) i s t h e raw spectrum of h e If no e r a s i n g i s made, a p p l i c a t i o n o f t h e sequence o f s t e p s would r e s u l t i n t h e 1 0 Hz mode coming o u t i n p u r e form. C l e a r i n g beyond fa y i e l d e d the r e s u l t shown by f i g u r e 2 3 ( b ) by the one-sided approach; c l e a r i n g 13 b e f o r e f a and beyond f b y i e l d e d the r e s u l t shown by f i g u r e 2 3 ( c ) , Damping and f r e q u e n c i e s f o r b o t h modes are ve ry good, Thus, b o t h lower modes were e x t r a c t e d , i n s p i t e o f t h e c l o s e n e s s o f a n o t h e r mode having a much lower v a l u e o f damping. SYSTEM PARAMETER IDENTIFICATION - POSSIBILITIES OF A NEW APPROACH A number o f d i f f e r e n t schemes have been s t u d i e d as means f o r o b t a i n i n g a more d e t a i l e d i d e n t i f i c a t i o n o f s y s t e m p a r a m e t e r s . These schemes g e n e r a l l y f a l l under th ree c a t e g o r i e s : 1) Curve f i t t i n g o f t h e f requency response f u n c t i o n 2 ) F i t t i n g o f t ime p l a n e i n f o r m a t i o n , such as t h e h f unc t i on 3) D i f f e rence -equa t ion approaches i n which t h e c o e f f i c i e n t s of a d i f f e r e n c e - e q u a t i o n model a r e e v a l u a t e d , from which sys tem roots may i n t u r n be e x t r a c t e d C o l l o c a t i o n p rocedures are sometimes used f o r t h e c u r v e - f i t t i n g o p e r a t i o n s b u t , more g e n e r a l l y , t h e approaches a r e based on t h e use o f l e a s t - s q u a r e s concep t s . Some o f t h e sys t em i d e n t i f i c a t i o n approaches are reviewed and developed i n r e f e r e n c e 1 and t h e r e f e r e n c e s c o n t a i n e d t h e r e i n . Thus, t h e y w i l l n o t be d i s c u s s e d f u r t h e r h e r e i n . I n s t e a d , t h e n o t i o n s o f a p o s s i b l e new approach w i l l be o u t l i n e d . A commonly used concept i n s u b c r i t i c a l f l u t t e r t e s t i n g o f an a i r c r a f t i s to make a p l o t o f damping g v e r s u s V , f i g u r e 2 4 . The b a s i c idea i s to e s t a b l i s h t h e t r e n d o f t he damping c u r v e s and to e x t r a p o l a t e forward to e s t i m a t e t h e f l i g h t speed a t which t h e damping v a n i s h e s (or r e d u c e s to some s t i p u l a t e d lower l e v e l ) . T h i s p rocedure i s r e a s o n a b l y s a t i s f a c t o r y f o r a m i l d approach t o t h e c r i t i c a l f l u t t e r speed , curve a , b u t i s q u i t e t r e a c h e r o u s when a n e x p l o s i v e f l u t t e r s i t u a t i o n i s encoun te red , curve b , f o r i n t h i s s i t u a t i o n t h e damping can d e t e r i o r a t e ve ry q u i c k l y w i t h o n l y a small i n c r e a s e i n speed. A way to o b v i a t e t h i s problem i s sough t . Reference 1 s u g g e s t s one p o s s i b l e p r o c e d u r e & The i d e a i s t o d e r i v e t h e c o e f f i c i e n t s o f t h e assumed govern ing d i f f e r - e n t i a l e q u a t i o n model and to watch how these c o e f f i c i e n t s va ry w i t h a i r speed . F i g u r e 25 , t a k e n from r e f e r e n c e 1, d e p i c t s re- s u l t s f o r t h e s i t u a t i o n o f a mi ld approach to f l u t t e r . The n a t u r e o f the e x t r a p o l a t i o n i s known by a n a l y t i c a l c o n s i d e r a t i o n s ; f o r example, the C o e f f i c i e n t s a3 , a2 , al, and a. a r e known t o vary I n a q u a d r a t i c manner. E x t r a p o l a t i o n to higher speeds seems s t r a i g h t f o r w a r d , With t h e e x t r a p o l a t e d c o e f f i c i e n t s , system 14 r o o t s f o r h i g h e r speeds may be e v a l u a t e d , from which an estimate o f t h e c r i t i c a l f l u t t e r speed may be made, F i g u r e 26 shows the behav io r of t h e c o e f f i c i e n t s f o r a s y s t e m which h a s e x p l o s i v e f l u t t e r c h a r a c t e r i s t i c s . I n f i g u r e 25 t h e v a r i a t i o n o f t h e coef- f i c i e n t s appears g radua l , wh i l e i n f i g u r e 26 two o f t h e coef- f i c i e n t s , s p e c i f i c a l l y a2 and a? , are changing q u i t e markedly w i t h V a w i t h speed appea r s as a t i p - o f f t h a t t h e s i t u a t i o n may b e o f t h e e x p l o s i v e f l u t t e r v a r i e t y . T h i s r a p i d , b u t n o t a b r i p t , change i n t h e c o e f f i c i e n t s We now combine t h e though t s a s s o c i a t e d w i t h f i g u r e s 25 and 26 w i t h t h e procedures d i s c u s s e d i n t he p rev ious s e c t i o n . Suppose t h a t t h e procedures o u t l i n e d i n t h e p rev ious s e c t i o n s t a n d t h e t e s t o f more e x t e n s i v e s t u d y and tha t t h e procedures indeed a r e r e l i a b l e i n e s t a b l i s h i n g the f r e q u e n c i e s and damping o f t h e v a r i o u s modes o f t he s y s t e m under s t u d y . With t he f r e q u e n c i e s and damping e s t ab l i shed , t h e governing d i f f e r e n t i a l e q u a t i o n can t h e n be formed. A s an example, c o n s i d e r t h a t t h r e e modes are i d e n t i f i e d ; r o o t s may t h e n be w r i t t e n as where gn = 2 ( k ) , From t h e s e r o o t s , t h e govern ing d i f f e r - C r n e n t i a 1 e q u a t i o n fo l lows as Expansion o f t h i s e q u a t i o n y i e l d s t h e c h a r a c t e r i s t i c e q u a t i o n 15 P6 -4- a5P 4- "4P h -4- a3P 4- a2P 2 t alp t a. = 0 which i n t u r n d e f i n e s t h e c o e f f i c i e n t s an o f t h e govern ing d i f f e r e n t i a l e q u a t i o n . I n accordance w i t h f i g u r e s 2 5 and 26, w e watch how t h e s e c o e f f i c i e n t s vary w i t h a i r speed . We n o t e t h a t curve f i t t i n g i n t h e f requency p l a n e o r t i m e p l a n e , o r any o t h e r e v a l u a t i o n o f c o e f f i c i e n t s t h rough use o f l e a s t - s q u a r e s p rocedures , i s p rec luded i n t h i s sugges t ed approach. The success depends s imply on the r e l i a b l e e s t i m a t i o n o f t h e mode f requency and damping v a l u e s . CONCLUDING REMARKS Which one o f the p rocedures o u t l i n e d h e r e i n f o r minimizing n o i s e e f f e c t s i s the b e s t ? No s p e c i f i c cho ice can r e a l l y be made. A s y s t e m a t i c s t u d y i s needed to try each procedure i n a number o f d i f f e r e n t a p p l i c a t i o n s and c i r cums tances . The cho ice of which i s bes t w i l l undoubtedly depend on t h e s i t u a t i o n encoun te red , Never- t h e l e s s , some comment abou t c e r t a i n f e a t u r e s o r drawbacks o f t h e procedures can be made. The p rocedure o f c l e a r i n g t h e impulse r e sponse f u n c t i o n h ( r e c t a n g u l a r t r u n c a t i o n ) should a l w a y s be used , no matter how h has been d e r i v e d . The e x p o n e n t i a l we igh t ing o f t h e raw h i s not sugges t ed i n g e n e r a l , s i n c e t h e c l e a r e d h p r o c e s s s e r v e s j u s t about as w e l l . The use of t h e cross-spectrum approach i s cons id- ered one of t h e b e s t b u t g e n e r a l l y i s more a p p l i c a b l e f o r t h e l o n g e r sweep t imes. The peak s h i f t i n g t echn ique i s very a t t r a c t i v e b u t o f cour se r e q u i r e s t h e i n t e r m e d i a t e s t e p o f s h i f t i n g and sum- ming t h e r e c o r d p o r t i o n s . Ensemble ave rag ing i s perhaps t h e bes t bu t i s probably prec luded i n most i n s t a n c e s because of t h e neces- s i t y f o r making a number of r e p e a t r u n s . Randomdec i s n o t advo- c a t z d u n l e s s a swept s i n e wave forming f u n c t i o n i s used ( w i t h a n o i s e i n p u t a l o n e , too many terms are r e q u i r e d i n t h e summation i n g e n e r a l ) . Where r e sponse in fo rma t ion only i s a v a i l a b l e , t h e a u t o c o r r e l a t i o n approach (or e q u i v a l e n t l y , t h e spectrum o f t h e r e s p o n s e ) s h o u l d , o f c o u r s e , be used. I n t h i s approach, c a r e shou ld be t a k e n t o e r a s e t h e "noisy" t a i l s o f t h e c o r r e l a t i o n f u n c t i o n , as mentioned i n t h e body o f t h e r e p o r t . Also , i n t h i s approach i t i s l i k e l y t h a t f a i r l y l o n g r e c o r d l e n g t h s a r e a v a i l - ab le ; t h i s works t o t h e f a v o r of t h e approach because , on t h e whole, t h e l o n g e r t h e r e c o r d t h e b e t t e r t h e r e s u l t s (as i n t h e g e n e r a l r u l e f o r most a l l approaches ) . A s a g e n e r a l comment, w h i l e t h e r e i s a s c i e n c e t o t h e pro- cedures for minimizing t h e n o i s e problem, t h e r e i s a l s o an a r t i n t h e i r a p p l i c a t i o n s . Depending on t h e c i r cums tances and t h e t y p e 16 o f a n a l y s i s equipment a t a p p r o p r i a t e p l a c e s a v a i l a b l e little " t r i c k s " can b e i n s e r t e d t o g a i n an improvement 9n t h e end r e s u l t s , REFERENCE 1, Houbolt , John C . : sub critical^ F l u t t e r Test ing an Z d e n t i f i c a t i o -132480, Aug 1 7 A f 0 Figure 1.- Three basic ways f o r estimating modal frequencies and damping. 18 C 2 P Bcr - z . 0 5 0 2 4 6 8 IO 12 14 f,, Hz Figure 2 . - Appearance of resonance peaks o f d i f f e r e n t damping. 19 + CN h 20 n 5 -P co h m a,. a m 21 n M a, 5 53 M h m I L n a, k 3 td m a, rn c 0 a m 22 c .ri 0 rn TI 0 c c 0 a, c E 23 B h Figure ‘ I / 1 ‘ I 1 ?-’ I---/-- t- -r. 7-1- I I 1 I--l------l--i-t--+ ! 1I 1’ ,m . I . . . ! . . . . . , I . . . . . . . , . . . . I / 7.- Frequency response and h functions obtained by single swept sine r u n with noise in input. 24 25 r. ; 1 . ! ; 1 . I i I I I ! ' i . / . . : i , . . . .I:'. I i 2 * * 1 w h r o w b- 1 I . - 1 . . . . c I F i g u r e 9.- Improved f requency r e s p o n s e f u n c t i o n by e x p o n e n t i a l we igh t ing of h f u n c t i o n . 26 k 0 0 s - ' G-P - Q 5 a 0 x 5 0 I 0 r i 27 28 a, k 5 bo .rl G 29 .. A 2 B2 . . w F i g u r e 1 3 . - U s e of ensemble ave rag ing o f s i n e sweep runs t o e l i m i n a t e n o i s e . original sweep, IO sec - - ' IO sec 25 Hz concentrated sweep ~ 3 Hz 8 Hz 12 Hz F i g u r e 1 4 . - Use o f sweep o v e r narrow f requency band. 30 Y P a Shift y3 to a c= Shift y4 ta a and invert F i g u r e 1 5 . - "Randomdec" p r o c e s s to d e r i v e h-type f u n c t i o n . 31 M -8. a a a * r i m I a c 0 6( 0 m 32 M 33 x ? cd k a, d 34 35 F i g u r e 20 . - Pure r e s u l t s f o r t h e low-frequency mode o b t a i n e d by s u c c e s s i v e c o r r e l a t i o n s o f t h e one- s i d e d c o r r e l a t i o n f u n c t i o n . 36 Figure 21.- Regeneration of modal response characteristics after truncation in the frequency plane. 37 Figure 22.- Isolation of modes by frequency plane erasing, two-mode system. 38 Figure 2 3 . - Isolation of specific modes by frequency plane erasing, three-mode system. 9 Mi Ex \ Id f l u t t e r I plosive a V Figure 24.- Damping curves for mild and explosive flutter cases. 39 an 1 .o .5 0 100 4 -v a40r - Evaluated by collocation procedure I I I I I I 60 70 60 90 100 110 120 it' 2v v = - C Figure 25.- Variation of differential equation coefficients w i t h airspeed, mild flutter. 40 1 .o an 0 60 70 80 90 100 110 120 2v v = - C F i g u r e 26.- V a r i a t i o n o f d i f f e r e n t i a l e q u a t i o n c o e f f i c i e n t s w i t h a i r s p e e d , e x p l o s i v e f l u t t e r . 41 CURVE FITTING OF AECROELASTIC TRANSIENT RESPONSE DATA WITH EXPONENTIAL FUNCTIONS Robert M. Bennett and Robert N. Desmarais NASA Langley Research Center SUMMARY The problem of e x t r a c t i n g frequency, damping, amplitude, and phase in fo r - mation from unforced t r a n s i e n t response d a t a is considered. These q u a n t i t i e s are obtained from t h e parameters determined by f i t t i n g t h e d i g i t i z e d t i m e - h i s t o r y d a t a i n a least-squares sense with complex exponent ia l funct ions. The h i g h l i g h t s of t h e method are descr ibed and t h e r e s u l t s of several test cases are presented. The e f f e c t s of n o i s e are considered both by us ing a n a l y t i c a l examples with random n o i s e and by est imat ing t h e standard d e v i a t i o n of t h e parameters from maximum-likelihood theory. INTRODUCTION One of t h e fundamental t a s k s i n f l u t t e r t e s t i n g is t h e determinat ion of t h e frequency and damping of a e r o e l a s t i c modes. r eco rds are o f t e n used f o r e x t r a c t i n g t h i s information and may be generated d i r e c t l y by a method such as t h e resonant dwell and c u t (e.g. , see r e f . l), o r i n d i r e c t l y through t h e u s e of a u t o c o r r e l a t i o n o r randomdec types of data- r educ t ion techniques ( r e f s . 2 and 3 ) . Graphical o r manual techniques have o f t e n been used t o determine frequency and damping, b u t , with t h e widespread u s e of automated data-reduction procedures, numerical c u r v e - f i t t i n g techniques of com- p l ex exponent ia l func t ions o r damped s i n e waves are f r e q u e n t l y used. There may b e s t r o n g i n t e r a c t i o n s between t h e c u r v e - f i t t i n g method and t h e da t a -co l l ec t ion process , espec ' ia l ly i n t h e areas of record l e n g t h requirements and spec i f i ca - t i o n s of no i se level and d i s t o r t i o n . f o r t h e c u r v e - f i t t i n g process ( r e f s . 4 t o 6 ) . The purpose of t h i s paper is t o d e s c r i b e a method t h a t takes a somewhat d i f f e r e n t approach from the previous works. The emphasis h e r e is on developing a n e a r l y real-time d i g i t a l technique t h a t is not only computationally f a s t but is a l s o s t a b l e i n t h e presence of real-world n o i s e o r contamination e f f e c t s . A simple d i r e c t s ea rch technique f o r ob ta in ing a least-squares f i t us ing exponent ia l func t ions has been developed and i s presented. The a p p l i c a t i o n t o s e v e r a l test cases is presented and d i s - cussed. Some e f f e c t s of measurement no i se are evaluated by comparing test-case r e s u l t s f o r d i f f e r e n t signal-to-noise r a t i o s , and by developing estimates of t h e s tandard dev ia t ions of t h e parameters from maximum-likelihood theory ( r e f . 7 , e . g . ) . T rans i en t response o r free decay Several procedures are c u r r e n t l y a v a i l a b l e It should b e kep t i n mind t h a t although i n a p r a c t i c a l engineering sense t h e u s e of exponent ia l func t ions f o r t h e a n a l y s i s of d a t a may be s a t i s f a c t o r y , t h e a e r o e l a s t i c equat ions are n o t s t r i c t l y cons t an t - coe f f i c i en t ordinary 43 d i f f e r e n t i a l equat ions ( r e f , 8 ) and may involve o the r func t ions . Furthermore, t h e e x t r a p o l a t i o n of damping measured a t s u b c r i t i c a l cond i t ions t o f l u t t e r may a l s o have shortcomings. For example, a case presented i n r e f e r e n c e 9 ind ica t ed a s lope and cu rva tu re away from a f l u t t e r c ros s ing i n a p l o t of damping a g a i n s t v e l o c i t y , even up t o w i t h i n 2 percent of t h e f l u t t e r speed. SYMBOLS 0 a k a bk E E f A fi i k N R1 A S t v vf Y c o e f f i c i e n t i n curve f i t , t h e o f f s e t o r s ta t ic va lue (en. (1 ) ) c o e f f i c i e n t of k t h cos ine t e r m i n curve f i t (eq. (1)) c o e f f i c i e n t of k t h s i n e t e r m i n curve f i t (en. (1) ) mean-squared e r r o r (eq. (2) ) expected v a l u e (eq. ( 3 ) ) frequency , Hz i t h d a t a p o i n t of d i g i t i z e d time h i s t o r y d a t a po in t index, 1 t o N parameter index number of modes i n curve f i t modal index, 1 t o K number of d a t a p o i n t s i n d i g i t i z e d time h i s t o r y ou tpu t e r r o r covar iance mat r ix parameter s e n s i t i v i t y m a t r i x t i m e , seconds v e l o c i t y f l u t t e r v e l o c i t y curve-f i t t i n g express ion (eq. (1)) f r a c t i o n of c r i t i ca l damping damping c o e f f i c i e n t (eq. (1)) w frequency , r ad / s ec 44 ANALYSIS Least-Squares F i t t i n g Procedure Given a f r e e decay record conta in ing t h e response of one o r more v i b r a t i o n modes i n t h e form of a d i g i t i z e d t i m e h i s t o r y , t h e problem is t o determine the modal damping, f requency, ampli tude, and phase of each mode. A l eas t - squares cu rve f i t is made wi th complex exponent ia l f u n c t i o n s (or damped s i n e waves) i n t h e form -qkt (ak cos w t + b s i n w t) k k k Y ( t > = a. + 1 e k = l by minimizing t h e squared-error d i f f e r e n c e between t h e ou tpu t f i t t h e i n p u t t i m e h i s t o r y f i . The e r r o r is g iven by Y ( t i ) and Inspec t ion of equat ion (1) shows t h a t i f '7k and wk are preassigned, i t is p o s s i b l e t o compute ao, ak, and bk by so lv ing a l i n e a r leas t - squares prob- l e m . The nonl inear parameters ?& and wk must be determined by some type of s ea rch algori thm. Although t h i s is a s tandard nonl inear , unconstrained optimi- z a t i o n problem f o r which several methods are a v a i l a b l e f o r t r i a l , f o r s i m p l i c i t y a d i r e c t search technique is used t o search t h e coord ina te space (nk,wk) u n t i l t h e va lues t h a t minimize equat ion (2) are obta ined . A t each s t e p , v a l u e s f o r r& and wk are determined, t h e s m a l l l i n e a r system so lved , and t h e e r r o r recomputed . The technique has been programed f o r t h e Xerox Sigma 5 I n t h e program, t h e coord ina te s tepping process proceeds as (1) A s t a r t i n g set of coord ina te s I)k,wk (k = 1, e . s t e p s i z e are fu rn i shed t o t h e program. d i g i t a l computer. fol lows: , K ) and a s t a r t i n g (2) The e r r o r E is computed a t ('7k,%) and a t 4 K a d d i t i o n a l p o i n t s obtained by adding and s u b t r a c t i n g t h e s t e p s i z e t o o r from each va lue of and wk" If t h e c e n t r a l e r r o r E is less than any of t h e 4 K p e r i p h e r a l va lues of E , t h e s t e p s i z e i s reduced by 75 percent , and t h e c a l c u l a t i o n s are repea ted . qk ( 3 ) Otherwise, t h e p o i n t t h a t gave t h e lowest v a l u e of E i s taken t o be t h e new central p o i n t , and t h e s t e p s i z e is increased by 10 percent . ( 4 ) The procedure is terminated when e i t h e r t h e s t e p s i z e has been reduced below a preassigned threshold o r a preassigned number of s t e p s have been executed. 45 The method r e q u i r e s s t a r t i n g va lues f o r ?& and Wke For a s i n g l e mode t h e starters can b e a r b i t r a r y . However, f o r t h e multiple-mode case, t t i m e can b e s i g n i f i c a n t l y reduced by choosing good starters, procedure has been found t o be a reasonable way of g e t t i n g starters f o r multiple-mode cases: The fol lowing (a) Generate a one-mode s o l u t i o n us ing a r b i t r a r y starters. (b) Compute t h e d i f f e r e n c e between t h e one-mode s o l u t i o n and t h e input d a t a , t h a t is , t h e output e r r o r . Then gene ra t e a one-mode f i t t o t h e e r r o r . (c ) U s e t h e '?k and Wk va lues from s t e p s ( a ) and (b) as t h e starters f o r t h e two-mode s o l u t i o n . (d) For higher modes, s t e p s (b) and ( c ) are repea ted us ing t h e d i f f e r e n c e between t h e c u r r e n t ml t ip l e -mode s o l u t i o n and the o r i g i n a l d a t a t o estimate t h e next h igher mode. Although t h i s procedure i s cumbersome, i t appears t o be s t a b l e and, a t least f o r t h e single-mode case, s u r p r i s i n g l y f a s t . It would a l s o be very help- f u l t o set t h e method up on an i n t e r a c t i v e b a s i s s i m i l a r t o t h e technique descr ibed i n r e f e r e n c e 10 . One of t h e schemes i n t h e l i t e r a t u r e is r e f e r r e d t o as Prony's method ( r e f . 4 ) . It computes rik and "k by so lv ing a 2K-order polynomial equat ion whose c o e f f i c i e n t s are determined from a l eas t - squa res process . f o r t h e c o e f f i c i e n t s ao, ak, and bk is then determined by a l i n e a r least- squares procedure, as i s done here . S ince t h i s method is e l egan t and computa- t i o n a l l y e f f i c i e n t , i t w a s examined dur ing t h e p re sen t s tudy. However, i t has been the au tho r s ' experience t h a t a l though Prony's method works w e l l f o r p e r f e c t d a t a , i t is so s e n s i t i v e t o real-world n o i s e t h a t it i s e s s e n t i a l l y u s e l e s s even f o r genera t ing starters f o r t h e search algori thm. The s o l u t i o n Uncer ta in ty Levels of Estimated Parameters The s tandard d e v i a t i o n s of t h e es t imated parameters , o r u n c e r t a i n t y levels, can be determined from maximum-likelihood theory ( r e f . 7 , e .g . ) . This type of estimate has provided some u s e f u l r e s u l t s i n t h e f i e l d of s t a b i l i t y and c o n t r o l (e .g . , r e f . 11). Assuming only measurement no i se t h a t is Gaussian and white, t h e expected va r i ance of t h e parameter v e c t o r is A where S is t h e parameter s e n s i t i v i t y matrix, R 1 is t h e output e r r o r covari- ance mat r ix , h e r e a cons t an t , and T denotes matrix t ranspose. The parameter vec to r p is made up of ao, ak, bk, '?k, and k&, and t h e s e n s i t i v i t y matrix is given by S j (ti) = . These elements of t h e s e n s i t i v i t y ma t r ix can b e 46 -t a y ( t i ) aPj ca lcu la t ed by d i r e c t l y d i f f e r e n t i a t i n g equat ion ( l ) , and t h e va r i ance is a normal output parameter. Thus, f o r a s i n g l e channel of d a t a , as considered here , t h e s e parameter u n c e r t a i n t y levels can be r e a d i l y c a l c u l a t e d a f t e r t h e cu rve - f i t t i ng process is completed. RESULTS AND DISCUSSION The c u r v e - f i t t i n g method has been appl ied t o t h r e e sets of d a t a as test cases . The f i r s t case is a c a l c u l a t e d damped s i n e wave w i t h n o i s e added wi th a random-number gene ra to r . The t r u e answer is thus known. The second case is wind-tunnel d a t a from t h e dynamic c a l i b r a t i o n of an a i r c r a f t g u s t vane. The t h i r d case is a set of d a t a c o n s i s t i n g of t h e s u b c r i t i c a l randomdec s i g n a t u r e s of t h e response t o i n p u t no i se of a two-dimensional f l u t t e r model t h a t w a s implemented on a n analog computer. Ana ly t i ca l T e s t Case The ca l cu la t ed d a t a f o r t h e a n a l y t i c a l test case wi th no added n o i s e are shown i n f i g u r e l ( a ) and are compared wi th t h e f i t t e d curve, which i s exact i n t h i s case. For t h i s case, t h e a n a l y t i c a l i n p u t func t ion w a s a s i n g l e mode wi th o f f s e t and i s g iven by -5 t Y ( t ) = 1 - e cos 3 0 t The curve f i t s f o r va r ious levels of random no i se are shown i n f i g u r e s l ( b ) t o l ( d ) . The n o i s e level is de f ined as t h e r m s level of t h e Gaussian n o i s e and is g iven as t h e f r a c t i o n of t h e maximum ampli tude of t h e mode t h a t is 1. The r e s u l t s of the curve f i t are summarized i n f i g u r e 2. Only modest degrada t ion of t h e r e s u l t s is shown f o r r easonab le va lues of no i se level of up t o 0.10 or 0.20. Also shown, as b racke t s on t h e po in t s , are t h e s tandard d e v i a t i o n s of t h e parameters, o r u n c e r t a i n t y levels, c a l c u l a t e d from equat ion (3) u s ing t h e r e s u l t s ou tput from t h e curve- f i t procedure. parameters are known and i t is p o s s i b l e t o c a l c u l a t e a p red ic t ed u n c e r t a i n t y level from t h e exact parameters by assuming t h a t t h e output e r r o r covar iance is t h e v a l u e f o r the n o i s e only. Both r e s u l t s g i v e a good i n d i c a t i o n of t h e a c t u a l scatter, and thus t h e confi- dence level, w i t h n o i s e l e v e l . It might b e noted t h a t t h e e f f e c t of n o i s e is l a r g e r on the c o e f f i c i e n t s a1 and b l than on t h e damping, frequency, o r o f f s e t . Thus, one must be more cau t ious i n us ing t h e magnitude and phase information from such procedures. I n t h i s case t h e exact modal These p red ic t ed levels are shown as dashed l i n e s . These r e s u l t s amply demonstrate t h a t t h e a lgor i thm works w e l l i n t h e pres- ence of random measurement no i se . It has been t h e au tho r s ' experience, however, t h a t a test case of t h i s type does no t i n d i c a t e t h a t a method w i l l be s a t i s f a c - t o r y i n p r a c t i c e . The no i se h e r e is random w i t h zero mean, whereas i n t h e real world, t h e e f f e c t s of frequency d r i f t , meandering means, and harmonic d i s t o r t i o n are more severe. 47 Gust Vane Data The two cases considered are from a wind-tunnel dynamic c a l i b r a t i o n of a l i g h t b a l s a vane used t o sense atmospheric tu rbulence on a n a i r c r a f t . The vane w a s mechanically d isp laced and r e l eased r e p e t i t i v e l y . S ince t h e response t o tunnel tu rbulence w a s a s i z a b l e f r a c t i o n of t h e t o t a l response and the release condi t ions somewhat ill def ined , t h e t r a n s i e n t s w e r e ensemble averaged. The background n o i s e w a s thus diminished, bu t a pure s t e p response w a s n o t obtained. The two cases considered are c a l l e d t h e low-damping case and t h e high-damping case (although t h e low-damping case is r e l a t i v e l y h igh ly damped by s t r u c t u r a l s tandards) . The d a t a f o r t h e low-damping case and t h e one-mode f i t are shown i n f i g u r e 3 ( a ) . The f i t is reasonable , bu t t h e r e is some sys temat ic d e v i a t i o n , p a r t i c u l a r l y near t h e r igh tmost po r t ion of t h e da t a . A two-mode f i t w a s com- puted and, as shown i n f i g u r e 3(b) , g ives a s i g n i f i c a n t l y improved r e s u l t . The r e s u l t s of t h e one- and two-mode f i t s are summarized as fo l lows: One-mode f i t Y(t) = 0.0444 -e -39*9 t (~ .239 cos 140t - 0.452 s i n 140 t ) Two-mode f i t Y( t ) = 0.0450 (0.137 cos 133t - 0.372 s i n 133 t ) -e -e -34'6t(0.086 cos 190t - 0.026 s i n 190 t ) -35.lt A s compared w i t h t h e one-mode r e s u l t s , t h e two-mode d a t a i n d i c a t e t h a t t h e of f - set is nea r ly t h e same, t h e frequency of t h e f i r s t mode is reduced by about 5 percent , and t h e damping is reduced by about 10 pe rcen t , along wi th s i z a b l e changes i n t h e c o e f f i c i e n t s of t h e f i r s t mode. The phys ica l s i g n i f i c a n c e of t h e second mode is no t clear i n t h i s case; i t may be low-frequency n o i s e t h a t has no t completely averaged o u t i n t h e ensembling process . However, it i s thought t h a t t h e r e s u l t s f o r t h e f i r s t o r p r i n c i p a l mode obta ined i n t h e two-mode f i t are more r e p r e s e n t a t i v e of t h e system response. The r e s u l t s f o r t he h igh ly damped case are presented i n f i g u r e s 4 (a ) and 4(b) . The r e s u l t s and t r ends are similar t o those of t h e low-damping case. This case is a p a r t i c u l a r l y d i f f i c u l t one t o analyze, as i t has h i g h damping, a l a r g e o f f s e t , and a low-frequency d i s t o r t i o n . The a lgor i thm of t h i s paper appears t o g i v e a reasonable r e s u l t f o r t h i s case. Randomdec-Analog F l u t t e r Data Some s u b c r i t i c a l randomdec s i g n a t u r e s of t h e response of a two-dimensional, two-degree-of-freedom f l u t t e r model t o i n p u t no i se on a n analog computer are a l s o t r e a t e d . The mathematical model and test se tup w e r e t h e same as those of t h e i n v e s t i g a t i o n of r e f e r e n c e 9. The s i g n a t u r e s and a one-mode curve f i t are 48 shown i n f i g u r e s 5 (a ) t o 5(d) as t h e v e l o c i t y approaches f l u t t e r , A s f l u t t e r is approached t h e s i g n a t u r e s show l i t t l e scatter o r d i s t o r t i o n , i n c o n t r a s t t o t h e lower v e l o c i t i e s . The s i g n a t u r e s con ta in two modes, b u t t h e lower frequency mode i s apparent ly unconverged i n t h e randomdec procedure and could n o t be ade- qua te ly resolved by t h e cu rve - f i t procedure, The r e s u l t s f o r t h e f l u t t e r mode are compared wi th t h e exac t s o l u t i o n i n f i g u r e 6. The agreement i s q u i t e good i n both frequency and damping, w i t h t h e f l u t t e r speed underpredicted by less than 1 percent , which is w i t h i n t h e expected accuracy of t h e analog se tup . Thus, t h e curve- f i t procedure appears t o be a p r a c t i c a l means of analyzing randomdec s igna tu res , CONCLUDING RFJURKS A l eas t - squares curve-f i t t i n g procedure t o e x t r a c t frequency, damping, amplitude, and phase information from f r e e decay records has been presented . The method appears t o be s t a b l e and t o g ive reasonable r e s u l t s i n t h e presence of no ise . Some of t h e e f f e c t s of n o i s e on t h e parameter estimates can b e assessed by c a l c u l a t i n g t h e u n c e r t a i n t y levels from maximum-likelihood theory. The method is r e l a t i v e l y f a s t f o r a one-mode f i t , gene ra l ly r e q u i r i n g 5 t o 15 seconds on a Xerox Sigma 5 computer (which would be about 1 second on a CDC 6600 computer) and thus is a candida te f o r a real-time method. The two- mode s o l u t i o n , however, r e q u i r e s 2 t o 5 minutes, and a three-mode s o l u t i o n is very long t o c a l c u l a t e . Fur ther work is needed t o accelerate t h e multiple-mode c a l c u l a t i o n s . It would a l s o be ve ry h e l p f u l t o set t h e method up on a n i n t e r - active b a s i s . Cur ren t ly , t h e only mult iple-channel c a p a b i l i t y is t o f i t each channel of d a t a s e p a r a t e l y , determine a weighted mean f o r frequency and damping, and then r e c a l c u l a t e t h e c o e f f i c i e n t s f o r each channel. This procedure may be s a t i s f a c t o r y f o r engineer ing purposes , but t h e development t o a t r u e mul t ip le - channel method may be d e s i r a b l e . 49 REFERENCES 1. 2. 3. 4. 5. 6. 7 . 8. 9. 10 e 11. Rosenbaum, Robert: Survey of A i r c r a f t S u b c r i t i c a l F l i g h t F l u t t e r Tes t ing Methods. NASA CR-132479, 1974. Cole, Henry A., Jr,: On-Line F a i l u r e Detec t ion and Damping Measurement of Aerospace S t r u c t u r e s by Random Decrement S igna tures . NASA CR-2205, 1973. Brignac, W. J.; Ness, H. B . ; and Smith, L. M. : The Random Decrement Tech- n ique Applied t o YF-16 F l i g h t F l u t t e r Tests. May 1975. AIAA Paper No. 75-776, Hildebrand, F. B. : I n t roduc t ion t o Numerical Analysis . M c G r a w - H i l l Book Co., Inc. , 1956. Wilcox, P h i l l i p R. ; and Crawford, W i l l i a m L . : A L e a s t Squares Method f o r t h e Reduction of Free-Osci l la t ion Data. NASA TN D-4503, 1968. Chang, C . S.: Study of Dynamic C h a r a c t e r i s t i c s of A e r o e l a s t i c Systems U t i l i z i n g Randomdec Signatures . NASA CR-132563, 1975. Grove, Randall D . ; Bowles, Roland L . ; and Mayhew, S tan ley C . : A Procedure f o r Est imat ing S t a b i l i t y and Cont ro l Parameters From F l i g h t T e s t Data by Using Maximum Likel ihood Methods Employing a R e a l - T i m e D i g i t a l System. NASA TN D-6735, 1972. Richardson, J. R.: A More Real is t ic Method f o r Rout ine F l u t t e r Calcula- t i o n s . AIAA Symposium on S t r u c t u r a l Dynamics and A e r o e l a s t i c i t y , Aug.-Sept. 1965, pp. 10-17. Houbolt, John C . : S u b c r i t i c a l F l u t t e r Tes t ing and System I d e n t i f i c a t i o n . NASA CR-132480, 1974. Hammond, Charles E . ; and Doggett, Robert V . , Jr.: Determination of Sub- c r i t i ca l Damping by Moving-Block/Randomdec Appl ica t ions . on F l u t t e r Tes t ing Techniques, O c t . 1975. (Paper No. 3 of t h i s compilat ion.) NASA Symposium I l i f f , Kenneth W . ; and Maine, Richard E.: P r a c t i c a l Aspects of Using a Maximum Likelihood Est imator . Methods f o r A i r c r a f t State and Parameter I d e n t i f i c a t i o n , AGARD-CP-172, May 1974, pp. 16-1 - 16-15. 50 1.5 AMPLITUDE 1.0 .5 0 f - .5 0 .1 .2 .3 .4 .5 .6 .7 TIME, sec (a) No added noise . 2.5 2 .o 1.5 AMPLITUDE 1 .o .5 0 - .5 I I I I I I I 0 .1 .2 .3 .4 .5 .6 "7 TIME, sec (b) Noise, 0.05. Figure 1.- Curve f i t f o r a n a l y t i c a l ca se wi th random noise . 51 2.5 2.0 1.5 AMPLITUDE 1.0 .5 0 -.5 I 1 1 1 1 1 1 0 .1 .2 .3 .4 .5 .6 .7 TIME, sec ( c ) Noise, 0.10. 2.5 r 2.0 1.5 AMPLITUDE 1.0 .5 0 -.5 ' I 1 1 1 1 1 1 0 .1 .2 .3 .4 .5 .6 .7 TIME, sec (d) Noise, 0.50. Figure 1.- Concluded. 52 W -------- FREQUENCY, 30 rad/ sec -- PREDICTED UNCERTAINTY LEVEL I UNCERTAINTY LEVEL CALCULATED FROM CURVE FIT 10 --- rl DAMPING. I I I I I I 0 .1 .2 . 3 .4 .5 1/ sec NOISE LEVEL (a) Frequency and damping. PREDICTED UNCERTAINTY LEVEL -- COEFFl ClENTS I UNCERTAINTY LEVEL CALCULATED 2 FROM CURVE FIT 0 ’ 1 a OFFSET bl’ 0 - - SINE a -- 1’ -1 COSINE -- I I I I 0 .1 .2 .3 .4 NOISE LEVEL (b) Amplitude coefficients. .5 Figure 2.- Results of analytical case with random noise. 53 AMPLITUDE I I I I I I I 0 .02 .04 .06 .08 , l O .12 .14 TIME, sec (a) One-mode f i t . .4 .3 .2 AMPLITUDE .1 0 -.1 -.2 I I I I I I I 0 .02 .04 .06 .08 .lo .12 .14 TIME, sec (b) Two-mode f i t . Figure 3. - Gust-vane curve f i t f o r low-damping case. 54 .35 .30 .25 AMPLI TU DE .20 .15 .10 .05 - 1 1 1 1 1 1 1 .35 .30 .25 AMPLI JUDE .20 .15 .lo 0 .02 .04 .06 .08 .10 .12 .14 TIME, sec (a) One-mode f i t . .05 0 .02 .04 .06 .08 .10 .12 .14 TIME, sec (b) Two-mode f i t . Figure 4 . - Gust-vane curve f i t f o r high-damping cas e. 55 AMPLITUDE 0 .1 .2 -3 .4 .5 .6 .7 TIME, sec (a) V/Vf = 0.684. AMPLITUDE .MO I I I I I I I I 0 .1 .2 .3 .4 .5 .6 .7 TIME, sec (b) V/Vf = 0.855. Figure 5.- Curve fit of randomdec-analog data. 56 .045 r AMPLITUDE I I I I I I I 0 .1 .2 .3 .4 .5 .6 .7 TIME, sec (c) V/Vf = 0.941. .06 (d) V/Vf = 0.992. Figure 5.- Concluded. 57 14 f, Hz 10 6 - .04 0 i: .04 .08 0 .2 .4 .6 V I V , ,8 1 .o 1.2 Figure 6.- Comparison of curve f i t of randomdec-analog d a t a wi th exact c a l c u l a t i o n s . 58 DETERMINATION OF SUBCRITICAL DAMPING BY MOVING-BLOCK/RANDOMDEC APPLICATIONS Charles E. Hamond Langley Di rec to ra t e , U.S. Army A i r Mobil i ty R&D Laboratory Robert V. Doggett , Jr. NASA Langley Research Center SUMMARY Two techniques are descr ibed which a l low t h e de te rmina t ion of s u b c r i t i c a l dampings and f r equenc ie s dur ing a e r o e l a s t i c t e s t i n g of f l i g h t v e h i c l e s . The two techniques are t h e moving-block technique and t h e randomdec technique. The moving-block technique is shown t o have t h e advantage of being a b l e t o provide damping and frequency information f o r each mode which might be p re sen t i n a s i g n a l t r ace , bu t i t has t h e disadvantage of r equ i r ing t h a t t h e s t r u c t u r e be exc i t ed t r a n s i e n t l y . The randomdec technique r e q u i r e s on ly random turbulence f o r e x c i t a t i o n , bu t t h e randomdec s i g n a t u r e is d i f f i c u l t t o ana lyze when more than one mode is p resen t . It i s shown t h a t by us ing t h e moving-block technique t o ana lyze t h e randomdec s i g n a t u r e s the b e s t f e a t u r e s of both methods are gained. Examples are presented i l l u s t r a t i n g the d i r e c t a p p l i c a t i o n of t he moving-block method t o model h e l i c o p t e r r o t o r t e s t i n g and a p p l i c a t i o n of t h e combined moving- block/randomdec method t o f l u t t e r s t u d i e s of two f ixed-wing models. INTRODUCTION Determination of s u b c r i t i c a l damping dur ing f l u t t e r tests both i n wind tunne l s and i n f l i g h t is a s u b j e c t which is c u r r e n t l y r ece iv ing widespread a t t e n t i o n . S ince f l u t t e r is a p o t e n t i a l l y dangerous a e r o e l a s t i c i n s t a b i l i t y which can lead t o c a t a s t r o p h i c s t r u c t u r a l f a i l u r e , i t is d e s i r a b l e t o o b t a i n t h e f l u t t e r boundary without a c t u a l l y experiencing f l u t t e r . wind-tunnel f l u t t e r model tes t procedures have been t o treat f l u t t e r as a n event t h a t e i t h e r occurs o r does n o t occur. The models are a c t u a l l y taken t o t h e f l u t t e r cond i t ion , and by vary ing tunne l parameters (Mach number and dynamic p res su re ) , s u f f i c i e n t f l u t t e r p o i n t s are obtained t o d e f i n e t h e f l u t t e r boundary. Th i s p r a c t i c e has i n t h e p a s t l e d t o t h e t o t a l d e s t r u c t i o n of some ve ry expensive models. Although t h e need f o r s u b c r i t i c a l damping d a t a has long been recognized, ob ta in ing t h e s e d a t a is n o t a n easy t a s k , and s u b c r i t i c a l damping techniques have no t been r o u t i n e l y used i n t h e p a s t . A l a r g e p a r t of t h e d i f f i c u l t y has been a s soc ia t ed wi th t h e i n a b i l i t y t o reduce, ana lyze , and d i s p l a y model damping d a t a i n near real t i m e so t h a t t h e damping can b e continu- ous ly monitored dur ing approach t o t h e f l u t t e r boundary. The i n s t a l l a t i o n of t h e computer c o n t r o l l e d d a t a a c q u i s i t i o n system has now made it p r a c t i c a l t o apply s u b c r i t i c a l damping methods t o f l u t t e r tests i n t h e Langley t r anson ic dynamics tunnel . T r a d i t i o n a l l y , 59 This paper desc r ibes two techniques which are c u r r e n t l y being used i n wind-tunnel a e r o e l a s t i c model tests of bo th h e l i c o p t e r r o t o r s and f i x e d wings, The two techniques t o bedescr ibed are t h e so-cal led moving-block technique and t h e randomdec technique. Although n e i t h e r of t h e techniques is new, i t is f e l t t h a t t h e combined a p p l i c a t i o n of t h e two ana lyses i s unique, p a r t i c u l a r l y wi th r e s p e c t t o fixed-wing f l u t t e r t e s t i n g . SYMBOLS A ampli tude of t r a n s i e n t response F (w) Four ie r t ransform a t frequency w i imaginary number, Fl k a n i n t e g e r i n equat ion (14) N an i n t e g e r i n equat ion (10); t o t a l number of d a t a samples i n equat ion (13) - N number of d a t a samples i n block used f o r f requency opt imiza t ion T per iod of boxcar func t ion t t i m e A t u ( t ) boxcar func t ion , equat ion (2) time between d i s c r e t e d a t a samples Y(t) t r a n s i e n t response of single-degree-of-freedom system, equat ion (1) c damping r a t i o T s ta r t t i m e of boxcar func t ion cp phase a n g l e w damped n a t u r a l frequency undamped n a t u r a l f requency "'n MOVING-BLOCK TECHNIQUE The moving-block technique w a s o r i g i n a l l y developed by t h e Lockheed- C a l i f o r n i a Company, and i ts u s e i n r o t a r y wing a e r o e l a s t i c s t a b i l i t y t e s t i n g has been repor ted i n r e fe rences 1 and 2. A formula t ion of t h i s technique has 60 been developed a t t h e Langley Research Center , and i t has been implemented on t h e r e c e n t l y i n s t a l l e d d a t a a c q u i s i t i o n system f o r t h e Langley t r anson ic dynamics tunnel . The moving-block technique is a method which a l lows t h e de te rmina t ion of . modal dampings and f r equenc ie s from a response s i g n a l of a s t r u c t u r e which has been exc i t ed t r a n s i e n t l y . The t r a n s i e n t e x c i t a t i o n may c o n s i s t of a s i n u s o i d a l i npu t which h a s been a b r u p t l y terminated o r i t may be a n impulsive e x c i t a t i o n . I n any event, i f t h e damping and frequency of a p a r t i c u l a r mode are d e s i r e d , it is necessary t h a t t h i s mode b e exc i t ed by t h e type of e x c i t a t i o n chosen. This requirement t h a t t h e s t r u c t u r e b e exc i t ed and then b e allowed t o decay f r e e l y i s one of t h e disadvantages of t h e method, b u t f o r many a p p l i c a t i o n s i t is no t a n over ly burdensome requirement . This is p a r t i c u l a r l y t r u e i n h e l i c o p t e r a p p l i c a t i o n s where t h e e x i s t i n g con t ro l system can b e used t o supply t h e necessary e x c i t a t i o n of t h e r o t o r system. - I n o rde r t o i l l u s t r a t e how t h e moving-block technique works, cons ider t h e t r a n s i e n t response of a single-degree-of-freedom system which may be w r i t t e n as -w 1 or where : { # } = = modal displacement matrix modal displacement vectors at point p @P [ Jl = mass matrix Rearranging the above equation gives: showing that the generalized modal mass (I) is a function of the incremental mass (6m); the modal displacement ( 6 ) at the location 6m is attached; and the modal frequencies are evaluated with and without 6m in pyace (w1 and 0). 91 REFERENCES 1. Kennedy, C. C. and Pancu, C. D. P.: Use of Vectors in Vibration Measurement and Analysis. Journal of the Aeronautical Sciences, November 1947. 2. Small, E. F.: Evaluation of Vibration Methods to Separate Closely Spaced Modes. The Boeing Company, D6-9447, TN, May 1968. 3. Olsen, N. L.: Flight Flutter Measurements Using The Analog Aeroelastic Modal Analysis System (AMAS). The Boeing Company, D6-33241, INF., February 1972. 4. Winter, W. A.: Flutter Testing of Aircraft in Flight. British Communications and Electronics, April 1963. 5. White, R. G.: Dynamic Analysis of Structures by 'I'ransient Excitation. Thesis, Institute of Sound and Vibration, University of Southampton, March 1970. 6. Olsen, N. L.: Vibration Testing Methods and Techniques-Technical Notes. The Boeing Company, D6-6597, INF., June 1975. 7. Hewlett Packard 545 1 B Fourier Analyzer System Manuals. 8. Richardson, M. and Potter, R.: Identification of Modal Properties of an Elastic Structure From Measured Transfer Junction Data. 20th International Instrumentation Symposium, Albuquerque, N.M., May 1974. 9. Potter, R. and Richardson, M.: Mass, Stiffness, and Damping Matrices From Measured Modal Parameters. International Instrumentation-Automation Conference, New York, October 1974. 10. Cohen, G. C., Cotter, C., and Taylor, D. L.: Use of Active Central Technology to Improve Ride Qualities of Large Transport Aircraft. NASA Symposium on Active Control Technology, July 1974. 1 1. Ryneveld, A. D.: Transient Excitation Techniques for Wind Tunnel and Flight Flutter Testing of SST Configurations. SST Technology Follow-On Program-Phase 11, FAA-SS-73-14, May 1974. 92 Table 1.- Comparison of system parameters derived from figure 7. KEN N E DY -PANCU~ MODAL ON WINDOWED DATA^ MODE FREQUENCY, DAMPING MODE FREQUENCY, DAMPING, Hz CICO Hz CICO - 1 1.76 0.048 1 1.772 0.0427 2 2.27 0.030 2 2.224 0.0386 3 2.44 0.049 3 2.432 0.0544 MODAL ON RAW DATA MODE FREQUENCY, DAMPING, Hz CICO 1 1.768 0.0420 2 2.21 7 0.0342 3 2.44 0.0528 aCORRECTED FOR THE WINDOW. 93 -I -I 0 K a w -I N m a t; 2 - 0 m U 0 I- >. 0 - 2 t a ( u L O - 0 0 0 0 0 g g g g m w 0 0 5: 0 2 0 a 5: !- m w LO 94 MODE MODE MODE Table 3.- 727 T-tail model ground vibration test. F R EQU ENCY, Hz GENERAL I ZED MASS. kq crn2 (Lt3-IN-SEC2) 3.68 8.79 16.57 25.40 34.28 40.13 53.2 1 65.21 388.66 (4.13) 7.067 (0.0751) 1 .I 20 (0.01 19) 0.285 (0.00303) 1.223 (0.01 30) 5.092 (0.0541 0.863 (0.00917) 0.882 (0.00937) Table 4.- Comparison of modal parameters for 727-300 empennage model data (fig. 16). F R EQU ENCY, Hz 3.8 9.3 16.7 MODAL ON RAW DATA FREQUENCY, Hz 3.77 9.22 16.765 DAMPING, clco 0.0162 0.0397 0.0335 DAMPING, CICO 0.016 0.037 1 0.031 2 aCORRECTED FOR THE WINDOW. 95 -30 m U N I \ > - hl -1 10 0 , 10 20 Hz m U N I \ > N -1 -30 r -39.25 dB PSEUDORANDOM AMPLITUDE 3a= l - V PEAK - 30 L INEAR SWEEP RATE 1-V PEAK AMPLITUDE 10 0 10 20 30 Hz -34.58 dB (5% RAMP) 0- LOG SWEEP RATE (5% RAMP) l - V PEAK AMPLITUDE U * ti \ \ Hz Figure 1 .-Comparison of excitation signal input powers, dB. 96 +I Figure 2.- Raw transfer function from a wind tunnel test. 1.0 0 +R + 7-12 0 - 7-12 TIME Figure 3.- Impulse response of figure 2. 97 - 7-12 Figure 4.- Typical window function. + I +R Figure 5.- Windowed transfer function. 98 -1.0 (REF. 7) Figure 6.- The imaginary part of the transfer function of a simple resonator with poles at s = -0.1 rtj0.5. 99 + I + I +R a. Windowed Data +I +R b. Fit of Windowed Data +R c. Raw Data +I +R 1 d. Fit of Raw Data . Figure 7.- 747 Flight flutter test-R.H. wingtip/rudder position. 100 MACH = 0.86 A LT = 31 000FT SWEEP = 1.2TO 3.0Hz INTERVAL= 0.012 Hz (1 FT = 0.3048 m) +I Figure 8.- 747 flight test-Lateral fuselage response to lower rudder yaw damper actuator command signal. 101 + I 120 knots 80 knots (1 knot = 1.85 km/H R) +I 130 knots 135.5 knots Figure 9.- Transfer functions for windowed data of SST low-speed flutter model (ref 1 1). 102 103 104 105 26 24 N I >- 22 0 z W = 12 U a W LL 10 8 6 4 A L A C A L. u u L - TRUE AIR SPEED, MPH ( 1 MPH = 1.61 km/HR) Figure 1 2.- Variations in modal frequencies and damping derived from figure 1 1 . 106 24 22 N I 0 A A A A A 0 A Y U Y Y U A 0 P 0 T R U E AIR SPEED, MPH (1 MPH = 1.61 km/HR) Figure 13.- Frequency and damping variations for model with free elevators. 53.21 Hz Figure 14.- Still air antisymmetric mode shapes of 727-300 transonic empennage model. 108 109 + I I . -.. I +R +I +R NOTE: FREQUENCY = Figure 16.-Typicai transfer function plots from transonic empennage model test. 110 20 MACH = 0.70 MACH = 0.59 (1 LB/FT2 = 47.88 Pa) 15 10 5 0 200 400 600 800 1000 .05 .04 .03 .02 .01 DYNAMIC PRESSURE, L B / F T ~ @ 0 200 400 600 800 1000 DYNAMIC PRESSURE, L B / F T ~ Figure 17.- Dynamic pressure versus damping and frequency. 111 MACH = 0.7 DYNAMIC PRESSURE = 800 LBIFT~ ( 1 LB/FT2 = 47.88 Pa) 10 20 30 TIME, MIN Figure 18.- 727-300 T-tail flutter model. 112 + I a. Lef t Wingtip Vertical .- d. No. 2 Nacelle Vertical + I - e, A f t Body Lateral Lateral I I Figure 19.- 747-200 with JT9D-70 engines-Transfer functions relative to rudder excitation. 113 TURBULENCE EXCITED FREQUENCY DOMAIN DAMPING MEASUREMENT AND TRUNCATION EFFECTS Jaak Soovere Lo ckhe edrC a1 i f or n i a Cornp any S W R Y Ex i s t ing frequency domain modal frequency and damping analysis methods are d iscussed . The e f f e c t s of t runca t ion i n t h e Laplace and Four ie r t r a n s - form d a t a a n a l y s i s methods are descr ibed i n d e t a i l . Methods for e l imina t ing t runca t ion e r r o r s from measured damping are presented . Impl ica t ions of t r u n c a t i o n e f f e c t s i n fast Four i e r t ransform a n a l y s i s are d iscussed . Limited comparison wi th test d a t a i s presented . INTRODUCTION F l i g h t f l u t t e r t e s t i n g i s gene ra l ly a timerconsuming procedure. It involves t h e i n s t a l l a t i o n of complex e x c i t a t i o n genera tors such as vanes ., i n e r t i a e x c i t e r s , or impulsive devices ( r e f . 1) as w e l l as t h e response t r ansduce r s and t h e a s soc ia t ed e l e c t r o n i c equipment. During f l i g h t t e s t i n g , many f l i g h t s are r equ i r ed t o f u l l y explore t h e a i r c r a f t c r i t i c a l . f l i g h t spec- t r u m , producing a l a r g e amount of t e s t d a t a which must be subsequent ly analyzed. Considerable s i m p l i f i c a t i o n i n equipment i n s t a l l a t i o n may be obta ined i f tu rbulence e x c i t a t i o n can be used in s t ead of mechanical e x c i t a t i o n . I n any even t , atmospheric tu rbulence and buf fe t degrade t h e response d a t a from a l l t ypes of mechanical e x c i t a t i o n , except f o r random e x c i t a t i o n , where it would most probably h e l p more than h inde r ( r e f . 2 ) . Thus, t h e a v a i l a b i l i t y of s u i t a b l e random response analysis methods, i n add i t ion t o t h e e x i s t i n g har- monic ana lys i s methods, would be a g rea t advantage. The random a n a l y s i s methods, l i k e t h e cu r ren t harmonic ana lys i s methods, p l a c e t h e burden of d a t a reduct ion on t h e computer, which., when used i n t h e i n t e r a c t i v e mode w i t h t h e t e s t engineer , can provide a basis f o r real-time f l u t t e r t e s t i n g . The e x c i t e r i n s t a l l a t i o n and d a t a a c q u i s i t i o n and a n a l y s i s problems are f u r t h e r compounded i n space s h u t t l e t ype v e h i c l e s , where weight i s o f para- mount importance and t h e c o s t of explor ing the e n t i r e c r i t i c a l f l i g h t spectrum wi th many f l i g h t s p roh ib i t i ve . The nons ta t ionary na ture of t h e f l i g h t envi- ronment and t h e r e l a t i v e l y s h o r t dura t ion of each f l i g h t w i th in t h e atmosphere p l ace a premium on t h e need f o r t r a n s m i t t i n g as much response d a t a as p o s s i b l e , 115 and as quick ly as p o s s i b l e , t o t h e ground s t a t i o n . An inc rease e i t h e r i n t h e rate of sampling o f t he t r ansduce r s , or i n t h e number of t r ansduce r s , i s pos- s ib le , i f t h e d a t a sample l e n g t h can be reduced without a loss i n t h e accuracy of t h e a n a l y s i s . A reduct ion i n t h e sample l eng th o f t h e random response d a t a i s accom- panied by a r educ t ion i n t h e s t a t i s t i c a l accuracy of t h e frequency domain modal response s p e c t r a . The s t a t i s t i c a l accuracy can be r e s t o r e d at t h e expense of r e s o l u t i o n through a corresponding inc rease i n t h e e f f e c t i v e anal- y s i s bandwidth. This i n c r e a s e i n a n a l y s i s bandwidth produces a t r u n c a t i o n e f f e c t i n t h e response s p e c t r a . The t r u n c a t i o n e f f e c t can occur i n t h e fre- quency domain modal a n a l y s i s der ived from t h e Four ie r t ransform of not only t h e impulse response t i m e h i s t o r y but a l s o t h e cross- and au to -co r re l a t ion func t ions o f response due t o random and impulse-type e x c i t a t i o n s . The e f f e c t o f t r u n c a t i o n is s tud ied by us ing a single-degree-of-freedom system. E x i s t i n g frequency domain harmonic a n a l y s i s methods are b r i e f l y d iscussed as an in t roduc t ion t o t h e t r u n c a t i o n e f f e c t and t o i l l u s t r a t e t h e format of t h e d a t a p re sen ta t ion . HARMONIC ANALYSIS The s imples t method f o r ob ta in ing a i r c r a f t modal frequency and damping d a t a i s through s t i c k pu l se generated f ree decay d a t a ( f i g s . 1 and 2 ) . eve r , narrow band f i l t e r i n g i s r equ i r ed bo th t o i s o l a t e each mode i n t u r n and t o minimize n o i s e due t o t h e presence of t u rbu lence . squares f i t methods such as t h e Moving Block Analysis ( r e f . 3) can be used t o o b t a i n damping d a t a from t h e l o g decrement of t h e decay once t h e resonant f requencies have been i d e n t i f i e d by s p e c t r a l a n a l y s i s . How- Computerized least S t i c k p u l s e s , i n gene ra l , may not e x c i t e a l l t h e modes of i n t e r e s t and may produce an unconservat ive estimate of t h e damping. For c l o s e resonances, narrow band f i l t e r i n g m a y no t i s o l a t e each mode, r e s u l t i n g i n a b e a t i n g decay response ( f i g . 1). Under such circumstances, it is p o s s i b l e t o extract meaningful data only i f t h e modal damping and amplitudes are comparable i n each of t h e modes. It is , however, p o s s i b l e , through t h e Four i e r t ransform, t o t ransform t h e decay d a t a i n t o t h e frequency domain ( f i g s . 3 and 4) and thereby r e so lve %he modes. This Four i e r t ransform process can be i l l u s t r a t e d mathematically by cons ider ing t h e r e l a t i o n s h i p between t h e response y ( t ) o f a l i n e a r system and a genera l f o r c e x ( t ) , given by 116 where h ( 7 ) i s t h e impulse response funct ion of t h e system a t t ime 7. For a single-degree-of-freedom system, t h e impulse response func t ion i s given by where : m i s t h e general ized m a s s , wr 6 i s t h e angular resonant fyequency, and i s the viscous damping c o e f f i c i e n t . I f t h e force i s of s u f f i c i e n t l y s h o r t durat ion t h a t it can be considered t o be an impulse I 6 ( t ) , where 6 ( t ) is the del ta funct ion, then the response t i m e h i s t o r y reduces t o The response spectrum y( iw) , obtained from Fourier t ransform of t h e time h i s t o r y (eq . (l)), i s r e l a t e d t o t h e force spectrum x(iw) by where H ( i w ) i s t h e frequency response funct ion of t h e system. degree-of-freedom system, For a s ingle- The Fourier transforms o f t h e response y ( t ) and t h e fo rce x ( t ) a r e def ined by and 117 r e s p e c t i v e l y . fo rce spectrum reduces t o Again, i f x ( t ) can be cons idered an impulse I 6 ( t ) , t hen t h e T I x ( i o ) = - 27r and t h e response spectrum t o which i s simply t h e system frequency response func t ion m u l t i p l i e d by a cons t an t . Two formats can be used i n t h e p r e s e n t a t i o n of t h e frequency domain response d a t a . t h e resonant frequency is l o c a t e d approximately a t t h e peak response, and t h e v iscous damping c o e f f i c i e n t , which i s tw ice t h e s t r u c t u r e damping, i s obta ined by d iv id ing t h e h a l f power po in t bandwidth by twice t h e resonant frequency. I n t h e response modulus vs frequency p r e s e n t a t i o n ( f i g . 3) , It i s a c c u r a t e f o r wel l -separated modes. For c l o s e modes, as t h e modulus r ep resen t s t h e t o t a l response vec to r from t h e o r i g i n and not n e c e s s a r i l y t h e modal v e c t o r , e r r o r s i n t h e measured modal frequency and t h e viscous damping c o e f f i c i e n t may r e s u l t . by t h e f a i l u r e t o r e so lve t h e h a l f power p o i n t s ( f i g . 3 ) . The e x t r a c t i o n of modal damping may even be prevented To overcome t h e s e l i m i t a t i o n s , bo th amplitude and phase are r e t a i n e d and presented i n a format of a Nyquist p l o t ( f i g . 4) i n which t h e real p a r t of t h e response i s i n phase and t h e imaginary p a r t i s out of phase r e l a t i v e t o t h e e x c i t a t i o n . This method of modal a n a l y s i s w a s f i r s t suggested by Kennedy and Pancu ( r e f . 4). curve where t h e rate of change i n a r c l e n g t h wi th frequency i s a t a maximum. The viscous damping c o e f f i c i e n t i s obta ined from t h e h a l f power p o i n t s as previous ly descr ibed or by f irst measuring t h e angle Ip subtended a t t h e modal o r i g i n , by t h e a r c between any frequency po in t f and t h e resonant frequency po in t f and t h e n us ing t h e r e l a t i o n s h i p The resonant frequency i s l o c a t e d a t t h e p o i n t on t h e r' A s t r o n g feature of t h e Nyquist p l o t response d a t a r e p r e s e n t a t i o n i s t h a t mode shapes can be i d e n t i f i e d by means o f t h e modal response vec to r . The more common method o f genera t ing t h e response Nyquist p l o t s i s by means of a slow s i n e sweep us ing mechanical i n - f l i g h t e x c i t a t i o n , such as i n e r t i a e x c i t e r s , i n which t h e fo rce output i s used as re fe rence . This method has been computerized f o r multimodal a n a l y s i s ( r e f . 5 ) , employing a l e a s t 118 squares curve f i t technique t o minimize t h e e f f e c t of extraneous no i se and used i n a computer / tes t engineer i n t e r a c t i v e mode f o r f l u t t e r t e s t i n g . I n t ransforming t h e free decay d a t a as previous ly d i scussed , no t runca- t i o n e f f e c t s w e r e observed due t o t h e r e l a t i v e l y high modal damping and t h e need f o r i nc lud ing one bea t as a m i n i m u m i n t h e decay sample. I n t h e second example of a s t i c k pu l se e x c i t e d decay ( f i g . 21, t h e decay w a s prematurely t runca ted a f t e r one and f i v e seconds t o i l l u s t r a t e t h e effect on t h e frequency domain response ( f i g . 5 ) . The Nyquist p l o t s of t h e response become more ova l i n appearance as t h e decay sample du ra t ion i s p rogres s ive ly reduced. Nyquist p l o t s are analyzed by t h e convent ional method desc r ibed above, uncon- s e r v a t i v e estimates of t h e damping are ob ta ined , t o ob ta in u s e f u l damping d a t a from t h e s e Nyquist p l o t s , a method e l imina t ing t h e e f f e c t of t r u n c a t i o n from t h e damping must f i r s t be developed. If t h e (See table 1.) I n o r d e r TRUNCATION THEORY Due t o t h e s i m i l a r i t y between t h e c ros s -co r re l a t ion and t h e impulse- response func t ions wi th t h e au to -co r re l a t ion func t ion Ryy ( 7 ) of a s i n g l e - degree-of-freedom system e x c i t e d by a cons tan t spectrum f o r c e , Sp ( ref . 2 ) and def ined by it i s only necessary t o d e s c r i b e t h e equat ions f o r any one of t h e above f u n c t i o n s , The impulse-response func t ion and t h e c ros s -co r re l a t ion func t ion of a single-degree-of-freedom system, when e x c i t e d by cons tan t spectrum f o r c e , e x i s t only f o r p o s i t i v e t i m e . I f t h e Laplace t ransform or t h e s ing le-s ided Four ie r t ransform of the a u t o c o r r e l a t i o n func t ion of t h e response Ryy (7) i s used, w i th limits of in te - g r a t i o n from zero t o i n f i n i t y , i n s t e a d of t h e f u l l Four ie r t ransform, phase information i s r e t a i n e d i n t h e response spectrum ( r e f . 2 ) . response spectrum S ( i w ) i s g iven by The r e s u l t i n g s ( i w ) = sP (e H ( i w ) + 2 6 H ( i o ) 4mwr 6 S( i w ) The c h a r a c t e r i s t i c response func t ion - This method sP frequency response func t ion H ( i o ) . has p r o p e r t i e s similar t o t h e provides a powerful t o o l i n 119 modal response a n a l y s i s of random as w e l l as impulse response d a t a i n t h e frequency domain. damping and frequency can b e employed as long as no t r u n c a t i o n e f f e c t i s p resen t e The p rev ious ly desc r ibed methods for e x t r a c t i n g t h e modal I f we l e t y ( t ) r ep resen t any of t h e above t i m e f u n c t i o n s , w i th t h e understanding t h a t t hey exist only f o r p o s i t i v e t i m e , t h e complex response spectrum y ( i w ) i s obta ined from Four i e r t ransform o f y ( t ) . - i w t d t 1 y( iw) = - 2n where y ( t ) = 0 f o r t < O I n r e a l i t y , t h e response t i m e h i s t o r y i s t r u n c a t e d a t some f i n i t e The r e s u l t i n g e s t ima ted response spectrum y( iwl) ( r e f . 6 ) i s A t i m e Tm. g iven by t h e r e l a t i o n s h i p (13) - i w t d t where D ( t ) i s t h e weight ing or t h e t r u n c a t i o n func t ion . Three weight ing func t ions ( r e f . 7 ) are considered i n t h i s paper . They are t h e "do-nothing" or t h e boxcar weight ing , g e n e r a l l y def ined by D ( t ) = 1 f o r - T m < t < T , = 0 elsewhere t h e Hanning weight ing func t ion def ined by D ( t ) = (1 + COS f o r - T m < t , < T m 2 = o e l sewhere and t h e Ba r t l e t t weight ing func t ion de f ined by f o r - Tm < t < T m (16) = o elsewhere 120 The reverse Fourier t ransform f o r t h e respoase is given by Y ( t ) = On s u b s t i t u t i n g f o r y ( t ) i n equation (14) and rearranging t h e order of t h e i n t e g r a t i o n , t h e est imate of t h e spectrum becomes where - i ( w -o)t Tm D ( t , ) e d t y ( i o ) d w A 1 2T y ( i o ) = - Trn -i (wl- w) t D ( t ) e d t 1 Q(u~-u) = - 2n Q(o -w) i s r e f e r r e d t o as t h e s p e c t r a l window. The weighting func t ions def ined &y equat ions (16) t o (18) and t h e corresponding s p e c t r a l windows a r e i l l u s t r a t e d i n f i g u r e 6 . s p e c t r a l windows a r e complex ( r e f . 6 and 8) s ince t h e weighting func t ions a r e one s ided and e x i s t only i n p o s i t i v e time from zero t o 7 . m I n t h e app l i ca t ion discussed i n t h i s paper, t h e TRUNCATED DATA REDUCTION For a l i n e a r system exc i t ed by random f o r c e (or impulse) of constant s p e c t r a l dens i ty , t h e response spectrum y ( iw) i s propor t iona l t o t h e frequency response func t ion of t h e system. frequency response funct ion of a single-degree-of-freedom system and a constant force spectrum, has been in t eg ra t ed by using contour in t eg ra t ion f o r t h e "do-nothing" and t h e B a r t l e t t weighting i n re ferences 6 and 8 , respec- t i v e l y . It has r ecen t ly been solved by t h e author f o r t h e Hanning weighting. A t y p i c a l e f f e c t of t h e t r u n c a t i o n due t o t h e Hanning weighting i s i l l u s t r a t e d i n f i g u r e 7 . The single-degree-of-freedom response p l o t s have been normalized r e l a t i v e t o t h e untruncated p l o t . only i n t h e degree of t runca t ion e f f e c t . The "do-nothing" weighting func t ion , while exh ib i t i ng t h e smallest t runca t ion e f f e c t , s u f f e r s from t h e undes i rab le s i d e lobes ( f i g . 5 ) which may be mistaken f o r modes o r may i n t e r f e r e wi th o the r nearby modes. The Bart le t t weighting func t ion s u f f e r s a g rea t e r resolu- t i o n l o s s , as can be seen by comparing f i g u r e 8 with f i g u r e 5. Equation (lg), with y ( iw) replaced by t h e The o t h e r two weighting func t ions d i f f e r The resonant frequency i s s t i l l i d e n t i f i e d by t h e peak r a t e of change of a rc length with frequency, but t h e procedure f o r es t imat ing t h e damping from t h e t runca ted curves i s d i f f e r e n t f r o m t h e methods previous ly descr ibed. A t 121 f i r s t ( r e f . 6 and 8 ) , the damping coe f f i c i en t w a s ex t rac ted w i t h t h e assist- ance of a nondimensional parameter defined by t h e peak rate of change of a rc length w i t h frequency, divided by t h e r ad ius of curvature at t h e resonant frequency, from t h e o r e t i c a l l y predicted curves. I n t h e s e curves, t h e above parameter i s p l c t t e d as a func t ion of t h e resonant frequency mul t ip l ied by t h e t r u e damping coe f f i c i en t . use i n high frequency s t r u c t u r a l response s tud ie s and consequently are unsuitable f o r f l u t t e r d a t a ana lys i s due t o t h e r e l a t i v e l y low a i r c r a f t response frequencies. These curves were o r i g i n a l l y developed f o r A more use fu l graphica l format, which provides d i r e c t damping readout, i s presented i n t h i s paper and i l l u s t r a t e d i n f igu re 9 for t h e Hanning trun- ca t ion . The measured damping coe f f i c i en t 6% i s p lo t t ed against t h e t r u e damping coe f f i c i en t 6 as a func t ion of t h e r a t i o of t h e e f f e c t i v e d a t a ana lys i s bandwidth Af divided by t h e resonant frequency. The e f f e c t i v e ana lys i s bandwidth Af is r e l a t e d t o t h e maximum t runca t ion t i m e T by m 1 Af = - 2Tm The measured damping coe f f i c i en t 6% i s defined by 6% = 2 (E) where p i s t h e radius of curvature a t resonance, and ds i s t h e arc l eng th at resonance contained wi th in t h e frequency i n t e r v a l of di^ It can be observed t h a t as t h e maximum t runca t ion time becomes l a r g e , t h e measured viscous damping coe f f i c i en t approaches t h e t r u e va lue . This method of obtaining t h e damping from t h e truncation-affected single- degree-of-freedom system Nyquist p l o t s has been computerized f o r p o t e n t i a l use i n real-time ana lys i s . The number of i t e r a t i o n s requi red t o converge t o t h e cor rec t damping f r o m t h e estimated damping i s i l l u s t r a t e d i n f i g u r e 10 . The convergence i s ca r r i ed out i n two or t h r e e sequences and is very rap id . The number of s t eps i n t h e i n i t i a l sequence i s se lec ted t o speed up t h e i t e r a t i o n , e spec ia l ly i n cases of severe t runca t ion . The damping of t h e free decay record ( f i g . 2 ) as obtained by t h e comput- e r i zed method for t h e "do-nothing", Hanning, and B a r t l e t t t runca t ions , a l e a s t squares f i t t o t h e free decay, and t h e res tored Nyquist p l o t method ( f i g . 11) a r e summarized i n t a b l e 2. The method of r e s to r ing the Nyquist ( re f . 9) p l o t involves t h e weighting of t h e decay with a known exponential weighting t o meet t he requi red 55 dB dynamic range c r i t e r i a (ref. 10) for t h e decay. Analysis i s t h e r e a f t e r ca r r i ed out conventionally and t h e damping 122 corresponding t o t h e exponential weighting i s subtracted from t h e measured damping t o arrive a t t h e t rue modal damping. It is more common t o apply t h e exponent ia l weighting funct ion t o t h e c o r r e l a t i o n funct ion. This method has been used i n f l i g h t f l u t t e r t e s t i n g i n England ( r e f . 11). The r e s u l t s from t h e ana lys i s of t h e one-second decay record i n d i c a t e t h e ex is tence of a lower bound on t h e accuracy f o r t h e above frequency domain ana lys i s methods. TRUNCATION I N POWER SPECTRAL DENSITY A method based on the c ross -spec t ra l ana lys i s previously discussed w a s developed t o p r e d i c t t h e t runca t ion e f f e c t i n power s p e c t r a l dens i ty (PSD) ana lys i s . The e f f e c t of t h e t runca t ion on t h e normalized PSD i s i l l u s t r a t e d i n f i g u r e 1 2 f o r t h e Hanning weighting. A computer program w a s developed t o obta in t h e damping from the 3 dB poin ts by using t h e quadra t ic curve f i t . A graphica l method f o r obtaining t h e t r u e damping c o e f f i c i e n t 6 from t h e A measured damping c o e f f i c i e n t 6 f o r various r a t i o s of e f f e c t i v e ana lys i s bandwidth t o resonant frequency i s i l l u s t r a t e d i n f i g u r e 13. A Hanning smoothed power s p e c t r a l dens i ty p lo t of a t y p i c a l a i r c r a f t response t o high-speed bu f fe t i s i l l u s t r a t e d i n f i g u r e 1 4 . Due t o t h e very high speed, no r e l i a b l e f l u t t e r t e s t da t a a r e ava i l ab le f o r comparison. The ana lys i s bandwidth of 0.5 Hz produces a t runca t ion error i n t h e two predom- inant modes at 10.2 Hz and 14 .6 Hz. On allowing f o r t h e t runca t ion e f f e c t , t h e viscous damping c o e f f i c i e n t s from t h e measured 3 dB po in t values of 0.11 and 0.044 are reduced to 0.068 and 0.02 f o r t h e two frequencies , r e spec t ive ly . This method s u f f e r s from t h e same inaccuracies as t h e modulus methoa pre- v ious ly discussed. It does, however, provide an ind ica t ion of t h e damping where none previously ex i s t ed . FAST FOURIER TRANSFORM AND TRUNCATION The above methods have been b a s i c a l l y developed f o r t h e Blackman and Tuckey type of' ana lys i s ( r e f . 7 ) . Truncation e f f e c t s occur a l s o i n t h e fas t Four ie r transform (FFT) method of ana lys i s . An ind ica t ion as t o t h e type of t runca t ion p resen t i n FFT ana lys i s o f cross spec t r a i s obtained from r e f e r - ence 12* E [Sxy(f,T,k)] i s given by The expected c ross -spec t ra l es t imate A s t h e c ross -cor re la t ion funct ion of a single-degree-of-freedom system exc i ted by white no i se i s one s ided , as previously d iscussed , it i s concluded t h a t t h e est imated c ross spectrum obtained from FFT ana lys i s i s subject t o E a r t l e t t t runca t ion e r r o r s . 1 2 3 The e f f e c t o f t r u n c a t i o n on t h e normalized PSD and c r o s s s p e c t r a l peak response i s i l l u s t r a t e d i n f i g u r e 15 as a func t ion of t h e resonant frequency m u l t i p l i e d by t h e m a x i m u m t i m e de lay and t h e viscous damping c o e f f i c i e n t , f, Tm 6 e reaches u n i t y near f, Tm 6 = 1. c r i t e r i a f o r c ros s - spec t r a l a n a l y s i s e s t a b l i s h e d i n r e fe rence 9 , but a l s o t o t h e r u l e of thumb f o r PSD r e s o l u t i o n f o r t h e a n a l y s i s bandwidth t o be one- f o u r t h of t h e 3 dB po in t response bandwidth. It i s observed t h a t f o r t h e "do-nothing" t r u n c a t i o n , t h e curve This corresponds not only t o t h e damping At t en t ion i s drawn t o t h e f a c t t h a t t h e Bar t le t t t r u n c a t i o n curve con- verges t o u n i t y ve ry slowly. Thus t h e use o f c ros s -co r re l a t ion func t ions obta ined from t h e i n d i r e c t method of first computing t h e s p e c t r a us ing t h e FFT and then t ransforming t o t i m e domain, w i l l not on ly have t h e Bar t le t t t r u n c a t i o n e r r o r b u t a l s o an a d d i t i o n a l t r u n c a t i o n e r r o r i n t ransforming from t h e frequency domain t o t h e t i m e domain. These t r u n c a t i o n e r r o r s i n c o r r e l a t i o n func t ions are d i scussed i n r e f e r e n c e s 13, 14 and 1 5 . l a r g e number of t r ans fo rma t ion po in t s must be used i n determining t h e co r re l a - t i o n func t ion through t h e i n d i r e c t method. Thus a very CONCLUSION Methods f o r e l imina t ing t r u n c a t i o n e r r o r s from modal frequency and damping d a t a have been presented f o r t h e c ros s - and power-spectral a n a l y s i s . These methods have t h e p o t e n t i a l f o r use i n a computer / tes t engineer i n t e r - a c t i v e mode, f o r random and impulsive-type response d a t a a n a l y s i s . Future work w i l l i nc lude an eva lua t ion of t h e methods aga ins t s imulated and real f l u t t e r t e s t d a t a wi th b u f f e t and turbulence e x c i t a t i o n and t h e s tudy of t r u n c a t i o n e f f e c t s i n FFT-type a n a l y s i s involv ing m u l t i p l e Four ie r t ransform opera t ions . 124 REFERENCES 1. Baird, E. F . , and Clark, W . B . : Recent Developments i n F l i g h t F l u t t e r Test ing i n t h e United S t a t e s . AGARD Report No. 596, Dee. 1972. 2. Kandianis, F . : Frequency Response of S t ruc tu res and t h e Ef fec t s of Noise on i t s E s t i m a t e s from t h e Transient Response. J . Sound Vib. 1 5 ( 2 ) , 1971. 3. Hurley, S. R . : The Applicat ion of D i g i t a l Computers t o Near-Real-Time Processing of F l u t t e r T e s t Data. Techniques, Oct. 1975. (Paper No. of t h i s compilat ion) NASA Symposium of F l u t t e r Test ing 4 . Kennedy, C . C ., and Pancu, C.D.P. : Use of Vectors i n Vibra t ion Measure- ment and Analysis . J. Aero. S c i . , 1947. 5 . Gaukroger, D. R . , Skingle , C . W . and Heron, K. H . : Numerical Analysis of Vector Response Loci. J. Sound Vib. 2 9 ( 3 ) , 1973. 6 , Clarkson, B. L.,and Mercer, C . A . : U s e of Cross Cor re l a t ion i n Studying t h e Response of Light ly Damped S t ruc tu res t o Random Forces , A I M J . 3 , 1965 * 7 . Blackman, R . B. , and Tukey, J. W . : Measurement of Power Spec t ra . Dover Publ ica t ions , 1959. 8 . Soovere, J . , and Clarkson, B. L . : Frequency Response Function from Cross Corre la t ion : Bart le t t Weighting Function. A I M J. 5 , 1967. 9 . White, R . G. : Evaluation of t h e Dynamic C h a r a c t e r i s t i c s of S t r u c t u r e s by Transient Tes t ing . J. Sound Vib. 1 5 , 1971. 10 . White, R . G . : U s e o f Transient Exc i t a t ion i n t h e Dynamic Analysis of S t ruc tu res . R . A e . S. J . 73, 1969. 11. Baldock, J. C. A . , and Skingle , 6. W . : F l u t t e r Technology i n t h e United Kingdom. AIAA Dynamics S p e c i a l i s t Conference, Williamsburg, 1973. 12 . Bendat, J. S., and P i e r s o l , A. G . : Random Data: Analysis and Measurement Procedures. Wiley-Interscience, 1971. 13. Mercer, C . A. : Note on D i g i t a l Estimation of Corre la t ion Functions. J. Sound Vib. 27( 2 ) , 1973. 1 4 . Holmes, P. J.: On t h e P r a c t i c a l Estimation of Spec t ra and Corre la t ion Functions of Transient S igna l s . J. Sound Vib. 3 2 ( 4 ) , 1974. 15 . Brownlee, L. R . : Comment on "Note on D i g i t a l Estimation of Corre la t ion Functions. ' I J . Sound V i b e 32 ( 4 ) , 1974. 125 TABLE 1. VISCOUS DAMPING COEFFICIENT OF TRUNCATED PLOTS DETERMINED BY USING EQUATION (10). Decay T i m e , "Do-Nothing" Hanning Seconds Truncat ion Truncat i on 1 0.186 0.336 5 0.048 0.073 Bar t le t t Truncat i o n 0.248 0.068 TABLE 2 . COMPARISON OF VISCOUS DAMPING COEFFICIENT BY VARIOUS IviETHODS. Decay T i m e , Seconds 1 5 Least Restored TRUNCATION THEORY Square Nyquist Decay P l o t "Do-Not hing " Hanni ng B a r t 1 e t t 0.045 0.092 0.037 - 0.035- 0.059 0.038 0.040 0.030 0.037 0.044 126 i ci I w 3 rl a, r.2 127 tn 0 z 0 cn Y II s F a a k w v r-i 3.0 .O FREQUENCY - HZ 3.0 Figure 3. Modulus of t h e Fourier Transform of Beating S t i c k Pulse Excited Decay. 129 130 131 -1 .O 0 1.0 T/T, WEIGHTING FUNCTIONS 1.0' 1 I -1 .o -0.5 - - - DO-NOTHING ~-~ HANNING BARTLETT (f - fl ITm SPECTRAL WINDOWS Figure 6 . Spec t r a l Windows and Weighting Functions. 132 REAL PART OF NORMALIZED CROSS SPECTRUM 6 =0.015 df = 0.003 - fr Figure 7 . The Effec t of Truncation on t h e normalized Cross by White Noise ,- Banning Weighting. Spectrum of a Single-Degreerof-Freedom System Excited 133 E - II - I c P *rl 3 3 0 a, I 3 134 0 0.08 0.07 0.06 0.05 6' 0.04 0.03 0.02 0.01 0 0.01 0.02 0.03 0.04 0.05 0.06 ACTUAL DAMPING - S Figure 9 . Method for Obtaining Damping from Truncation Affected Cross Spectra of a Single-Degree-of-Freedom System - Hanning Weighting. 135 d Y v) z 0 k E w LL 0 U W rn k 3 z G 0 I a, -0 i. d PI c! 0 .rl c, cd k a, c, H ri d 0 0 r-l 136 a, a 24 a, rl ho F: .d m ri r i 137 0. fr?n 00 40 30 20 10 6 Figure 12. The Effect of Truncation on the Normalized PSD of a Single-Degree-of-Freedom System Excited by White Noise - Hanning Weighting Function. 138 0.08 0.07 0.06 0.05 A 8 0.04 0.03 0.02 0.01 0 Figure 13. Correction t o 3 dB Point Measured Damping from Single-Degree-of-Freeaom System Response PSD - Hanning Weighting. 6 139 tJ a, k k 3 m AIISN3a l V U I 3 3 d S WMOd 140. 1 .o H 3 U I- n B 8 n a 2 5 fn v) LT 0 z cl Y n n N -I 0.5 a w z 0 z I DO NOTHING HANNING ~-~ ~~-~ BARTLETT 1 .o 2.0 f r Trn 3.0 Figure 15 . Ef fec t of Truncation on t h e Peak PSD and Cross Spec t r a l Response Resolution of a Single-Degree-of-Freedom System Excited by White Noise. 141 SPECIFICATION OF INPUTS AND INSTR~NTATION FOR FLUTTER TESTING OF MULTIVARIABLE SYSTEMS Narendra K, Gupta and We E a r l H a l l , Jr. Systems Cont ro l , Inc, SUMMARY This paper d e a l s wi th t h e a p p l i c a t i o n of system i d e n t i f i c a t i o n methods i n f l u t t e r t e s t i n g of a e r o e l a s t i c s t r u c t u r e s . The accuracy wi th which f l u t t e r parameters are es t imated depends upon t h e test plan and on the a lgor i thms used t o reduce t h e da t a . The techniques f o r s e l e c t i n g t h e k inds and opt imal posi- t i o n s of i n p u t s and ins t rumenta t ion , under t y p i c a l test c o n s t r a i n t s , are pre- sen ted , and t h e va lues of phys i ca l parameters are presented. opt imal i npu t spectrum and t h e accelerometer l o c a t i o n f o r e s t ima t ing f l u t t e r parameters of a two dimensional wing are obta ined us ing t h e s e a lgor i thms. Current work on applying system i d e n t i f i c a t i o n methods t o h igh o rde r t h r e e dimensional a e r o e l a s t i c s t r u c t u r e s is d iscussed . I d e n t i f i c a t i o n r e s u l t s f o r both t h e input /output t r a n s f e r func t ion Numerical r e s u l t s on t h e INTRODUCTION The o b j e c t i v e of f l u t t e r a n a l y s i s is t o quan t i fy t h e c r i t i c a l p o i n t s o r boundaries of f l u t t e r and t h e s t a b i l i t y margins a s s o c i a t e d wi th s u b c r i t i c a l responses. While i t i s t r u e t h a t a n a l y t i c a l p r e d i c t i v e techniques have become inc reas ing ly u s e f u l t o t h i s ob jec t ive , a c t u a l t e s t i n g and da ta a n a l y s i s i s always r equ i r ed f o r v e r i f i c a t i o n of t h e s e ana lyses , o r t o provide r e s u l t s where a n a l y t i c a l assumptions are suspect . Thus, f l u t t e r test a n a l y s i s tech- n iques are be ing developed which use experimental d a t a (usua l ly noisy) t o provide a c c u r a t e estimates of bo th s u b c r i t i c a l s t a b i l i t y margins as w e l l as a i d e x t r a p o l a t i o n t o t h e c r i t i ca l po in t s ( r e f s . 1 and 2 ) . To be most u s e f u l , t hese techniques should provide real t i m e (or near real t ime) estimates t o keep test t i m e s a t a minimum. Fur ther requirements on t h e s e test a n a l y s i s techniques are emerging due t o new a i r c r a f t concepts. New s t r u c t u r a l concepts , such as l i g h t weight com- p o s i t e s technology, and c o n t r o l concepts, such as t h e active c o n t r o l of maneu- ver loads and f l u t t e r margins, w i l l r e q u i r e mul t iva r i ab le t e s t i n g a n a l y s i s methods, These m u l t i v a r i a b l e a n a l y s i s techniques are necessary t o d e f i n e the modal f r equenc ie s and damping of many i n t e r a c t i v e s t r u c t u r a l components i n complex aerodynamic regimes. To m e e t t h e cha l lenging requirements of e s t ima t ing accu ra t e s u b c r i t i c a l f l u t t e r test parameters and t o use t h e s e r e s u l t s t o e f f e c t i v e l y p r e d i c t f l u t t e r boundaries f o r m u l t i v a r i a b l e systems, a sys temat ic approach m u s t be adopted. This approach should i n t e g r a t e t h e s p e c i f i c a t i o n of test ins t rumenta t ion and i n p u t s wi th mul t i input /mul t iou tput da t a a n a l y s i s procedures. 143 The key elements of such a n a e r o e l a s t i c i n t e g r a t e d t e s t i n g a n a l y s i s of a model o r of a pro to type v e h i c l e are shown i n f i g u r e 1. F i r s t , t he test o b j e c t i v e must be quan t i f i ed , H i s t o r i c a l l y , t h i s test o b j e c t i v e has progressed from f ind ing t h e f l u t t e r boundary t o more c u r r e n t de te rmina t ion of t h e f r e - quency and damping of t h e s u b c r i t i c a l s t a b i l i t y margin. The need t o be a b l e t o b e t t e r u se s u b c r i t i c a l d a t a t o p r e d i c t t h e boundary r e q u i r e s determinat ion of t h e parameters of a f l u t t e r model which may con ta in two o r more states of t he system, Of course, accuracy s p e c i f i c a t i o n s f o r t hese v a r i o u s levels must be set. Second, t h e opera t ing p o i n t s (of a wind tunnel o r f l i g h t regime) must be set t o provide t h e b a s i s f o r meeting the o b j e c t i v e s w i t h i n test s a f e t y con- s t r a i n t s . To implement t h e test o b j e c t i v e s a t t h e requi red p o i n t s , an ex tens ive a n a l y s i s of test i n p u t s and ins t rumenta t ion w i l l minimize t h e p r o b a b i l i t y of i n e f f e c t i v e r e s u l t s due t o t h e improper e x c i t a t i o n of cr i t ical modes and low s i g n a l / n o i s e r a t i o s . With t h e test conf igu ra t ion s p e c i f i e d , t h e d a t a are c o l l e c t e d and analyzed using e i t h e r a s p e c t r a l a n a l y s i s technique (e .g . , f a s t Four i e r t ransform (FFT, r e f . 3) o r Randomdec ( r e f . 4 ) ) o r an advanced parameter i d e n t i f i c a t i o n algori thm. This paper focuses on Che s p e c i f i c a t i o n of test i n p u t s and ins t rumenta t ion . S p e c i f i c a l l y , t h e t h r e e major elements of t h e test conf igu ra t ion are: ( a ) Choice and l o c a t i o n of ins t ruments (e.g. , accelerometers , s t r a i n (b) Choice of i npu t s w i t h respect t o type (e .g . , s i n u s o i d a l , swept s i n e s , gages gyros 1. random), and l o c a t i o n of i npu t s and f requencies , and energy of i npu t s . (c) 'Required c a p a b i l i t y o f test a n a l y s i s procedures. Ana ly t i ca l methods f o r input des ign and instrument s e l e c t i o n t o o b t a i n t h e most accu ra t e estimates of parameters i n models desc r ib ing t h e f l u t t e r behavior of aerodynamic s t r u c t u r e s are developed. The methods, based on system i d e n t i f i c a - t i o n technology, minimize t h e expected covariance of e r r o r s i n estimates of unknown parameters. The l o c a t i o n s of t h e ins t ruments and t h e inpu t s ( i f vari- a b l e ) may a l s o be opt imal ly se l ec t ed . This paper desc r ibes a s imple model of an a e r o e l a s t i c wing. The dynamics of t h e wing can be formulated as a state v a r i a b l e model, The a n a l y t i c a l formu- l a t i o n of t h e i n p u t design problem f o r state v a r i a b l e models wi th unknown para- meters i s given, a long wi th a d e s c r i p t i o n of t h e methods used f o r s e l e c t i n g t h e k ind , accuracy, and l o c a t i o n s of ins t ruments . Some r e s u l t s on t h e selec- t i o n s of ins t ruments and i n p u t s t o accu ra t e ly i d e n t i f y t h e f l u t t e r charac te r - i s t i c s of a two dimensional wing are descr ibed. F i n a l l y , t h e techniques are app l i ed t o l a r g e aerodynamic s t r u c t u r e s and t h e conclusions drawn from t h i s work are discussed. 144 STATE SPACE EQUATIONS FOR A TWO DIMENSIONAL WING I N FLUTTER F l u t t e r i s an i n t e r a c t i o n between nonsteady aerodynamic fo rces and elastic f o r c e s i n a s t r u c t u r a l component. f o r f l u t t e r t e s t i n g , a r e fe rence model f o r t h e f l u t t e r o f a two dimensional wing is given based on t h e work of Houbolt ( r e f , 5 ) . The symbols used fol low those of r e fe rence 5, To s tudy t h e experimental design techniques An o s c i l l a t i n g two dimensional a i r f o i l i n an incompressible flow .can be modeled as shown i n f i g u r e 2. Various f o r c e s a c t i n g on t h e a i r f o i l are: ( a ) l i f t L a t q u a r t e r chord and l i f t L2 a t three-quar te r chord, (b) r e s t o r i n g f o r c e and moment through t h e e l a s t i c axis loca ted a t ( a ) , ( c ) fo rce and moment a s s o c i a t e d wi th t h e i n e r t i a of t h e subs tance c o n s t i t u t i n g the medium ( t h e s e w i l l be neg lec t ed ) , and (d) e x t e r n a l f o r c e s and/or moments, used t o e x c i t e f l u t t e r o r i n a d v e r t e n t l y t r ansmi t t ed through t h e s t r u c t u r e . L2 are modeled wi th appropr i a t e delays. Houbolt ( r e f . 5) shows t h a t t he aero- elastic equat ions f o r t h e wing can be w r i t t e n i n terms of nondimensional vari- a b l e s as fo l lows (see a l s o f i g . 2 ) : 1 The l i f t s L and 1 2 -2 I-ls + MUy 2 -urs 2 1 -prs - - 2 s - 2 - 2 1 km -2 -2 2 2 -2 ($ k m 1-r - s2 + - r s + - w c c 2 2a s + 2b2s -2r a s2 - ( a 2 + 2b r ) s - b2 - 2 2 2 2 2 - -1 1 -r s + b 2 - . - 1 f r 0 - - By def in ing w A ; 1 - 145 equation (1) becomes or _. r. -yr 0 k2 lJ$ 0 C -2r a 1 - 2 2 Therefore d - dP - W. I 4- U W 4 - = A2 + A3 - - 1 W $1 U - - - 0 k2 m -2 ?J 2 -b2 c - 1 2 - - 1 - 2 r2 + A4 F + 146 where I i s an i d e n t i t y matrix, a e r o e l a s t i c wing and can be w r i t t e n compactly as This is t h e state space representa t ion of an * x = Fx + Gu (4) where x i s t h e state vec tor , u is the inpu t vec tor , and F and G are t r a n s i t i o n matr ices which conta in unknown parameters. An accelerometer placed a t e w i l l measure 0 e y = w + q .. C The q u a n t i t i e s Then and b, can be expressed i n t e r m s of x using equat ion (3). 1 y = Hx + Du ( 6 ) The t r a n s f e r func t ion between y and u i s b s 4 + b 3 s 3 + b 2 s 2 + b s + b s 5 + a s 4 + a s 3 + a s 2 + a s + a o 0 + D, s = j w - 4 1 - 4 3 2 1 (7) This t r a n s f e r func t ion can be w r i t t e n again i n t o a s ta te space form, o f t en r e fe r r ed t o as a canonical form. OPTIMAL SELECTION AND LOCATION OF INPUTS AND INSTRUMENTS A s shown above, the f l u t t e r equations of a wing can be wr i t t en i n e i t h e r t h e state v a r i a b l e form o r t h e t r a n s f e r func t ion form. The mul t ivar iab le state equations and measurement equat ions are equations (4) and (6). I n p rac t i ce , t h e measurements, y , are corrupted by a d d i t i v e noise , v , so t h a t y = H x -I- Du + v 1 4 7 where v is assumed t o be a whi t e no i se source wi th power s p e c t r a l d e n s i t y ma t r ix R, i n p u t s and ins t ruments ) are imbedded i n t h e matrices F, G, and He The unknown parameters, whose es t imated w e are i n t e r e s t e d i n , w i l l be denoted by 0 . The unknown parameters and some c o n t r o l parameters ( l o c a t i o n s of The accuracy of t h e parameter estimate 0 is expressed i n terms of t h e b i a s and covariance p r o p e r t i e s of t h e estimate. It is assumed t h a t an unbiased and e f f i c i e n t e s t ima t ion procedure is used so t h a t t h e i n p u t design and instrument s e l e c t i o n can b e c a r r i e d ou t independent ly of t h e e s t ima t ion procedure. This makes i t p o s s i b l e t o compute e r r o r s i n t h e parameter estimates based on t h e Cramer-Rao lower bound, This bound i s computed around an a p r i o r i va lue 0 f o r t h e parameters 0 . The informat ion matrix M i s r e l a t e d t o t h e e r r o r i n es t imated by t h e fol lowing r e l a t i o n 0 where 6 i s t h e estimate of 0 . The information matrix depends upon t h e i n p u t energy d i s t r i b u t i o n and i t s l o c a t i o n and instrument accu rac i e s and t h e i r l oca t ions . The design procedures presented he re w i l l work w i t h t h e p r o p e r t i e s of t h e informat ion matrix. phys ica l reasons, a quadra t i c c o n s t r a i n t is p laced on t h e inpu t s and t h e state v a r i a b l e s For 0 where A i s a symmetric p o s i t i v e semide f in i t e matr ix . mation matrix, under t h e c o n s t r a i n t of equat ion ( lo ) , i n t h e frequency domain i s now obtained, An equat ion f o r t h e in fo r - Information Matr ix i n t h e Frequency Domain The r e l a t i o n between y and u i n frequency domain i s y(w> = { H ( j w I - F)-'G + D) u(w) 148 where T(w,8) i s t h e t r a n s f e r func t ion from t h e input , u(w), t o the measurement Y (a) Equation (10) i s w r i t t e n i n the frequency domain as (23 {uiw) u*(w) + Tr(Ax(w) x*(w))) dw - < E 0 where T r i s t h e trace opera tor and I * ' denotes conjugate transpose. I f S(w,e) is t h e t r a n s f e r funct ion between x and u, equation (12) may be w r i t t e n as X(w,O) u(w) u*(w) dw = E The inequa l i ty s i g n can be removed f o r l i n e a r systems because inc reas ing the i n p u t amplitude w i l l i nc rease t h e accuracy of a l l parameters. The information mat r ix f o r parameters 8 from measurements y , pe r u n i t t i m e , is as fol lows (see r e f s . 6 and 7 f o r d e t a i l s ) : W * aT aT - U(W) u*(w) dw -ae ae M = R e J 0 14 9 Equations (13) and (14) become - u(w) uJ((w) dw = E 0 0 The information matrix, M, se rves as the bas i c quant i ty upon which the input and instrumentat ion requirements are t o be determined. Maximizing M by appropr ia te input and instrumentat ion design parameters l eads t o output da ta which have a high information content on the system parameters. That is, the s e n s i t i v i t y of t h e outputs t o parameters, f o r example, i s maximized by exc i t i ng t h e modes which are most a f f e c t e d by the parameters. Basing t h e design on M, though mathematically s i m p l e r , has some disadvantages i n p rac t i ce . I f the trace of M (e.g. , t h e sum of diagonal elements) is maximized, an almost singu- l a r information mat r ix may r e s u l t . The inve r se of M is the lower bound on the parameter covariance matrix. I f M is nea r ly s ingu la r , i t s inverse may contain l a r g e diagonal elements, leading t o l a rge e r r o r s i n the estimates. For t h i s reason, i t i s more des i r ab le t o work d i r e c t l y with the inverse -1 of t h e information matr ix , M . This mat r ix can be viewed as the e l l i p s o i d of uncertainty of t h e parameters. Though mathematically more d i f f i c u l t t o minimize, t h i s matrix gives use fu l r e s u l t s s ince w e are minimizing t h e para- m e t e r covariances d i r e c t l y . Two types of methods can be used t o minimize -1 M . These are based on the following func t ions of M-l : -1 (1) Minimize D e t (M ): This method w i l l minimize the volume of the uncer ta in ty e l l i p s o i d . This a l s o minimizes maximum e r r o r i n the estimate of the t r a n s f e r funct ion. (2) Minimize T r (WM-l): This method minimizes a weighted sum of t h e parameter estimate covariances (W is the weighting matr ix which penal izes c e r t a i n estimate e r r o r s more heavi ly than o the r s ) . The weighting matr ix se rves two purposes. Since the covariances of d i f f e r e n t parameters have d i f f e r e n t u n i t s , the weighting mat r ix con- v e r t s each t e r m i n t h e sum t o t h e same un i t s . Secondly, the weight- ing mat r ix o f f e r s tremendous f l e x i b i l i t y because i t is poss ib l e t o ass ign varying importance t o parameters through weights on t h e i r nondimensional covariance, This i s considered t o be one of t he most s u i t a b l e performance cri teria, s i n c e i t works wi th parameter estimate covariances d i r e c t l y . 150 Choice and Locat ion of Optimal Input The optimal i n p u t possesses c e r t a i n p r o p e r t i e s which are q u i t e important . presented h e r e without proof ( r e f , 6) : The opt imal i npu t has a d i s c r e t e spectrum (o r p o i n t spectrum). number of f requencies w i t h nonzero power does no t exceed where m i s t h e number of parameters. I f t h e spectrum of u con ta ins fewer than m/(2p) f requencies , t h e informat ion matrix i s s i n g u l a r (i.e., a l l t h e parameters cannot be iden ti f i e d ) . The opt imal input which minimizes D e t ( M e r r o r c r i t e r i o n . I n o t h e r words, t h i s i npu t g ives t h e b e s t estimate of t h e t r a n s f e r func t ion . The m ( m + l > 2 5 -1 ) s a t i s f i e s a minimum output They s a t i s f y two important theorems (see r e f s . 6 t o 8) , which convert t h i s complex non l inea r problem i n t o a computation technique. 6 It has been demonstrated t h a t t h e computation procedure summarized i n ' appendix A can be app l i ed t o select t h e i n p u t spectrum which g ives the des i r ed m i n i m u m of M . -1 P r a c t i c a l cons ide ra t ions i n t h e computation of opt imal input . - The algo- r i t hm of appendix A w i l l produce an opt imal i npu t design wi th a s u f f i c i e n t num- b e r of i t e r a t i o n s . However, a t each i t e r a t i o n , t he procedure adds one p o i n t . t o t h e spectrum of t h e input . For p r a c t i c a l implementation, i t i s d e s i r a b l e t o have as few f r equenc ie s i n t h e opt imal i n p u t as poss ib l e . During t h e compu- t a t i o n , a few s t e p s can be taken t o reduce t h e number of p o i n t s i n t h e spectrum. Suppose t h e normalized i n p u t a t any s t a g e has k f requencies w (i=l , 2 , . . . , k) . with power a i i Then : (a) Frequencies less than Aw a p a r t can be lumped i n t o one frequency. * Suppose q f requencies w are wi th in a band be r ep laced by one frequency w* w i t h power i and q * a* = c ai i= 1 Aw wide. Then they can a* where ai (b) From t h i s new inpu t , a l l frequencies wi with power less than a threshold a' are dropped, t he cons t r a in t of equation (13), so the design is renormalized. The remaining frequencies do not s a t i s f y Steps (a) and (b) should be ca r r i ed out t o ensure t h a t the design does not become degenerate, This "prac t ica l iza t ion" requi res judgment of Aw and a. Choice of loca t ion of input.- The t r a n s f e r functions T(w,0) ( the input- to-output t r a n s f e r function) and S(w,0) ( t he input-to-state t r a n s f e r function) are both l i n e a r functions of t he cont ro l d i s t r i b u t i o n mat r ix G. The loca t ion of t he input a f f e c t s G i n a l i n e a r fashion. Therefore, i f B is an inpu t loca- t i o n parameter, t h e t r a n s f e r functions T(w,B) and S(w,e) can be w r i t t e n as Equations (13) and (14) can, therefore , be wr i t t en as i .e. , and 2 M = YIMll + 2BM12 + M221 y is a scalar which ad jus t s t h e energy i n the input t o s a t i s f y the quadra t ic cons t r a in t on the input and t h e states. Equations (19) and (20) can be com- bined i n t o one equation, E [Mll +2BM12 + B 2 M22I Y 0 L B L M = 1 + CIB+ C2B 152 -1 -1 B can be se lec ted t o minimize IM In f a c t , an algorithm siailar t o t h a t of appendix A f o r input frequency and power s e l e c t i o n can be developed. I o r Tr(WM 1. I n a more genera l case, when there is more than one input and each input may be placed over any poin t i n two or more dimensions, the number of para- meters B which must be se l ec t ed optimally is more than one. The optimization becomes somewhat more d i f f i c u l t , but the bas i c approach remains the same. Choice and Location of t he Instruments I n addi t ion t o s e l e c t i n g t h e loca t ion and type of t he e x c i t a t i o n sigr,al , t he re are two o t h e r design considerations i n planning a f l u t t e r test. are t h e determination of t he kind of instruments which must be used t o record f l u t t e r response and t h e choice of instrument loca t ion ( i f t he re i s a choice). Though t h e problem of instrument s e l ec t ion and loca t ion can be t r ea t ed simul- taneously, f o r s ake of s impl i c i ty we treat them separa te ly . These Selection of instruments.- The se l ec t ion of instruments i s a tradeoff between dynamic range, accuracy, and cos t . The dynamic loads are o f t en l imi t ed by s t r u c t u r a l cons t r a in t s , and i t w i l l be assumed t h a t the instruments cover t h i s range. The accuracy with which the parameters may be estimated i s then determined by t h e accuracy of the instruments. It is clear from equation (14) t h a t t h e information matrix has an inverse r e l a t ionsh ip with the measure- ment no i se covariances. 03 - aT* u(w) u*(w) du 29 M = Re 0 For the purpose of instrument s e l e c t i o n i n general , the measurement noise covariance matrix i s diagonal, i .e . , where l / r is t h e covariance of random no i se i n the 5 t h instrument. The t o t a l cos t of t he p instruments i s a sum of t h e c o s t of ind iv idua l instruments 11 The t o t a l cos t of t h e instrument package is assumed t o 3e f ixed . E i the r of the cri teria of equation (17) may be minimized under the cos t cons t r a in t and 153 r > O ii - The Lagrange mul t ip l i e r approach may be used f o r optimization. i f t he c r i t e r i o n requi res t h e minimization of IM i s For example, -1 I, t he modified c o s t function if P i= 1 -1 - J = I M I + c (Airii - wi(r i i ) ) + I-~C where X i = 1 y 2 9 . n . , p , and v are Lagrange mul t ip l i e r s . The following optimiza- t i on equations r e s u l t : i’ r = O , o r A = O ii i aci arii arii , i = l y 2 , . . . , P * (27) -1 a M 1 M I 2 T r { M - } + Ai - 1-1 = 0 Equations (24) and (27) are 2p+l equations i n 2p+l unknowns X r and U. i’ ii Note tha t i f any rii is zero, t h e corresponding instrument has i n f i n i t e e r r o r ; i n other words, t h i s instrument should not be used. The optimal value of r would act as a guideline i n se l ec t ing the ins t ru- ment. Often, i t is not poss ib l e t o obta in an instrument with mean square e r r o r of - r ii ii exac t ly and cost Ci(rii). * Location of instruments.- The t r a n s f e r function T(U,B) is a l i n e a r func- t i on of t h e measurement d i s t r i b u t i o n mat r ix H, and, therefore , t he pos i t i on of t h e instrument. For t h i s reason, optimal choice of instrument loca t ion can be determined i n t h e s a m e w a s as the optimal pos i t ion ing of inputs. RESULTS To demonstrate the appl ica t ion of t h e methods described above t o multi- var iab le f l u t t e r problems, a two dimensional wing i s considered. The values of t he parameters are as follows: r 2 2 The ve loc i ty i s taken as 1 5 . 2 5 ~ = 10, (km/c ) = a = 0.1, a/c = 0.35, = 0.1, r 1 2 = 0.4, a2 = 0 . 6 , and b2 = 0.3. *meters/sec (50c f t / s e c ) and t h e n a t u r a l frequencies of the r o t a t i o n a l and ver- 154 t ical motions are 10 he r t z and 2 h e r t z , respectively. matrices f o r t h e nondimensional state equations as This gives t h e system F = and 0 0.05 0.1 -0.01579 0 0 -0.2 0 , l 0 -0 3948 - -0.6 0.684 -0.372 0.01895 0.1105 1 0 0 0 0 0 1 0 0 0 e -0.12 -0.48 “r , 0 01 C GT = c 0 . l - C The measurement d i s t r i b u t i o n matrices are e e e 0 0 -0.01579 , -0 .3948O ] (29) C c 9 C H = [ o 0 .5 -0 .2 - 0 . 1 + 0 . 1 - e ef 0 D = (0 .1 4- - e - ) e C C e 0 are parameters which define the loca t ions of the input ac tua tor ef where - and - C C and t h e accelerometer. The n o i s e i n the accelerometer i s assumed to be white, with a standard devia t ion of 0.02 i n dimensionless u n i t s ( t h i s corresponds t o about 0.61 meters/sec/sec (2 f t / s e c / s e c ) ) and a sampling i n t e r v a l of 4 m i l l i - seconds. It is assumed t h a t w e are i n t e r e s t e d i n estimating the parameters -2 -2 wy9 wo9 r2’ a2’ b2’ a. The poles and zeros of t h e t r a n s f e r function between t h e measurement and e ef 0 t h e input - and - b o t h equal t o 0.1, are, i n radians per second ( the nondimen- C C s i o n a l values are mul t ip l ied by 100) 155 Poles -5,76 5 55 ,6 j -19,4 1 6 , 6 j -6-83 Zeros -0,163 2 76.2j -30.0 -5.68 Input Design A s mentioned before , t h e i n p u t s are designed t o maximize the i d e n t i f i a b i l - i t y of f l u t t e r parameters from output . seconds. This is a f a i r l y s h o r t test, b u t i n terms of t h e n a t u r a l frequency of t h e wing i n f l u t t e r , i t i s long enough so t h a t t he s t eady state i n p u t design can be appl ied . I n t h e design procedure, t h e l o c a t i o n s of t he e x c i t a t i o n and the accelerometer are kep t f i x e d , and t h e i n p u t frequency spectrum and power i n each frequency of t h e spectrum are se l ec t ed . The test du ra t ion w a s s e l e c t e d as 2 To s impl i fy t h e procedure, t h e parameters i n t h e F, G, and H matrices are i d e n t i f i e d d i r e c t l y (D does n o t conta in any unknown parameter) . The inpu t is designed t o produce t h e most accu ra t e estimates of t h e underl ined parameters i n equat ions (27) and (28) i n t h e sense of minimizing t h e determinant of t h e in- verse of t he informat ion matr ix . S t a r t i n g from the topmost spectrum of f i g u r e 3 w i t h a v a i l a b l e power d i s t r i b u t e d equal ly among f i v e f requencies a t 2, 4 , 6, 8, and 10 cyc les p e r second, t h e i t e r a t i v e des ign procedure g ives the r e s u l t s shown i n t h e f igu re , I n every i t e r a t i o n , t h e des ign procedure adds a new frequency or inc reases t h e power a t a frequency a l r e a d y included i n the spectrum. This l e a d s t o a l a r g e number of f requencies i n t h e computed spectrum. A s mentioned above, t h i s des ign can be s i m p l i f i e d , When f requencies w i t h relative power less than 5 per c e n t o r c l o s e r than 0.4 h e r t z are merged wi th t h e neighboring f r e - quencies , t h e r e s u l t i n g des ign i s shown i n f i g u r e 4. There are e i g h t frequen- cies i n t h e opt imal spectrum--three each c l u s t e r e d around t h e two o s c i l l a t o r y modes and one each a t a low and an in t e rmed ia t e frequency. Of t h e t h r e e f r e - quencies around t h e o s c i l l a t o r y modes, one is below, one i s above, and one is c l o s e t o t h e n a t u r a l frequency. This c h a r a c t e r i s t i c seems t o be q u i t e genera l and s u b s t a n t i a t e s Gerlach 's i n t u i t i v e choice of input f requencies f o r t h e iden- t i f i c a t i o n of t h e s h o r t pe r iod parameters of a n a i r c r a f t ( r e f . 9) . A 2 second t i m e trace f o r t h i s i npu t spectrum wi th i n i t i a l phases s e l e c t e d a t random i s shown i n f i g u r e 5. Choice of Accelerometer Location I n the f l u t t e r a n a l y s i s of a two dimensional wing, t y p i c a l l y only one accelerometer is used. It is gene ra l ly d e s i r e d t h a t t h e b e s t accelerometer w i t h i n the test budget be s e l e c t e d . There may be a p o s s i b i l i t y of us ing two poorer q u a l i t y accelerometers . This t radeoff w a s no t s tud ied , 156 The loca t ion of t h i s accelerometer is an important parameter, The follow- ing performance index i s considered: J = (Fr i=l where 8 ( i=1 ,2 ,* . e9m) i s t h e set of parameters of i n t e r e s t and ae i i standard deviation of estimation e r r o r i n the i t h parameter. Figure 6 shows the values of t h e performance index f o r constant input rms value and constant output r m s value as a function of t h e accelerometer pos i t ion . The m i n i m u m of t h e curves gives t h e pos i t ions of t h e optimal loca t ion of t h e accelerometer under t h e two cons t r a in t s . i s the Simulation and Maximum Likelihood I d e n t i f i c a t i o n The f l u t t e r equations f o r t h e t r a n s i t i o n matrices of equations (27) t o (29) f e e 0 are simulated with t h e input of f i gu re 5. Both - and - are taken as 0.1, and the accelerometer rms random e r r o r is 0-02 i n t he nondimensional un i t s . The t r a n s f e r function between t h e inpu t and t h e output i s as follows: C C 4 3 2 ( s + 0.360s + 0.599s + 0.208s+0.0099) 4 3 2 -0.0155 (s +0.572s +0.457s +0.158s +0.0292s+0.00139) Three i d e n t i f i c a t i o n runs w e r e made: (a) The underlined parameters i n equations (27) and (28) are estimated. Note t h a t H i s a l i n e a r combination of t h e f i r s t two rows of F. The estimated and the measured t i m e h i s t o r i e s a r e shown i n f igu re 7. (b) The input /output r e l a t i o n i s represented as a f i v e pole, four zero t r a n s f e r function. The c o e f f i c i e n t s of the t r a n s f e r function are i d e n t i f i e d d i r ec t ly . This requi res estimation of 10 parameters. The measured and estimated t i m e h i s t o r i e s of t he accelerometer response are shown i n f igu re 8. The match between t h e two t i m e h i s t o r i e s is comparable t o tha t i n f i g u r e 7. The i d e n t i f i e d t r a n s f e r func t ion i s 3 2 4 3 2 (33) (S4 + 0.432s + 0.593s + 0.229s + 0.00844) (s +0.525s +0.451s +0,145s +0.0297s+0.00116) -0.0137 15 7 C e r t a i n i d e n t i f i a b i l i t y problems w e r e i n d i c a t e d by the a n a l y s i s of t h e information matr ix . This, t oge the r wi th t h e f a c t t h a t one zero is v e r y c l o s e t o a p o l e (eq. (30 ) ) , i nd ica t ed t h a t a lower o rde r model may be more use fu l . (c) The input /output r e l a t i o n s h i p i s represented by a four po le , t h r e e zero model. The c o e f f i c i e n t s of t h e fou r th o r d e r t r a n s f e r func t ion are i d e n t i f i e d by us ing t h e m a x i m u m l i i re l ihood method. The t i m e h i s t o r y p l o t s are shown i n f i g u r e 9, and t h e i d e n t i f i e d t r a n s f e r func t ion is as fol lows: (s3 + 0 . 2 5 0 ~ ~ + 0.569s + 0.139) 3 -0.0157 (s + 0.467s + 0 . 4 0 0 ~ ~ + 0.119s + 0.0195) (34) Though t h e f i t t o t h e t i m e h i s t o r y responses is poorer than before , no i d e n t i f i a b i l i t y problems are ind ica t ed , implying t h a t t h e f o u r t h o rde r t r a n s f e r func t ion i s an adequate r e p r e s e n t a t i o n f o r t h e accel- erometer ou tput l shaker input r e l a t i o n s h i p s . This is a l s o i n d i c a t e d by t h e p l o t s of t h e ga ins and t h e phases of t h e f i f t h o rde r and f o u r t h o r d e r i d e n t i f i e d t r a n s f e r func t ions i n f i g u r e s 10 and 11. The po le s and zeros o f t h e t r a n s f e r func t ion used i n the s imula t ion and t h e i d e n t i f i e d t r a n s f e r func t ions i n each of t h e t h r e e cases given above are shown i n f i g u r e s 12 and 13. The c loseness of po les and zeros i n every case in- d i c a t e s t h a t t h e p o l e s and zeros of t h e t r a n s f e r func t ion can be i d e n t i f i e d q u i t e accu ra t e ly and t h a t o f t e n lower o r d e r models may g ive as good o r b e t t e r r e s u l t s . I t , s h o u l d a l s o b e noted t h a t t h e mode which i s poor ly damped is iden- t i f i e d more a c c u r a t e l y than t h e mode which has h igher damping. APPLICATION TO LARGE AEROELASTIC STRUCTURES A major a p p l i c a t i o n of t h e inpu t des ign and instrument s e l e c t i o n procedures i s t h e e s t ima t ion of t h e f l u t t e r c h a r a c t e r i s t i c s of l a r g e t h r e e dimensional s t r u c t u r e s . In genera l , t h e dynamic f l u t t e r behavior of such s t r u c t u r e s is descr ibed by p a r t i a l d i f f e r e n t i a l equat ions i n space and t i m e . t i o n of dynamic s t a b i l i t y and s t r u c t u r a l loads , however, a modal a n a l y s i s o r a f i n i t e element a n a l y s i s is s u f f i c i e n t l y a c c u r a t e and conve r t s t h e more complex p a r t i a l d i f f e r e n t i a l equat ions i n t o ord inary d i f f e r e n t i a l equat ions. The d i f - f e r e n t i a l equa t ions desc r ib ing t h e f l u t t e r c h a r a c t e r i s t i c s of l a r g e s t r u c t u r e s can be w r i t t e n as follows: For t h e evalua- I& + C k + K x = Du 158 (35) where M i s the general ized mass matrix, C is t h e damping matrix, K i s the spr ing constant matrix, and D i s the inpu t o r fo rce d i s t r i b u t i o n matrix. In t h e vec tor x, each t e r m corresponds t o a l i n e a r o r angular displacement of one of the modes. may be unknown parameters i n M, C , K, and D. An accelerometer measures acceler- The vec to r u is a vec to r of de t e rmin i s t i c o r random inputs . There a t i o n a t one po in t , which, i n general , i s a linear ponents of 2, i .e., where H represents t h e parameters which determine a combination of s e v e r a l com- ( 3 6 ) the loca t ions of the accel- erometers. The s t r a i n gages measure displacements, so t h a t t h e i r ou tputs are l i n e a r combinations of x, as follows: y s = H x S (37) Again, Hs determines t h e loca t ions of var ious s t r a i n gages. t he inpu t s are determined by c e r t a i n parameters i n the matr ix D. The t r a n s f e r func t ion between y The loca t ions of and u is a and t h e t r a n s f e r funct ion between y and u i s S This mul t ivar iab le problem can be solved i n much the s a m e way as described and demonstrated above. r o t o r vehic le f o r tunnel test. It i s c u r r e n t l y being appl ied t o a 19-mode model of tilt CONCLUSIONS This paper descr ibes how techniques of system i d e n t i f i c a t i o n can be appl ied t o t h e problem of determining accura te estimates of c e r t a i n c r i t i c a l parameters i n a e r o e l a s t i c s t ruc tu res . It w a s shown t h a t information t h e o r e t i c approaches can be used f o r the s e l e c t i o n of i n p u t spectra and instruments. I n p a r t i c u l a r , var ious func t iona ls of t h e inverse of t h e information matrix provide usefu l measures of t he accuracy of the parameter estimates. The parameter es t imat ion accuracy depends upon both the input spectra and the po in t s where the inpu t s are appl ied. The func t iona ls of t h e inverse of t h e information matr ix can be minimized under p r a c t i c a l con- 159 s t r a i n t s of t o t a l cost?, t h e c o s t versus t h e accuracy of var ious ava i l ab le in- struments and c e r t a i n loca t ion cons t r a in t s , t h e set of instruments which must be used, and t h e pos i t ions a t which they should be loca ted can be op t I n some cases, t h e instruments are already i n s t a l l e d , b u t t h e maximum number of channels i s f ixed because of telemetry, recording, computer capacity, and many o the r reasons. A tradeoff can be made between various instruments and the p o s s i b i l i t y of having two o r more instruments share one channel. I n the app l i ca t ion of system i d e n t i f i c a t i o n methodology t o a e r o e l a s t i c s t r u c t u r e s , t h e importance of an e f f i c i e n t parameter i d e n t i f i c a t i o n program cannot be overestimated. approach t h a t u t i l i z e s an eigenvalue ana lys i s of t he information mat r ix provides not only e f f i c i e n t parameter estimates but a l s o important d iagnos t ics regarding t h e i d e n t i f i a b i l i t y of various model parameters and t h e relevance of various models. An a e r o e l a s t i c ana lys i s of a two dimensional wing, f o r example, showed t h a t a lower order t r a n s f e r func t ion may be adequate t o represent t he input / output re la t ionships . A good method based on the maximum l ike l ihood Maximum u t i l i z a t i o n of these techniques w i l l , of course, be r e a l i z e d i n l a r g e aerodynamic s t r u c t u r e s where i d e n t i f i a b i l i t y could be a ser ious problem. Further work i n t h e development of these techniques is under way. 160 APPENDIX A ALGORITHM FOR CHOOSING OPTIMAL INPUT SPECTRUM The following procedure may be used t o determine the optimal input spec- trum: (a ) Choose a nondegenerate inpu t f (w) ( i . e e 9 cons i s t ing of more than 0 m - f requencies , with a f i n i t e power i n each frequency), 2P (b) Compute t h e funct ion J,(w,f) where aT* -1 $(w,f) = R e [ T r R-' M-l(f) 1 t o minimize I M ( f ) l 80 = Re[Tr R-I WM-2 ( f ) g] t o minimize Tr(M-'(f)W> Find i t s maximum a t w under the cons t r a in t of equation ( 1 3 ) . 0 (c) Evaluate t h e information matrix M(w ) a t w I 0 0 (d) Update t h e design f = (1-a ) f o f aof(wo) 0 < a o < l 1 0 a is chosen t o minimize /M-l(f) I o r Tr(M-'(f)W) where 0 It can be shown t h a t such an a e x i s t s , 0 (e ) Repeat s t e p s (b) through (d) u n t i l des i red accuracy is obtained, I n the procedure described above, t h e funct ion J, has many l o c a l m a x i m a , It is computationally t i m e consuming t o f i n d w where $(w,f) i s maximum. I n t h e computer implementation of t h e algorithm, w e consider f i n i t e number of val- ues w and search through a l l values of $ (us ) t o f ind the maximum. Most s t a b l e systems of i n t e r e s t are low pass f i l t e r s . Thus, i n most cases i t is poss ib le t o f i n d a subset of [ o , ~ ] , where t h e search need be ca r r i ed out. 0 i 1 There are seve ra l ways t o see i f the input design is c lose t o optimal. These methods use t h e following criteria: (a) The information mat r ix does not change s u b s t a n t i a l l y from one s t e p t o t h e next , o r t h e optimizing func t ion does not improve s i g n i f i c a n t l y with i t e r a t i o n s , (b) The value of a . which optimizes the value of t he des i red func t ion approaches zero. I n o the r words, l i t t l e power i s placed a t newly chosen frequencies. 1 (c) The m a x i m u m value of t h e function I) i s not much higher than the i maximum value f o r t h e optimum design ( i . e . , m i f we maximize ] M I and T r (M-l(f*)W) i f we minimize Tr(M-lW). In our implementation, (a) and (b) are used as the termination cri teria and (c) i s used as a check. 162 APPENDIX E: SYMBOLS ( A l l Uni t s A r e Metr ic) a Elas t ic a x i s p o s i t i o n from l ead ing edge 1 a Gain c o e f f i c i e n t of l i f t response t o s t e p change i n a n g l e of a t t a c k 2 =1-a 2 a a ( i=1 ,2* . . ) C o e f f i c i e n t s of t r a n s f e r f u n c t i o n denominator A S t a t e weighting ma t r ix i A1,. . .A4 Coef f i c i en t matrices def ined by equat ion (2) T i m e cons tan t of l i f t response t o s t e p change i n ang le of a t t a c k bl b2 =blc/2V b . ( i -1 ,2 ...) C o e f f i c i e n t s of t r a n s f e r f u n c t i o n numerator C Wing chord 1 C Cost func t ion of a l l ins t ruments ; genera l ized damping Cost c o e f f i c i e n t of a s i n g l e instrument 'i d D e r iva t i v e D Contro l d i s t r i b u t i o n matrix to measurements; c o n t r o l ma t r ix (equat ion ( 3 5 ) ) e P o s i t i o n of c .g . , re la t ive t o e l a s t i c a x i s Dis tance of f o r c e a p p l i c a t i o n from e l a s t i c axis ( p o s i t i v e forward) ef e Dis tance of accelerometer from elastic a x i s ( p o s i t i v e forward) E Energy c o n s t r a i n t 0 f ((4 Nondegenerate inpu t func t ion f o (w) f p ) . . * F System dynamics mat r ix ; t o t a l s e c t i o n l i f t , i npu t f o r c e F =F / 2nqS S t a r t i n g guess of f(w) f o r des ign algori thm In termedia te v a l u e s of f . (w) 1 - 163 G Control d i s t r i b u t i o n mat r ix H Measur emen t d is tr i b u t ion matrix Accelerometer measur emen t s t a t e d i s t r i b u t i o n matrix S t r a i n gage measurement s ta te d i s t r i b u t i o n mat r ix Ha j =a S H J Cost func t iona l k Reduced frequency, k=~c /2V k V e r t i c a l s p r i n g rste k k Mass rad ius of gyra t ion K Generalized s p r i n g ra te Y Tors iona l s p r i n g ra te @ m Quar t e r chord l i f t Three q u a r t e r chord l i f t L1 L2 m Mass; number of parameters i n 8 1 m M V i r t u a l m a s s Information m a t r i x ; genera l ized mass Elements of information ma t r ix Mi j ( i j = l 9 2 * - .> Nondimensional d i s t a n c e = 2Vt/c; number of measurement 2 Dynamic p res su re = 1 / 2 W ; number of f r equenc ie s r Nondimensional elastic axis p o s i t i o n , r=e/c r Nondimensional l oca t ion of accelerometer , r =eo/c 0 0 'f Nondimensional input f o r c e l o c a t i o n , r =e /c f f =a/c -114 = 3 / 4 -a/c 1 r r2 r ( i = 1 9 2 a . . ) Diagonal elements of measurement no i se power s p e c t r a l dens i ty mat r ix i j 164 Measurement n o i s e power s p e c t r a l d e n s i t y mat r ix R e a l p a r t Laplace operator,T-t'(d/dp) Wing area = cb S t a t e t r a n s f e r func t ion S p e c i f i c a t i o n parameter S p e c i f i c a t i o n parameter T i m e T i m e i n t e r v a l (equat ion independent p a r t of S (W , e ) dependent p a r t of S(w,e) Output t r a n s f e r func t ion S p e c i f i c a t i o n parameter independent p a r t of T(w,B) S p e c i f i c a t i o n parameter dependent p a r t of T(w,f3) L i f t c o e f f i c i e n t , L1/ZnqS; c o n t r o l v a r i a b l e Measurement n o i s e Veloc i ty Nondimensional ver t ical displacement , y / c 91 C Information ma t r ix weighting mat r ix S t a t e Measurement v e c t o r (p x l), v e r t i c a l d e f l e c t i o n Accelerometer measurement nef l e c t i o n a t accelerometer l o c a t i o n Power a t frequency w * Cutoff power I n t e r p o l a t i o n c o e f f i c i e n t f o r update of t h e input des ign Input l o c a t o r parameter i 165 Y e i e A e u 'i P w w 0 w Y w Y w@ Wi* Sca l a r ad jus tment f a c t o r Parameter set Parameter of t h e set Parameter estimate =l+Tr (AS (a e ) S* (w ,e) ) Lagrange m u l t i p l i e r Mass parameter Lagrange m u l t i p l i e r A i r dens i ty Angular displacement Sec t ion p i t c h ra te , 4 Standard d e v i a t i o n of 0 Optimizat ion func t ion A i C i rcu la r frequency Undamped frequency; s t a r t i n g frequency f o r design a lgor i thm Tors iona l n a t u r a l frequency ,= Vertical n a t u r a l frequency = =+e/ 2v =w c/2v ' Frequencies w i t h i n Aw Power weighted average of f requencies w * i 166 REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9. Baird, E. F.; and Clark, W. B , : Recent Developments i n F l i g h t F l u t t e r T e s t - i n g i n t h e United S ta t e s . Volume 4, Chapter 10. AGARD Rept. 596, 1972. Supplement t o t h e Manual on A e r o e l a s t i c i t y , Rosenbaum, Robert: Survey of A i r c r a f t S u b c r i t i c a l F l i g h t F l u t t e r Tes t ing Methods. NASA CR-132479, Aug. 1974. Waisanen, P. R.; and Perangelo, H. J.: R e a l T i m e F l i g h t F l u t t e r Tes t ing V i a Z-Transform Analysis Techniques. AIAA Paper 72-784, Aug. 1972. Cole, Henry A . , Jr.: On-Line F a i l u r e Detec t ion and Damping Measurement of Aerospace S t r u c t u r e s by Random Decrement Signatures . NASA CR-2205, Mar. 1973. Houbolt, John C. : S u b c r i t i c a l F l u t t e r Tes t ing and System I d e n t i f i c a t i o n . NASA CR-132480, Aug. 1974. Gupta, Narendra K.; and H a l l , W. E a r l , Jr.: Input Design f o r I d e n t i f i c a - t i o n of A i r c r a f t S t a b i l i t y and Control Der iva t ives . NASA CR-2493, Feb. 19 75 .I Mehra, Raman K.: Optimal Input S igna ls f o r Parameter Est imat ion i n Dynamic Systems - Survey and New Resul t s . IEEE Trans. on Automatic Control , vo l . AC-19, Dec. 1974, pp. 753-768. Mehra, Raman K. ; and Gupta, Narendra K. : S t a t u s of Input Design f o r A i r - c r a f t Parameter I d e n t i f i c a t i o n . Methods f o r A i r c r a f t S t a t e and Parameter I d e n t i f i c a t i o n . AGARD-CP-172, Nov. 1974. Gerlach, 0. H.: The Determination of S t a b i l i t y Derivatives and Performance C h a r a c t e r i s t i c s From Dynamic Manoeuvres. Presented a t 38th Meeting of AGARD F l i g h t Mechanics Panel , Toulouse, France, May 1971. 167 SPECIFY THE SET OF TEST POINTS WHERE FLUTTER CHARACTERISTICS ARE TO BE DETERMINED INSTRUMENTS STRUCTURAL 0 COST 'I I TEST PLANNING AND EVALUATION 0 INSTRUMENTS AND THEIR LOCATIONS o INPUT TIME HISTORIES AND THEIR LOCATIONS (IF VARIABLE) 0 DURATION OF TEST, SAMPLING RATE, ROUNDOFF, ETC . CONDUCT THE TEST AND ADVANCED PARAMETER ESTIMATION PROGRAM Figure 1. Various steps in aeroelastic testing. 168 L1 F Figure 2. Model of a two dimensional wing i n f l u t t e r . 169 -4 .2 .4 > V 3 CY W & LL > z 4 I- Q & W a -I 4 I- O t- E .2 g .4 .2 . 4 . 2 STARTING VALUES 5 10 ITERATION 3 5 10 ITERATION 6 10 FINAL RESULT FREQUENCY (HERTZ) Figure 3 . parameters . Optimal i npu t design f o r t h e i d e n t i f i c a t i o n of f l u t t e r 170 5 FREQUENCY (HERTZ) 10 Figure 4. flutter parameters. Simplified optimal input spectrum for identification of 171 U w 0 a, U cd )-I U h )-I 0 U 172 P c i=l J I I I I I 0 .2 .4 .6 .8 1 .o t i Location o f Accelerometer Aft of Leading Edge (Fraction of Total Chord) F igu re 6. of accelerometer p o s i t i o n . Parameter e s t ima t ion e r r o r as a f u n c t i o n 173 .. Q N 0 % - E 0 3 0 0 0 0 0 0 0 0 0 0 0 ? ? Y C ? ? J " 9 7 ? 1 4 ? a, U V td a, 5 %I 0 u a td 174 I 0 0 0 0 0 0 0 0 0 0 0 0 0 ~ W ~ W N - ~ - N ~ U W 0 0 0 0 0 0 0 0 0 0 0 0 I I I I I . . . . . . . . . . . ind ino Y X ~ U O I I ( ~ ~ J J U 0 u r i m a l TI a s o E a, E C *d 0 175 e a C a NIV3 176 0 2 0 (S338930 1 3SYHd 177 SIMULATION FUNCTION 1 DENT IF I ED SYSTEM IDENTIFIED FUNCTION IDENTIFIED X 5TH ORDER TRANSFER + PARAMETERS OF 5TH ORDER A 4TH ORDER TRANSFER + X A e a I I I - * * T - 30 -20 - 10 ci (RAD SEC-’) 60 50 -3 0 -2 0 -10 Figure 1 2 . Poles of t h e s imula t ion t r a n s f e r func t ion and i d e n t i f i e d t r a n s f e r func t ion . 178 X 5 T H ORDER TRANSFER + PARAMETERS OF 5TH FUNCTION I D E N T I F I E D ORDER SYSTEM I D E N T I F I E D I V r A I u I I s x + -50.7 - 30 - 20 - 10 (I (RAD S E C - l ) 60 j w (RAD S E C - l ) c Figure 13. function and identified transfer function. Zeros of simulation transfer 179 SOME EXPERIENCE USING SUBCRITICAL RESPONSE METHODS I N WIND-TUNNEL FLUTTER MODEL STUDIES Jerome T , Foughner, Jr. NASA Langley Research Center SUMNARY Experiences obtained with four methods t o p red ic t f l u t t e r of wind-tunnel models from s u b c r i t i c a l response d a t a are descr ibed. The four methods are: co/quad, randomdec, power s p e c t r a l dens i ty , and t h e peak-hold spectrum. Model e x c i t a t i o n techniques included both forced (s inusoida l sweep) and random ( tunnel turbulence). These methods w e r e successfu l ly used t o measure t h e frequency and damping (or an inve r se response amplitude proport ional t o t h e damping) i n the predominant f l u t t e r modes. Implementation and app l i ca t ion of each method are discussed. presented. Some r e s u l t s and comparisons between methods are INTRODUCTION Transonic f l u t t e r model t e s t i n g has become an i n t e g r a l p a r t of t he develop- m e n t of high-speed a i r c r a f t such as the Grumman F-14, Rockwell B-1, Boeing 747, and Lockheed C-5A. Wind-tunnel s t u d i e s t o e s t a b l i s h t ransonic f l u t t e r clear- ances and t o provide d a t a f o r c o r r e l a t i o n wi th ana lys i s and with f l i g h t tests are made using dynamically scaled a e r o e l a s t i c models. l a t i o n between f l i g h t and wind-tunnel model tests i n the Langley t ransonic dynamics tunnel (TDT) are given i n re ference 1. These models s imulate t h e com- p l e t e a i r c r a f t under near f ree- f ly ing condi t ions and are q u i t e sophis t ica ted and expensive. Since f l u t t e r can be an explosive-type9 d e s t r u c t i v e i n s t a b i l i t y , t h e r e is a s u b s t a n t i a l r i s k of damaging the model when f l u t t e r is encountered. Consequently, t h e r e i s a need t o develop methods t o p red ic t t h e f l u t t e r condi- t i o n without having t o a c t u a l l y experience f l u t t e r . similar t o those i n f l i g h t f l u t t e r t e s t i n g , namely, t o i d e n t i f y the v i b r a t i o n modes cr i t ical t o f l u t t e r and t o measure and t r a c k the frequency and damping i n these modes as t h e test condi t ions are var ied , and the f l u t t e r boundary is approached. Some examples of corre- I The requirements are The state of the a r t of s u b c r i t i c a l f l i g h t f l u t t e r t e s t i n g w a s surveyed i n la te 1972 ( r e f . 2). A t t he time of t h i s survey, United S t a t e s indus t ry r e l i e d almost exclusively on s inusoida l e x c i t a t i o n provided by a u x i l i a r y aerodynamic vanes, i n e r t i a shakers , o r t h e power con t ro l system. Random e x c i t a t i o n techni- ques had not been used f o r f l i g h t f l u t t e r t e s t i n g . For a number of years t h e s t a f f of the TDT has used var ious s u b c r i t i c a l response methods i n wind-tunnel f l u t t e r model s t u d i e s . I n some cases ex te rna l e x c i t a t i o n of t h e model has been used, s i m i l a r t o f u l l - s c a l e f l i g h t f l u t t e r t e s t i n g . However, t he methods of e x c i t a t i o n of models are usua l ly more r e s t r i c t e d , For ins tance , the model 181 c o n t r o l system is normally provided f o r t r i m and is no t capable of high- frequency i n p u t s , Space and weight are a l s o usua l too l imi t ed t o a l low i n t e r n a l shaker equipment Consequently, m f t h e model s u b c r i t i c a l damping work a t Langley has been a s soc ia t ed w i t h methods t h a t u s e n a t u r a l wind-tunnel tu rbulence as t h e e x c i t a t i o n f o r c e . The purpose of t h i s paper is t o d e s c r i b e some experiences i n t h e appl ica- t i o n of fou r s u b c r i t i c a l response methods t o p r e d i c t model f l u t t e r c h a r a c t e r i s - t i cs i n t h e Langley TDT. The fou r methods examined are co/quad, which r e q u i r e s s i n u s o i d a l forced e x c i t a t i o n , randomdec and power s p e c t r a l d e n s i t y (PSD), which r e q u i r e only random e x c i t a t i o n , and t h e peak-hold spectrum method, which is appl ied t o bo th a forced and random e x c i t a t i o n system. The implementation of each method is descr ibed , and r e s u l t s from t h e a p p l i c a t i o n of a l l fou r methods t o a c a n t i l e v e r , delta-wing model i n t h e TDT are presented. Since t h i s model w a s designed and b u i l t f o r active f l u t t e r suppress ion s t u d i e s and w a s equipped wi th f a s t a c t i n g o s c i l l a t i n g c o n t r o l s , i t provided a unique oppor tuni ty f o r determining s u b c r i t i c a l response d a t a where s inuso ida l forced e x c i t a t i o n is requi red f o r comparison wi th damping d a t a obtained us ing random e x c i t a t i o n produced by turbulence. a complete, cable-mounted B-52 model are discussed. Also, co/quad and randomdec r e s u l t s ob ta ined by us ing FOUR PREDICTION METHODS The f o u r methods used t o measure t h e s u b c r i t i c a l (below t h e a c t u a l f l u t t e r speed) response c h a r a c t e r i s t i c s are r e f e r r e d t o h e r e i n as co/quad, randomdec, PSD, and peak-hold spectrum methods. These methods w e r e used t o measure t h e frequency and damping ( o r a n inve r se response ampli tude p ropor t iona l t o t h e damping i n t h e peak-hold spectrum case) i n t h e predominant o r c r i t i c a l v i b r a t i o n modes. v i b r a t i o n mode o r modes of i n t e r e s t , t h e f l u t t e r p o i n t can usua l ly b e estab- l i s h e d . With each method, i t w a s assumed t h a t t h e response can b e approximated by t h a t of a single-degree-of-freedom system. a n accelerometer on t h e model under e i t h e r a forced e x c i t a t i o n o r t h e random e x c i t a t i o n from t h e tunne l turbulence. A l l of t h e s e methods can b e used on-l ine, t h a t is, used t o t r a n s l a t e t h e response time h i s t o r y samples i n t o q u a n t i t a t i v e information f o r t h e test engineer whi le t h e test is i n progress . By s u i t a b l y p l o t t i n g and e x t r a p o l a t i n g the s u b c r i t i c a l damping i n t h e The response d a t a cons i s t ed of B r i e f l y , t h e co/quad method measures t h e in-phase and out-of-phase compo- nen t s of t h e forced response generated by t h e s i n u s o i d a l frequency sweep tech- nique. The randomdec method, a r e l a t i v e l y new method descr ibed i n r e f e r e n c e 3 , makes u s e of ensemble averaging of t r a n s i e n t response t o random e x c i t a t i o n . The PSD method is a well-known procedure f o r t h e a n a l y s i s of random response da t a . It i s obta ined d i r e c t l y from an ensemble average of t h e squa re of t h e magnitude of t h e Four ie r t ransform of a number of segments of t h e t ime h i s t o r y - I n t h e peak-hold spectrum method, Four ie r components of a number of t ime h i s t o r y segments are determined and t h e envelope of t h e peak v a l u e s of t h e s e components i s obtained as a func t ion of frequency. 182 DESCRIPTION AND IMPLEMENTATION Co/quad Method The co/quad method involved measuring t h e forced response of a model t o an input force such as t h a t generated by a trail ing-edge con t ro l sur face as i l l u s - t r a t ed schematically i n f i g u r e 1. I f a t r a n s f e r func t ion r e l a t i n g t h e response t o the input f o r c e is determined as a function of frequency, then the damping i n each mode can be obtained. For the model appl ica t ions presented herein, the e x c i t a t i o n fo rce w a s provided by o s c i l l a t i n g an aerodynamic con t ro l sur face , and t h e model dynamic response h w a s measured with an accelerometer. Since the measured ac tua tor phase l a g and amplitude v a r i a t i o n over t h e frequency range of i n t e r e s t w a s s m a l l and t h e aerodynamic phase l a g s of t h e con t ro l su r f ace w e r e assumed t o be s m a l l , t he con t ro l sur face ac tua to r command s igna l 6, w a s used as a measure of t h e exc i t a t ion force. Cross spectrum between t h e con t ro l sur- f a c e command s i g n a l and the model dynamic response w a s determined with a S p e c t r a l Dynamics SD109B co/quad analyzer. This analyzer presents two outputs i n t e r m s of in-phase (called co f o r coincident) and out-of-phase (ca l led quad f o r quadrature) components between s igna ls . Several means of ca l cu la t ing the damping are a v a i l a b l e d i r e c t l y from a co and quad type of presentation. A s indicated i n f i g u r e 1, the damping of a mode w a s estimated from the out-of-phase component by t h e frequencies labe led fA and fB. These are the frequencies a t the half-power poin ts and t h e s t r u c t u r a l damping g can be expressed i n t e r m s of these frequencies ( f i g . 1 ) . Randomdec Method To obtain a randomdec s igna ture , one simply c o l l e c t s a number of segments of t h e random response s igna l , each segment having the same i n i t i a l amplitude, and ensemble averages them. I f t h e sys t em is l i n e a r and t h e exc i t a t ion random, t h e ensemble average converges t o t h e t r ans i en t response of t h e system due t o t h e se lec ted set of i n i t i a l conditions. The implementation of randomdec as used i n t h i s paper is shown schemati- The response t i m e h i s t o r y shown i n f i g u r e 2 contains many c a l l y i n f i g u r e 2. modes and is normally recorded on analog tape. For t h e on-line randomdec process, a band-pass analog f i l t e r w a s used f o r mode i s o l a t i o n and no i se reduc- t ion . The s t a r t i n g poin t of each ensemble member w a s s e l ec t ed with t h e gating c i r c u i t (a standard laboratory oscil loscope t r igger ing c i r c u i t w a s used). A Technical Measurement Corporation 400C computer of average t r a n s i e n t s w a s used f o r ensemble averaging. A s t h e s igna ture develops, i t i s monitored on an oscil loscope. An e l ec t ron ic counter records the number of segments averaged and a X-Y p l o t t e r provides a hard copy of t h e f i n a l s igna ture . S t r u c t u r a l damping r a t i o may be determined d i r e c t l y as indicated on f i g u r e 2. With the implementation as described ( f ig . 2 ) , t h e d i f f e r e n t time segments w e r e averaged sequent ia l ly . That is , the computer processed a l l t h e r e s u l t s f o r one t i m e segment before beginning to c o l l e c t and average d a t a f o r t h e next segment. Also, i n t h e implementation as described, t h e averaging process f o r each time segment w a s obtained by taking only segments which c ross t h e se lec ted 183 t r i g g e r leve l wi th a pos i t i ve slope. Thus, t h e randomdec s igna ture represents t h e system t r a n s i e n t response due to an i n i t i a l amplitude and ve loc i ty , PSD and Peak-Hold Spectrum Methods The PSD and t h e peak-hold spectrum methods w e r e implemented as shown i n f i g u r e 3. Both methods w e r e implemented using a Spec t ra l Dynamics SD330A Spectrascope. This analyzer employs time compression techniques t o achieve minimum ana lys i s t i m e for t h e frequency-tuned band-pass f i l t e r t o convert t he input s igna l from t h e t i m e domain t o t h e frequency domain. s ion , the input s i g n a l is frequency analyzed using 250 synthesized f i l t e r loca- t i o n s t h a t are tuned by a b u i l t - i n sweep generator. With operator-selected modes of operation, t h i s analyzer i s highly f l e x i b l e . When t h e averaging mode of operagion is se l ec t ed , t h e average spectrum c h a r a c t e r i s t i c s of t h e random s i g n a l h a reobta ined . The averager examines successive ensembles of spectrum funct ions and computes the averaged sum over a predetermined length of time. Shown on the l e f t of f i g u r e ' 3 is a typ ica l PSD obtained from the model dynamic response h. The r e s u l t i n g s igna tu re has a peak f o r each s t r u c t u r a l mode and, f o r well-separated peaks, t h e damping r a t i o may be obtained. f i g u r e 3, t h e s t r u c t u r a l damping is equal t o t h e frequency bandwidth, taken a t t h e half-power poin t , and divided by t h e mode frequency. Following compres- A s ind ica ted i n An add i t iona l mode of opera t ion of t h e Spectrascope allows f o r de t ec t ion and s torage of t h e peak va lues f o r each of 250 frequency windows. I n t h i s mode of operation, an ensemble spectrum composed of 250 frequency windows i s obtained. Upon r ece ip t of each subsequent spectrum, peak f i l t e r response a t each loca t ion is updated i n a p o s i t i v e d i r ec t ion . That is, only an increase i n va lue causes an update to t h e new higher value. hold spectrum is shown. However, the r ec ip roca l of t h e peak spectrum amplitude 1/P is proportional t o t h e damping r a t i o and is used as a measure of system s t a b i l i t y . method w a s applied using two forms of exc i t a t ion , model response t o tunnel turbulence and model response t o s inusoida l force . On t h e r i g h t of f i g u r e 3 , a t y p i c a l peak- With t h i s method t h e damping parameter is not obtained. The peak-hold APPLICATIONS TO WIND-TUNNEL MODEL TESTING The four s u b c r i t i c a l response methods w e r e applied t o f l u t t e r test da ta of a delta-wing research model. methods were made using a B-52 f l u t t e r suppression model. comparisons are presented i n f i g u r e s 4 t o 7. Further app l i ca t ion of t h e co/quad and randomdec Some r e s u l t s and Delta-Wing F l u t t e r Model A photograph of t h e delta-wing model is shown i n f i g u r e 4. edge con t ro l su r f ace w a s used t o provide t h e forced exc i t a t ion . desc r ip t ion of t h i s wing is given i n re ference 4. model involves primarily the second na tu ra l v i b r a t i o n mode coupled with some primary bending. The t r a i l i n g - A de t a i l ed The f l u t t e r motion of t h i s 184 The s u b c r i t i c a l f l u t t e r c h a r a c t e r i s t i c s of t h i s model i n the TDT a t a Mach Two sets of t h e model da ta are shown. number of 0,90 is presented i n f i g u r e 5. Figure 5(a) presents t h e v a r i a t i o n of s t r u c t u r a l damp f l u t t e r mode wi th dynamic pressure. co/quad, randomdec, and PSD methods are indica ted with t h e open symbols. The model f l u t t e r e d a t a dynamic pressure of 5.89 kPa (123 l b f / f t 2 ) as indica ted with the closed symbol. The s o l i d l i n e i n t h e f i g u r e i s f a i r e d through the randomdec da ta which, of t he t h r e e methods shown, a p p e a r s t o g ive t h e most cons is ten t fo recas t of the f l u t t e r point. The damping r e s u l t s obtained with t h e A s a word of caution, i t should be noted t h a t frequency sweep methods, when used c lose t o a f l u t t e r condition, may lead t o dangerously l a r g e amplitude response as t h e forc ing frequency sweeps through the f l u t t e r mode frequency. A p l o t of t h e inverse amplitude of t h e peak spectrum (used as the s t a b i l i t y c r i t e r i a ) is presented i n f i g u r e 5(b) as a func t ion of dynamic pressure. Shown are r e s u l t s from forced e x c i t a t i o n (same e x c i t a t i o n system as used i n co/quad method) and r e s u l t s from random exc i t a t ion (model response t o tunnel turbulence). The b e s t r e s u l t s w e r e obtained with the forced e x c i t a t i o n ( f a i r ed da t a ) while t h e response-only d a t a showed some s c a t t e r . Although experience is l imi ted i n t h e use of t h i s method, i t is included s ince i t appears promising as a f l u t t e r ind ica tor . Further i l l u s t r a t i o n of t h e type of d a t a generated with the use of t he four s u b c r i t i c a l methods is presented i n f i g u r e 6. Shown are the da ta p l o t s from which the damping levels presented i n f i g u r e 5 w e r e obtained. The wind-tunnel conditions w e r e t h e same f o r each method (Mach number M = 0.90; dynamic pres- s u r e q = 5.42 kPa (113 l b f / f t 2 ) ) . a 3.33-minute logarithmic sweep from 5 t o 25 Hz w a s used. A damping level of 0.037 a t a frequency of 10.8 H z is indicated. Approximately 40 seconds of d a t a w e r e taken f o r t h e randomdec method giving a damping level of 0.048 f o r a f re - quency of 10.6 Hz. Forty seconds of data w e r e used f o r t h e PSD and peak-hold spectrum methods (3.33 minutes f o r t he peak-hold forced exc i t a t ion procedure). A frequency of 10.7 Hz and a damping l e v e l of 0.037 is indicated f o r t h e PSD method. The f l u t t e r mode frequency f o r t h e peak-hold spectrum is 10.6 Hz. I n t h e implementation of t he co/quad method, B-52 Model Further experience with t h e co/quad forced response method and t h e random- dec method w e r e obtained using a 1/30-scale, dynamic model of a B-52. w a s equipped wi th fas t ac t ing con t ro l sur faces f o r f l u t t e r suppression s tud ie s which are described i n re ference 5. For t h i s model, shown on the r i g h t of f i g u r e 7 , the a i l e r o n s w e r e used t o generate t h e forcing function. Thus, f o r t h e co/quad method, t he damping w a s estimated by determining the r a t i o of the outboard-accelerometer response t o t h e a i l e r o n command f o r a frequency range of 4 t o 24 Hz. The s u b c r i t i c a l f l u t t e r c h a r a c t e r i s t i c s of t h i s model i n t h e TDT are presented i n f i g u r e 7. The damping r e s u l t s obtained with the co/quad and the randomdec methods are indicated with t h e open symbols. methods s a t i s f a c t o r i l y p red ic t t h e measured f l u t t e r po in t a t a dynamic pressure of 2.65 kPa (55.4 l b f / f t 2 ) as indicated by t h e closed symbol. The model Both of these 185 OBSERVATIONS Although a l l four methods assumed t h a t t h e response can be charac te r ized by a single-degree-of-freedom system, they successfu l ly provided a measure of t h e s u b c r i t i c a l damping l e v e l . c i a l l y ava i l ab le instrumentat ion. The randomdec and PSD methods which depend on random unknown exc i t a t ion , i .e . , turbulence and bu f fe t ing , comp forced sweep co/quad method. tages . b e s t when t h e r e i s l a r g e response t o turbulence o r b u f f e t e x c i t a t i o n - t h e reg ion where co/quad da ta are least r e l i a b l e . One l i m i t a t i o n of t h e random e x c i t a t i o n methods is when t h e f l u t t e r condi t ion involves high frequency modes t h a t may not be exc i ted by random e x c i t a t i o n such as turbulence and buf fe t ing . I n t h i s ins tance t h e forced sweep method should be used. Each method can be implemented with commer- Both types of e x c i t a t i o n inpu t s have t h e i r advan- What is "noise" f o r co/quad is "input" f o r randomdec. Randomdec works D i f f i c u l t i e s t h a t may b e encountered wi th t h e use of s u b c r i t i c a l response methods include unwanted no i se and c lose ly spaced resonant f requencies . Methods ( cu r ren t ly used i n f l i g h t f l u t t e r t e s t ing ) f o r e l imina t ing o r masking noise e f f e c t s have been evaluated and seve ra l new techniques suggested i n re ference 6. Several system i d e n t i f i c a t i o n schemes w e r e a l s o developed i n re ference 6 t o handle the s i t u a t i o n where two o r more f requencies of t h e system are c l o s e together . A s a r e s u l t of experience gained during t h i s e a r l y implementation of the randomdec method, fu r the r development of t h i s method w a s undertaken. A cur ren t implementation ( u t i l i z i n g thenew TDT da ta system) of t h e randomdec procedure is presented i n r e fe rence 7. The f e a s i b i l i t y of using t h e randomdec method i n conjunction wi th a s igna ture ana lys i s procedure t o determine the damping and frequency va lues of a two-mode a e r o e l a s t i c system w a s es tab l i shed i n re ference 8. The s igna ture a n a l y s i s procedure w a s based on a least-squares curve f i t t i n g of t h e randomdec s igna ture . f l i g h t f l u t t e r tests and f o r t h i s app l i ca t ion provided a s a t i s f a c t o r y a l t e r n a t e t o more c o s t l y conventional s u b c r i t i c a l methods ( r e f . 9 ) . The randomdec method w a s appl ied during t h e YF-16 The reader is cautioned t h a t f o r a case where a few knots i nc rease i n speed s p e l l s the d i f f e r e n c e between a well-damped response and v i o l e n t f l u t t e r , sub- cr i t ical damping techniques may not be app l i cab le t o p r e d i c t the f l u t t e r condi- t i on . However, i n t h i s case, s u b c r i t i c a l techniques w i l l s t i l l be of va lue i n c o r r e l a t i o n wi th s u b c r i t i c a l a n a l y t i c a l d a t a and f o r u s e i n parameter i d e n t i f i - c a t i o n techniques t p def ine the system mathematical model. CONCLUDING REMARKS Four s u b c r i t i c a l response methods w e r e appl ied t o f l u t t e r test d a t a f o r t he same model, a can t i l eve r d e l t a wing. Exc i t a t ion methods included forced exci ta- t i o n (co/quad and peak-hold spectrum) and random e x c i t a t i o n (randomdec, PSD, and peak-hold spectrum). methods w a s obtained with f l u t t e r test d a t a of a complete cable-mounted B-52 Fur ther experience with the co/quad and t h e randomdec 186 f l u t t e r model, With both f l u t t e r models, t h e s u b c r i t i c a l methods t e s t e d i n t h e paper s a t i s f a c t o r i l y pred ic ted t h e measured f l u t t e r p o i n t s e REFERENCES 1. R e e d , Wilmer H . , 111: C o r r e l a t i o n With F l i g h t of Some Aeroe la s t i c Model S tudies i n t h e NASA Langley Transonic Dynamics Tunnel. NASA Symposium of F l u t t e r Tes t ing Techniques, O c t . 1975. (Paper No. 1 0 of t h i s compilat ion.) 2. Rosenbaum, Robert: Survey of A i r c r a f t S u b c r i t i c a l F l i g h t F l u t t e r Tes t ing Methods. NASA CR-132479, 1974. 3 . Cole, Henry A., Jr.: On-Line F a i l u r e Detec t ion and Damping Measurement of Aerospace S t r u c t u r e s by Random Decrement S igna tures . NASA CR-2205, 1973. 4 . Sandford, Maynard C . ; Abel, I rv ing ; and Gray, David L.: Transonic Study of Act ive F l u t t e r Suppression Based on a n Energy Concept. J. Aircr., vo l . 12, no. 2, Feb. 1975, pp. 72-77. 5. Redd, L. T . ; Gilman, J., Jr.; Cooley, D. E.; and Sevart, F. D.: Wind- Tunnel I n v e s t i g a t i o n of a B-52 Model F l u t t e r Suppression System. J. Aircr., v o l . 11, no. 11, Nov. 1974, pp. 659-663. 6. Houbolt, John C.: S u b c r i t i c a l F l u t t e r Tes t ing and System I d e n t i f i c a t i o n . NASA CR-132480, 1974. 7. Hammond, Char les E.; and Doggett , Robert V . , Jr.: Determinat ion of Sub- c r i t i ca l Damping by Moving-Block/Randomdec Appl ica t ions . of F l u t t e r Tes t ing Techniques, O c t . 1975. (Paper No. 3 of t h i s compilat ion e ) NASA Symposium 8. Chang, C. S.: Study of Dynamic C h a r a c t e r i s t i c s of A e r o e l a s t i c Systems U t i l i z i n g Randomdec Signatures . NASA CR-132563, 1975. 9. Brignac, W. J.; Ness, H. B. ; and Smith, L. M.: The Random Decrement Tech- nique Applied t o t h e YF-16 F l i g h t F l u t t e r T e s t s . AIAA Paper No. 75-776, May 1975. 187 FREQUENCY, Hz Figure 1.- Implementation of co/quad method. RESPONSE TIME HISTORY ~ l i lG,, ,w-J CONDITIONER c TIME- t TMC MODEL 400 C AVERAGER r----- 1 PLOTTER COUNTER Figure 2.- Implementation of randomdec method. 188 MODEL RESPONSE 0 PEAK HOLD SPECTRUM 0 PS D PSD fO FREQUENCY FREQUENCY Figure 3. - Implementation of spectrum methods. Figure 4 . - Delta-wing model. 189 METHOD 0 CO-QUAD -0- RANDOMDEC FLUTTER .04 0 EXCITATION *FORCED b RANDOM -+ li-i**; 4.0 4.4 4.8 5.2 5.6 6.0 FLUTTER :~~ (a) Co/quad, randomdec, PSD results. DYNAMIC PRESSURE, kPa (b) Peak-hold spectrum results. Figure 5.- Comparison of subcritical methods, delta-wing model (M = 0.90). r IN-PHASE h - bC " h I I I I 10 15 20 25 FREQUENCY. Hz g = 0.037 h"2 Hz 0 4 8 12 16 20 24 FREQUENCY, Hz (a) Co/quad. (c) PSD. PEAK AMPLITUDE f = 10.6 Hz 0 4 8 12 16 20 24 FREQUENCY, Hz 0.5 1.0 0 TIME, seconds (b) Randmdec. (d) Peak-hold spectrum. Figure 6.- Illustration of subcritical methods. M = 0.90; q = 5.42 kPa (113 lbf/ft2). 190 OUTBOARD AILERON ER .02 - 0 1.6 2.0 2.4 2.8 DYNAMIC PRESSURE, kPa Figure 7.- S u b c r i t i c a l response of B-52 model. 191 WIND TUNMEL I N ~ S T I ~ A T I O N OF SUPERSONIC WING-TAIL FZUTTER Lawrence J, Hut t se l l , Thomas E, No11 and Donald E, Holsapple Air Force F l igh t Dynamics Laboratory SUMMARY An experimental and a n a l y t i c a l study w a s undertaken t o e s t a b l i s h the f l u t t e r trends of a highly swept wing-tail configuration i n the low supersonic speed regime. Wind tunnel f l u t t e r d a t a w a s a l s o required f o r eva lua t ing a new supersonic aerodynamic method f o r p red ic t ing wing-tail i n t e r f e rence . A f l u t t e r model, cons is t ing of a wing, ho r i zon ta l t a i l , and s p l i t t e r p la te / fuse lage mechanism, w a s t e s t e d i n the Arnold Engineering Development Center (AEDC) Pro- pulsion Wind Tunnel F a c i l i t y (PWT) &Foot Transonic Tunnel in the Mach number range'1.1 t o 1.3. Two types of f l u t t e r w e r e encountered dur ing the t e s t i n g ; a wing-tail f l u t t e r mode and a t a i l bending-torsion f l u t t e r mode. The wing-tail f l u t t e r speed w a s found t o be a minimum at M = 1 . 2 fo r the configuration tes ted . (PSD) ana lys i s and Random Decrement (Randomdec) ana lys i s e Comparisons between the frequency and damping obtained from the PSD p l o t s and t h e Randomdec signa- t u re s agreed very w e l l . A l imi ted f l u t t e r ana lys i s w a s conducted using a Mach box unsteady aerodynamics method which accounted f o r i n t e r f e rence and a i r f o i l thickness. Analy t ica l comparisons wi th experimental f l u t t e r speeds agreed very w e l l . The analyses assuming zero thickness predicted f l u t t e r speeds higher than those measured, ranging from 1 percent a t M = 1,12 t o 8 percent a t M = 1.28. With the a i r f o i l thickness included the co r re l a t ion w a s improved such tha t predicted f l u t t e r speeds fo r a l l cases inves t iga ted were wi th in 2 percent of experimental speeds. F l u t t e r frequencies w e r e no t as w e l l predicted generally being somewhat higher than measured. Recorded model test d a t a w e r e d i g i t i z e d f o r a power s p e c t r a l dens i ty SYMBOLS b wing semichord measured streamwise and i n t e r s e c t i n g the e las t ic axis line a t 75-percent wing span f f requen cy g s t r u c t u r a l damping c o e f f i c i e n t m wing mass p e r u n i t span M freestream Mach number t o t a l p ressure pT 193 TI f Pees tream ve loc i ty at f l u t t e r P air dens i ty 1-I m model t o air m a s s r a t i o , - Tpb2 w f l u t t e r frequency % w8 uncoupled fuselage to r s ion frequency wing f i r s t coupled cantilever bending frequency INTRODUCTION Today's advanced m i l i t a r y aircraft must be capable of undertaking multi- mission ro l e s . Variable sweep wings are used on some a i r c r a f t configurations f o r improving performance at d i f f e r e n t f l i g h t conditions. Low wing sweep angles are attractive during takeoff, landing, and long range c ru i se when higher aspect r a t i o is required; high wing sweep angles, which reduce drag, are des i r ab le f o r high speed f l i g h t . I n i t i a l l y i t w a s thought t h a t f l u t t e r speeds would increase a t the high sweep angles thus complementing t h e use of t h e va r i ab le sweep wing. i n 1966, Topp, Rowe, and Shattuck (Reference 1) conducted a t h e o r e t i c a l and experimental program which determined t h a t t he re are cases where t h i s does no t occur. Model tests indica ted t h a t for l o w sweep angles , t h e cr i t ical f l u t t e r mode involved t h e high frequency bending-torsion motion of t he wing. expected, t h e f l u t t e r speed increased as t h e wing w a s i n i t i a l l y swept back. Near 58 degrees wing sweep, however, a new f l u t t e r mode involving the lower frequency modes of the wing, fuselage, and t a i l became evident. With fu r the r increases i n wing Sweep, t h e f l u t t e r speed dropped r ap id ly , and at 70 degrees, the f l u t t e r speed was lower than fo r the most forward swept case. The cause f o r the lower f l u t t e r speed and its rapid drop with increas ing wing sweep w a s no t f u l l y understood at t h i s time. Since t h i s w a s a new unforeseen phenomenon, not p red ic t ab le using ava i l ab le aerodynamic theor ies f u r t h e r t h e o r e t i c a l and experimental s t u d i e s were conducted i n t h e following years. However, As One of t h e f i r s t experimental programs i n t h e area following t h e e f f o r t by Topp, e t a l e , w a s sponsored by the A i r Force Flight Dynamics Laboratory (AFFDL). In 1966, Balcerak (Reference 2 ) designed, constructed, and t e s t ed a series of constant chord 45 degree and 60 degree swept wing-horizontal t a i l f l u t t e r models, Wing and t a i l su r faces were i d e n t i c a l i n planform. Testing w a s accom- plished at Mach numbers ranging from 0.4 t o 1.24 and defined the e f f e c t s of important wing-tail parameters on f l u t t e r . I n some cases t h e f l u t t e r speed continued t o decrease i n t o the low supersonic speed regime. In 1968, t h e AFFDL continued t h e i r i nves t iga t ion by conducting subsonic wind tunnel tests and analyses on a semispan model of a representa t ive va r i ab le sweep wing a i r c r a f t configuration (Reference 3) e Similar trends of f l u t t e r 194 speed versus sweep angle were found. i nves t iga t ion with a de ta i l ed t h e o r e t i c a l study. Both a doub le t - l a t t i ce method (Reference 4 ) and a kerna l function method ( t o p red ic t the aerodynamic i n t e r a c t i o n between t h e wing and ta i l , Both methods predicted the f l u t t e r frequencies extremely w e l l , F l u t t e r v a t i v e l y predicted ranging up t o 20 percent lower than t h e v e l o c i t i e s , increas ing subsonic Mach number. The AFFDL pa ra l l e l ed the experimental ences 5 and 6) w e Also, t h e theory predic ted the f l u t t e r speed t o decrease w i Since the t ransonic tests of Reference 2 showed decreased as t h e Mach number increased, at least up t ment of a method t o p red ic t unsteady aerodynamic loads fo r i n t e r f e r i n g su r faces w a s required f o r t h e supersonic speed regime. box method (References 7 and 8) w a s developed f o r supersonic i n t e r f e r i n g surfaces. This paper descr ibes supersonic f l u t t e r tests of a half-span f l u t t e r model which w a s dynamically sca led from the model used i n t h e earlier subsonic e f f o r t (Reference 3 ) , and t h e l imi t ed analyses which were conducted f o r veri- fy ing the Mach box aerodynamic method. Under AFFDL sponsorship, a Mach SUPERSONIC WING-TAIL FLUTTER MODEL The A i r Force F l igh t Dynamics Laboratory defined the general design of a half-span f l u t t e r model cons is t ing of a wing, hor izonta l ta i l , and s p l i t t e r p la te / fuse lage mechanism. performed by Atkins and Merrill Inc., Ashland, Massachusetts. The d e t a i l design and construction of the model was The supersonic model w a s designed t o f l u t t e r within t h e Arnold Engineering Development Center (AEDC) PWT &Foot Transonic Wind Tunnel by dynamically s c a l i n g the 60 degree sweep subsonic model of Reference 3, with the exception of t h e ho r i zon ta l t a i l , The design fundamental frequency f o r t h e supersonic t a i l model w a s twice t h a t of t h e wing. Higher t a i l freque'ncies were no t obtained because t h e high s t i f f n e s s c h a r a c t e r i s t i c s of t h e subsonic t a i l could n o t p r a c t i c a l l y be sca led due t o the very low m a s s requirements fo r t h e super- sonic model. Figure 1 provides a photograph of t h e model showing t h e wing and t a i l sur- faces, t h e s p l i t t e r p l a t e / fuse l age mechanism, and the tunnel mounting system. The fuselage mechanism the f a i r i n g between the s p l i t t e r p l a t e and tunnel ce i l ing . mounted from the tunnel c e i l i n g i n such a manner as t o simulate antisymmetric v ib ra t ion modes. which w a s supported by bear ings , thereby providing a r o l l degree of freedom. A r o l l s t i f f n e s s w a s provided by a s m a l l s p r i n g mounted between t h e s h a f t assembly and t h e s p l i t t e r p l a t e . Variation in t h e fuselage to r s iona l s t i f f n e s s w a s obtained by changing the e f f e c t i v e l eng th of a constant cross-sectional bar which connected t h e f o r e and a f t s h a f t assemblies. The wing and t a i l could e i t h e r r o l l toge ther or d i f f e r e n t i a l l y s ince the sha f t assemblies f o r t h e wing and t a i l sur faces w e r e interconnected only through the to r s ion bar. in t h e tors ion b a r length could be accomplished without a f f e c t i n g t h e separa t ion and t h e wing and t a i l attachments were enclosed within The model w a s This w a s achieved by a t t ach ing the models t o a sha f t assembly Variations 195 between t h e wing and t a i l , allow a v a r i a t i o n i n h o r i Two t a i l attachment po in t s were a lso provided t o The wing and t a i l models were t i o n technique. This composite con epoxy sk ins which were high-temperature cured under pressure with a honeycomb core, wing and t a i l t o ob ta in t h e required bending stiffness. t o t h e forward fuselage r o l l b a r by me with scaled to r s ion and bending s t i f f n fuselage r o l l assembly by means of a carry-through s t r u c t u r e with h igh s t i f f - ness. S t r i p s of graphi te were added along t h e span of t h e The wing w a s attached carry-through s t r u c t u r e as attached t o t h e a f t Natural mode shapes and frequencies w e r e computed us ing classical lumped m a s s methods. the f l u t t e r ana lys i s . d ic ted node lines and frequencies was good. The f i r s t mode (not shown i n t h e f igu re ) involves r o l l motion about the model r o l l axis wi th a measured f re - quency of 17.8 Hz; t he second mode involves primarily wing carry-through tors ion coupled wi th wing bending; t he t h i r d mode involves t a i l bending and wing bending; t he four th mode involves pr imar i ly wing second bending and carry- through tors ion; and the f i f t h mode i s pr imar i ly t a i l to rs ion . Figure 2 shows typ ica l r e s u l t s f o r four e l a s t i c modes used in I n general , agreement between t h e wing aeasured and pre- WIND TUNNEL TESTS The tests w e r e conducted i n t h e AEDC PWT &Foot Transonic Wind Tunnel. A schematic of t h e d a t a monitoring and recording system used during t h e f l u t t e r tests is shown i n Figure 3. During t e s t i n g , s t r a i n gage bridges w e r e used t o monitor and record t h e response of the model. j u s t outboard of t h e wing and t a i l roots t o measure t h e bending and t o r s i o n strains. and bending, t h e fuselage to r s ion , and t h e model r o l l motions. The e ight strain gage channels and a t i m e code were displayed on a Varian s t r i p recorder copied on tape together with a voice t rack . monitor the coupling of t he c r i t i ca l wing-tail modes; one of t h e osc i l loscopes displayed fuse lage tors ion (FT) and wing carry-through to r s ion (CT) responses ; the second osc i l loscope displayed wing carry-through bending (CB) and wing carry-through t o r s i o n (CT) responses. An on-line Time/Data analyzer w a s used t o d isp lay the frequency response (0-100 Hz) f o r e i t h e r t h e wing carry-through tors ion , t he wing carry-through bending, o r t h e fuselage to r s ion motion. The approximate frequency range of h igh model response w a s determined from such a display. width t racking f i l t e r t o de f ine the cri t ical frequency. S t r a in gage bridges were mounted Others were mounted on spr ings t o measure wing carry-through tors ion and Two X-Y oscil loscopes w e r e used t o Modes of i n t e r e s t w e r e s e l ec t ed and processed through a 5 Hz band- The test Mach number w a s approached from a low t o t a l p ressure (low dynamic pressure). number u n t i l f l u t t e r occurred. A t s e l ec t ed test conditions, t he response d a t a w a s recorded and the frequencies measured using the t r ack ing f i l t e r . Figure 4 presents the AEDC 4T wind tunnel standard operating envelope of t o t a l p ressure The t o t a l p ressure w a s increased at an e s s e n t i a l l y constant Mach 196 and dynamic pressure versus Mach number, and shows the f l u t t e r points obtained f o r each configuration tested. The f i r s t test configuration, wing bending t o fuselage tors ion frequency r a t i o (%/We) of 0.62, was t e s t e d at M = 1.2 up t o a t o t a l p ress t h e r e w a s s i g n i f i c a n t wing and t a i l motion, i nd ica t ing t h e proximity t o f l u t t e r . The s t r u c t u r a l damping coe f f i c i en t (g) w a s estimated t o be approximately 0.01. Tunnel l i m i t a t i o n s prevented f u r t h e r t e s t i n g of t h i s configuration. The fuse- l a g e t o r s i o n a l s t i f f n e s s w a s then adjusted t o g ive %/We = 0.32, and t h e model w a s again tes ted . The f l u t t e r frequency varied from 85 Hz at M = 1.12 t o 88 Hz at M = 1.28. Figure 5 presents a s t r i p c h a r t recording f o r t h e M = 1.28 test configuration. Both wing and t a i l responses are shown t o be diverging, i nd ica t ing t h a t t he test condition w a s s l i g h t l y i n t o an unstable region. in ca t a s t rop ic damage t o both su r faces as shown in Figure 6 . of 1 2 g e 3 W a (2700 psf) m NQ f l u t t e r was enco Wing-tail f l u t t e r was obtained a t M = 1.12, 1.2, and 1.28. The f l u t t e r mode resu l ted A t a i l bending-torsion f l u t t e r mode w a s encountered a t M = 1.08 while The frequency of t he t a i l f l u t t e r mode w a s 176 Hz which is reducing Mach number a t a constant t o t a l p ressure from the M = 1.12 wing-tail f l u t t e r point. s l i g h t l y above t h e t a i l tors ion mode shown in Figure 2. response record f o r t h e wing and t a i l strain gages are shown i n Figure 7 f o r t h i s mode of f l u t t e r . rapidly. motions f o r t h i s predominantly t a i l bending-torsion coupling. The t a i l sur face w a s r ap id ly destroyed following f l u t t e r onset. The time h i s t o r y The t a i l bending and tors ion gages diverged very The motion on the wing i s very s m a l l i n comparison t o the t a i l DATA REDUCTION Following the wind tunnel tests, se l ec t ed f l u t t e r model response d a t a were played back from analog tapes and d i g i t i z e d us ing an I T 1 4900-Preston A/D sys- tem. l i m i t the d i g i t i z e d response d a t a t o a frequency range of 0-200 Hz. Spec t r a l Density (PSD) and Random Decrement (Randomdec) analyses methods were used t o reduce t h e test data. Low pass analog f i l t e r s (48 dB per octave ro l l -o f f ) w e r e used t o band Both Power PSD Method Narrow band (0.46 Hz bandwidth) PSD analyses were performed using a Raytheon 704 Fas t Fourier Analyzer system. were averaged t o provide a spectrum which w a s p lo t t ed on t h e Raytheon/Gould 4800 p l o t t e r . random response d a t a f o r the model with Wh/We = 0.32 and M = 1.2 at two subcri- t i ca l test conditions ( t o t a l p ressures of 95.8 kPa (2000 ps f ) and 105.3 kPa (2200 ps f ) ) . increased with t o t a l pressure as f l u t t e r was approached. of 105.3 kPa (2200 p s f ) , the response i n a 176 Hz mode became more ev ident . The frequency and damping were estimated from the PSD p l o t s using standard tech- niques, and the r e s u l t s are presented i n Table I f o r the cr i t ical wing-tail mode a t the two test conditions discussed above and at two add i t iona l po in ts . Thirteen transforms with sample s i z e of 2048 Figures 8 and 9 present t he r e s u l t s of t h e PSD ana lys i s of the The response i n t h e 84-86 Hz mode (the cr i t ical wing-tail mode) A t a t o t a l pressure 197 Randomdec Method The Randomdec method, invented by He A. was applied in t h i s study t o analyze t h e resp t i o n fo r determining the frequency and damping of the modes of i n t e r e s t . Randomdec program used ensemble averaging of up t o 300 d i g i t a l samples of response d a t a (,07 seconds i n length). t i c response s igna ture , and t h e frequency and damping ra t io from t h e random response d a t a (0-200 Hz). A t y p i c a l Randodec s igna t shown i n Figure 10 f o r M = 1.2 and PT = 2000 psf. p l o t shown i n Figure 8. t u r a l damping can be e a s i l y determined. The The program ext rac ted the charac te r i s - f o r Wh/wg = 0.32 is This corresponds t o the PSD The Randomdec s igna tu re is very c lean , and t h e s t ruc- Comparison of Results Using PSD and Randomdec Methods The s t r u c t u r a l damping coe f f i c i en t and frequency f o r t h e cr i t ical wing- t a i l mode which w e r e obtained us ing PSD and Randodec methods are presented in Table I. comparisons between the two methods are within 0.012. 110.1 kPa (2300 p s f ) , f l u t t e r onset has been s l i g h t l y exceeded as shown by a s m a l l negative damping whereas the PSD method is no t capable of providing nega- tive damping. All frequency comparisons are wi th in 2 percent. S t r u c t u r a l damping A t a t o t a l p ressure of ANALYSIS AND CORRELATION Limited f l u t t e r analyses w e r e conducted using the supersonic Mach box program described i n References 7 and 8. l i f t i n g sur f aces in close proximity i n supersonic flow including aerodynamic in te r fe rence . The analyses were conducted f o r the f l i g h t conditions at which wing-tail f l u t t e r occurred f o r "h/oe = 0.32. both with and without a i r f o i l thickness included. The Mach box method includes an option f o r thickness cor rec t ions t o the pressure d i s t r i b u t i o n based on second order p i s ton theory. This method w a s developed t o analyze These analyses were conducted Table I1 presents comparisons of ca l cu la t ed f l u t t e r speeds and frequencies Without with corresponding measured values at Mach numbers 1.12, 1 .2 and 1.28. a i r f o i l thickness included, t he analyses predicted f l u t t e r speeds ranging from approximately 1 percent at M = 1.12 t o 8 percent higher than the measured speeds a t M = 1.28. With the a i r f o i l thickness included i n the analyses, f l u t t e r speed predic t ions were improved. A t M = 1.2, t h e ca lcu la ted f l u t t e r speed w a s wi th in 1.5 percent of the measured f l u t t e r speed, a 5 percent improve- ment over t h e analyses without a i r f o i l thickness. A t M = 1.28, t he analyses with a i r f o i l thickness included w a s within 1 percent of t h e measured f l u t t e r speed, an improvement of approximately 7 percent. F l u t t e r frequencies were not as w e l l predicted. higher than the measured values. The ca lcu la ted f l u t t e r frequencies were 8 t o 18 percent Both measured and ca lcu la ted f l u t t e r d a t a are presented i n Figures 11 and 12 i n the form of f l u t t e r parameters V/bwe fi and w/we versus Mach number. 198 The subsonic d a t a from Reference 3 are a l so shown for comparison, 11, the predicted subsonic t rend of V/bwe shown f o r uh/we = 0.62, The t rend f o r %/We = 0-32 is shown dashed, s ince analyses w e r e no t conducted f o r the configuration but w e r e estimated based on o the r similar t rends , These subsonic analyses ind ica t e t h a t V/bwe con- t i nues t o drop a t least up t o t ransonic speeds. f o r %/we = 0,32 i n d i c a t e t h a t a minimum f l u t t e r speed w a s obtained at M = 1.2. This was s i g n i f i c a n t l y lower than t h e M = 0 subsonic test r e s u l t s . A fu r the r increase i n Mach number t o M = 1.28 provided some a l l e v i a t i o n ; however, t he f l u t t e r parameter s t i l l remains below the M = 0 test r e s u l t s . The supersonic analyses with o r without a i r f o i l thickness included, show increas ing f l u t t e r speeds with inc reas ing Mach number. I n Figure is decreasing with Mach number as The supersonic test r e s u l t s Figure 12 presents &/we versus Mach number. T e s t r e s u l t s i nd ica t e an increas ing value of W / W ~ as the Mach number increases, while t h e analyses p red ic t a minimum f l u t t e r frequency r a t i o a t approximately M = 1.2 followed by an increase at the higher Mach number t e s t e d (M = 1.28). CONCLUDING REMARKS I n conclusion, t he r e s u l t s of t h i s wind tunnel i nves t iga t ion of a wing- t a i l f l u t t e r phenomena i n the Mach number range 1 .12 t01 .28 show less s t a b i l i t y (lower f l u t t e r speed parameter) than earlier corresponding subsonic da ta . However, the r e s u l t s i nd ica t e some increase i n f l u t t e r s t a b i l i t y a t M = 1.28 as compared with M = 1.2 data. A l s o , the Mach box ana lys i s procedure with aero- dynamic in t e r f e rence and a i r f o i l thickness e f f e c t s included w a s found t o adequately p red ic t the wing-tail f l u t t e r speeds of t h i s phenomena. 199 REFERENCES 1. Topp, L.J . , Rowe, W,S., and Shattuck, A.W.: Aeroe las t ic Considerations i n the Design of Variable Sweep Airplanes. na t iona l Congress of t h e Aeronautical Sciences, London, England, September 1966 e ICAS Paper 66-12, F i f t h In t e r - 2. Balcerak, J. C. : F l u t t e r T e s t s of Variable Sweep Configurations. AFFDL-TR- 68-101, September 1968. 3. Mykytow, W . J . , Noll , T.E., H u t t s e l l , L.J., and Shi rk , M.H.: Subsonic F l u t t e r Charac t e r i s t i c s of a Variable Sweep Wing and Horizontal T a i l Combination. AFFDL-TR-69-59, November 1970. 4 . Albano, E. and Rodden, W.P.: A Doublet Lattice Method f o r Calcu la t ing L i f t Dis t r ibu t ions on O s c i l l a t i n g Surfaces i n Subsonic Flows. Vol. 7 , No. 2 , February 1969, pages 279-285. A I M Journal, 5. Laschka, B. and Schmid, H.: Unsteady Aerodynamic Forces on Coplanar L i f t - i n g Surfaces i n Subsonic Flow (ing-Horizontal T a i l In te r fe rence) . Presented at AGARD S t ruc tu res and Materials P a n e l Meeting, O t t a w a , Canada, September 1967. 6. Albano, E. Perkinson, F., and Rodden, W.P. : Subsonic L i f t i n g Surface Theory Aerodynamics and F l u t t e r Analysis of I n t e r f e r i n g WinglHorizontal Ta i l Configurations. AFJ?DL-TR-70-59, September 1970. 7. I T , J .M. Borland, C . J . , and Hogley, J.R. : Predic t ion of Unsteady Aero- dynamic Loadings of Non-Planar Wings and Wing-Tail Configurations i n Supersonic Flow, P a r t I, "Theoretical Development, Program Usage, and Application". AFFDL-TR-71-108 , March 1972. 8. Kramer, G.D. and Keylon, G.E. : Predic t ion of Unsteady Aerodynamic Loadings of Non-Planar Wings and Wing-Tail Configurations i n Supersonic Flow, P a r t 11, I1 Computer Program Description". AFFDL-TR-71-108, March 1972. 9. Cole, H.A., Jr. : Method and Apparatus f o r Measuring Damping Characteris- t ics of a St ruc ture . United S t a t e s Pa ten t No. 3 , 620, 069, 16 November 1971. 10. Cole, H.A., Jr. : On-Line Fa i lu re Detection and Damping Measurement of Aerospace S t ruc tu res by Random Decrement Signatures. March 1973. NASA CR-2205, 200 Table I, - Damping Comparison f o r the Critical Wing-Tail Mode a t M = 1.2, %/We = Oe32. 9 PSD f (Hz) 84,O 0 8 100 86,O 0,070 86,5 0,020 86, l - Table 11. - A i r f o i l Thickness E f f e c t s on F l u t t e r Trends, %/we = 0.32. 201 Figure 1. - Supersonic Wing-Tail F l u t t e r Model. ----- ( f ) CALCULATED MODES (FREQUENCY IN Hz) MEASURED MODES (FREQUENCY I N Hz) f ROLL A X I S Figure 2. - Calculated and Measured Vibrat ion Node Lines and Frequencies, w ~ / w ~ = 0.32. 202 STAA I PI GAGE OUTPUTS NOMENCLATURE WR - WING BENDING WT - WIPJG TORSION TB - T A I L BENDING TT - T A I L TORSION FT - FUSELAGE TORSION RB - ROLL SPRING CB - WING CARRY-THROUGH BENDING CT - W I PIG CARRY-THROUGH TORS ION Figure 3. - Wind,Tunnel T e s t Data Monitoring and Recording System. 203 3600 3200 2800 N + \ u- 2400 5 5 2000 I W c/) v) W e n $ 1600 I- CJ + 1200 SO0 400 0 I 2 8 4 ,6 18 l l 0 L13 l , 4 MACH NUMBER AEDC P STANDARD OPERATING ENVELOPE Figure 4. Wind Tunnel Operating Envelope with Experimental F l u t t e r Data. (1 l b / f t 2 = 47.88 Pa. 204 Figure 5 . - Model Response a t M = 1.28 and PT = 118.5 kPa (2475 l b / f t 2 ) , %/we 0.32. Figure 6 . - Model Damage from Wing-Tail F lut ter at M = 1.28 , w /w = 0.32. h 0 205 Figure 7. - Model /we 206 FREQUENCY' - HZ Figure 8, - PSD P l o t f o r M =. 1.2 and PT = 95.8 kPa (2000 l b / f t 2 ) , W h / W e = 0.32. 207 Figure 9. - PSD P l o t f o r M = 1.2 and PT = 105.3 kPa (2200 l b / f t 2 ) , %/We 0.32. 208 Figure 10. - Randomdec Signature for M = 1.2 and P = 95.8 kPa (2000 l b / f t 2 ) , %/me = 0.32. T 209 SULID SYMEOLS - ANALYSIS OPEN SYMROLS - TEST BOLS - ANALYSIS WITH THICKNESS NEAR FLUTTER ONSET - 112 L O V 0,8 0,6 NOTE: SUBSONIC DATA FROM FEFFPENGF 3 0 0,4 0,8 182 i , 6 MACH NUVBER Figure 11. - V/bwg f i Versus Mach Number. 210 I S WITH TtiICI< NEAR FLLITTEI? ONSET 0 - 00 0 0 8 4 !1ACH NUMBER Figure 1 2 . - O/W Versus Mach Number. 9 211 THE DESIGN, ANALYSIS, AND TESTING OF A LOW-BUDGET WIND-T FLUTTER MODEL W I T H ACTIVE AERODYNAMIC CONTROLS* R. Bolding For t Worth Division, General Dynamics Corporation R. Stearman The University of Texas a t Austin SUMMARY Active c o n t r o l technology is playing a more s i g n i f i c a n t r o l e i n aerospace and aircraft veh ic l e design and gives rise t o t h e need t o introduce t h e bas i c technology i n t o t h e educational activit ies wi th in the profession. The present paper descr ibes a low-budget f l u t t e r model incorporating active aerodynamic con t ro l s f o r f l u t t e r suppression s tudies , designed as both an educational and a research too l . The study concentrates on t h e i n t e r f e r i n g l i f t i n g su r face f l u t t e r phenomenon i n the form of a swept wing-tail configuration. A f l u t t e r suppression mechanism w a s f i r s t demonstrated on a s i m p l e semirigid three-degree- of-freedom f l u t t e r model of t h i s configuration employing an a c t i v e s t a b i l a t o r cont ro l . This w a s then v e r i f i e d a n a l y t i c a l l y using a doublet l a t t i ce l i f t i n g sur face code and t h e model's measured mass, mode shapes, and frequencies i n a f l u t t e r ana lys i s . extend t h e ana lys i s t o the l a r g e r degree of freedom AFFDL wing-tail f l u t t e r model where add i t iona l a n a l y t i c a l f l u t t e r suppression s t u d i e s indicated s ign i f - i c a n t gains i n f l u t t e r margins could be achieved. mental design of a f l u t t e r suppression system f o r the AFFDL model i s presented along with the r e s u l t s of a preliminary pass ive f l u t t e r test. These preliminary s tud ie s w e r e s i g n i f i c a n t l y encouraging to The a n a l y t i c a l and experi- INTRODUCTION The increased importance t h a t active con t ro l technology plays i n a i r c r a f t and aerospace veh ic l e design necess i t a t e s t h e in t roduct ion of the b a s i c concept i n t o t h e educational a c t i v i t i e s within our profession. nology evolved wi th in the aerospace i n d u s t r i e s and the government l abora to r i e s , c e r t a i n problem areas appear s u i t a b l e f o r p u r s u i t i n an academic i n s t i t u t i o n having a combined educational and research objective. descr ibes one such attempt a t a low-budget program ca r r i ed out a t t h e graduate While t h e b a s i c tech- The present paper *This research w a s supported by the A i r Force Office of S c i e n t i f i c Research, Office of Aerospace Research, United States A i r Force. 213 level. This involved the design, construction, and wind-tunnel testing of an actively controlled wind-tunnel research flutter model. It focused on the development of a flutter suppression system for aerodynamically interfering lifting surfaces in the configuration of a closely spaced wing-tail geometry where the flutter mechanism is fairly well understood. In early experiments, Topp, Rowe, and Shattuck observed the phenomenon of wing-tail interference flutter for the variable-sweep configuration and indi- cated in reference 1 that it was the result of aerodynamic interaction and elastic coupling between the wing and tail. significantly reduce the flutter speed for the wing and tail below that for the isolated wing alone as illustrated in figure 1 taken from reference 1. systematic and extensive study of this phenomenon was carried out by Mykytow, Noll, Huttsell, and Shirk in reference 2 and the wing-tail interference flutter mechanism was fairly well clarified. A small, interesting semirigid flutter model demonstrating this flutter phenomenon was also developed within the industry, as illustrated in reference 3 . We later built and adapted this to the classroom demonstration model illustrated in figure 2. As the control con- figured vehicle and active control concepts further developed, a decision was made to extend the capabilities of this classroom model to demonstrate flutter suppression via active controls. This was undertaken with the hope that the objective could be accomplished, i.e., flutter suppressed over a significant velocity range, and that some insight could also be obtained as to the flutter suppression mechanism. The results of this study proved to be more encouraging than originally anticipated and further analytical studies were carried out on the AFFDL wing-tail flutter model of reference 2 which had several additional flexible degrees of freedom. Here again, parameter optimization techniques yielded control laws which demonstrated significant gains in flutter margin when an active stabilator or aileron control was employed. Flutter margins could be increased to that of the isolated wing. As a result of these analytical find- ings, it appeared desirable to evaluate the results in the wind tunnel and establish a level of confidence for the math modeling. The present study was undertaken with this objective in mind subject to the constraints of a low budget for model construction and wind-tunnel test time. This necessitated testing at a Mach zero condition in a subsonic wind-tunnel facility. tion, to cut costs, the existing AFFDL Wind-Tunnel Flutter Model design was selected where minor modifications to the design could be made to yield an active stabilator control. laws derived by parameter optimization techniques employing standard V-g, Vector Nyquist, and aerodynamic energy techniques. The experimental flutter data are to be correlated with analytical flutter calculations based upon lifting surface doublet lattice aerodynamics and experimentally determined mode shapes, generalized masses, and natural frequencies for the first five mode shapes of the system. The flutter suppression system analytical design studies are presented here along with a review of the model design and passive wind- tunnel flutter studies. For some sweep angles this can A In addi- The scope of the experiment was to evaluate control The cooperation of the Air Force Flight Dynamics Laboratory (AFFDL) in providing us with the basic model design details is appreciated. our visits with the Flight Controls staff of the Boeing Company, Wichita Division, were very helpful, Appreciation is also expressed to Emil Cwach, In addition, 214 General Dynamics, Forth Worth, and L t . Kenneth Gr i f f in , A i r Force F l i g h t Dynamics Laboratory, f o r t h e i r cont r ibu t ions t o t h e program. PRELIMINARY DESIGN STUDIES ON SEMIRIGID MODEL The a c t i v e l y cont ro l led f l u t t e r model, developed i n t h e following program, evolved from preliminary design s tud ie s of f l u t t e r suppression systems applied t o the small semirigid model i l l u s t r a t e d i n f i g u r e 2. A t w a s i n i t i a t e d i t appeared as though a f l u t t e r suppression re e a s i l y developed f o r t h i s type of model, t h a t is , it seemed p laus ib l e t h a t f l u t t e r suppression systems might s i g n i f i c a n t l y bene f i t t h e performance of variable-geometry a i r c r a f t w i th aerodynamic in t e r f e rence e f f e c t s while poss ib ly providing less impressive gains on more conventional a i r c r a f t . I n view of t h i s , exploratory wind-tunnel s t u d i e s w e r e i n i t i a t e d i n t h e University of Texas 3 f t by 4 f t low-speed wind tunnel with t h i s three-degree-of-freedom model. The degrees of freedom include a r i g i d body r o l l mode, one wing bending mode, and one fuselage to r s ion mode. con t ro l degree of freedom w a s incorporated as a s t a b i l a t o r p i t c h mode. f i n i t e degree of freedom o r semirigid f e a t u r e w a s achieved by concentrating elastic spr ings on t h e model a t t h e wing r o o t and a t one pos i t i on along t h e fuse lage as i l l u s t r a t e d by the component breakdown i n f i g u r e 2. For the a c t i v e l y cont ro l led model an add i t iona l This T r i a l and e r r o r low-speed wind-tunnel tests indica ted t h a t a 40% increase i n f l u t t e r margin could be e a s i l y achieved on t h i s model employing a simple feedback coupled t o a s t a b i l a t o r control. This w a s accomplished by tak ing t h e output from an accelerometer mounted on t h e s t a b i l a t o r o r fuselage and feeding it through a phase and gain network (or v a r i a b l e phase o s c i l l a t o r ) t o a s m a l l shaker with a fo rce output of 8.9 newtons (2 l b ) which ac t iva t ed t h e s t ab i - l a t o r cont ro l by means of a f l e x i b l e mechanical linkage. I n t e r p r e t a t i o n of high-speed movies of the study ind ica ted t h a t t h e more e f f e c t i v e phase and gain s e l e c t i o n s w e r e those which e s s e n t i a l l y ro t a t ed t h e s t a b i l a t o r con t ro l t o e l i m i - n a t e t h e induced downwash as i l l u s t r a t e d i n f i g u r e 3 . This f igu re represents a v i e w of a t y p i c a l sec t ion c u t t i n g through both wing and t a i l a t a given span- w i s e s t a t i o n . The typ ica l washout appearance of an upward bending swept wing is demonstrated he re inducing a downwash over the s t a b i l a t o r forc ing i t t o deform approximately 180" out-of-phase with the wing. The a c t u a l phasing w i l l depend upon the wing-tail separa t ion distance. A s ind ica ted , the most effec- t ive cont ro l command f o r suppressing t h i s i n t e r f e rence f l u t t e r w a s t h a t which pitched the s t a b i l a t o r approximately in-phase with the main wing, thus e l i m i - na t ing t h e induced downwash. To check t h e above hypothesis, an a n a l y t i c a l study of t h e model w a s c a r r i e d out employing the doublet lat t ice l i f t i n g sur face theory and t h e model's measured m a s s , mode shapes, and frequencies i n a V-g type f l u t t e r ana lys i s . The r e s u l t s of t h i s study are i l l u s t r a t e d i n f i g u r e s 4 and 5 f o r t h e con t ro l loop open (passive f l u t t e r s tud ie s ) . The experimentally measured f l u t t e r speed i s superimposed on the V-g da ta t o i l l u s t r a t e t he degree of co r re l a t ion between theory and experiment. t h e th ree generalized coordinates and t h e motion of a poin t on the wing and t a i l are i l l u s t r a t e d i n f i g u r e 5. A po lar p l o t of t h e open loop f l u t t e r mode i n terms of The a c t u a l phasing between the wing and t a i l 215 motion is seen to be a little less than the 180' that was suggested. polar plot of the closed loop c trated in figure 6 . This is ag modeling now including an active stabilator control and measured modes, frequencies, and model mass. The control deflection, that is, the stabilator pitch, is nearly in-phase with the wing motion which, according to figure 3 , eliminates the induced downwash. The wing displac lightly leads that of the control due to the wing-tail separation distanc gain in flutter in obtained from both the anal is illustrated gure 7. For the relatively hi found for the model structural modes, this represents over a 40% increase in flutter speed. increased by another 50% if the sensor or accelerometer had been placed in a more optimal position such as on the wing instead of the tail. A similar illustration of the Figure 8 illustrates that the flutter speed could be easily All these preliminary studies employed an assumed form of control law, originally introduced by Nissim in reference 4 , and utilized a parameter optimization procedure to select the control law coefficients which maximized the flutter speed. Details on this analysis can be found in reference 5 . One additional comment is in order concerning the aerodynamic modeling employed in this and the following studies. Both the semirigid and AFFDL model are half-span models; this considerably reduces the model cost and complexity of wind-tunnel installation and testing. These simplifying gains, however, result in the assumption that the model fuselage (in the semirigid case) and the wind-tunnel wall in the AFFDL configuration represents a reflecting plane through which no flow penetrates. In the lifting surface codes employed for the flutter analysis, this requires a symmetric mode input option into the study since the image system is performing a symmetric motion to satisfy the flow boundary condition. This should not lead to any serious problems since no attempt is made here to model a specific configuration where the actual wing-tail flutter mode is found to be antisymmetric. ANALYTICAL DESIGN STUDIES ON AN ACTIVELY CONTROLLED AFFDL WING-TAIL FLUTTER MODEL On the basis of the preliminary findings from the semirigid wing-tail model, further analysis seemed justified on a more complex flutter model of similar configuration. studied in the wind tunnel and its passive flutter characteristics well docu- mented in reference 2. It was therefore chosen as the best candidate for further investigation. principles and an approximate transient aerodynamic analysis was rejected as being too complex for the present study. analysis was carried out where the coefficients in an assumed form of control law were determined by parameter optimization procedures. employed the standard V-g method of flutter analysis as well as the aerodynamic energy and Vector Nyquist concepts. 4 , an assumed feedback control law was taken of the form The AFFDL wing-tail flutter model had been extensively A flutter suppression design based upon optimal control Instead a frequency domain design The design study Following the work of Nissim in reference 216 where ( 6 ) is a vector representing the displacements of the active aerodynamic control surfaces; {ql, the complex vector of generalized coordinates defining the motion of the main lifting surfaces; and [C + iC 3, a complex matrix relating the motion of the main lifting surfaces to that of the control surfaces. The [C] matrix is the assumed form of feedback control law and its elements may be a function of the frequency or reduced frequency of motion as well as other parameters defining the flight envelope. This assumed feedback control law also implies that all the system generalized coordinates must be observed. This is not practical or even necessary in most cases. Consequently the outputs from a discrete set of motion sensors are related to the generalized coordinates defining the system motion by R I { Z } = [Fl (4) (2) where I Z ) is a complex vector representing the sensor outputs and [F] is a matrix representing the displacement of the sensors for unit values of the generalized coordinates, The matrix [F] defines the sensor locations and ideally selects or isolates out only those generalized coordinates in the flut- ter analysis that are important to the flutter suppression system design. Since the number of sensors required in the flutter suppression system are in practice much less than the numberofgeneralized coordinates, the matrix [F] will be singular and the more practical control law expressible in the form I or i This may be incorporated into the standard flutter equation as where [K] and [MI are the generalized stiffness and mass, respectively, of the structure; [Q], the generalized aerodynamic force matrix excluding the contri- bution of the active controls; and [Q,], the sum of the generalized aerodynamic forces and inertias due to the active control input. eter g and flutter frequency w make up the flutter eigenvalue. In the analyti- cal design study, only M = 0, sea-level conditions were investigated since they represented the anticipated wind-tunnel conditions. Equation (5) was, therefore, solved initially by the standard V-g method employing a parameter optimization technique to determine the control coefficients that maximized the flutter speed for selected configurations of the AFFDL flutter model. The flutter damping param- This procedure employed only one active aerodynamic control in the form of a stabilator or aileron control. In addition, the study investigated control 217 feedback systems employing feedback from a l l t he generalized coordinates as w e l l as from those t h a t could be measured by emplo motion sensors, These sensors were placed i n 'an o planform t o sense t h e most s i g n i f i c a n t modes cont r ibu t ing t o the f l u t t e r ins ta - b i l i t y of t h e model.Details on t h i s ana lys i s can a l s o be found in re ference 5 . The accuracy of t he a n a l y t i c a l modeling on t h e AFFDL f l u t t e r model is i l l u s t r a t e d i n f i g u r e 9 where t h e experimentally determined f l u t t e r speed from reference 2 i s superimposed on t h i s f i gu re . s l i g h t l y from t h e computed AFFDL f l u t t e r r e s u l t s . This is ought t o be due t o t h e d i f f e r e n t input mode shape procedures followed i n t h e present study. This study u t i l i z e d b a s i c a l l y a n ex te rna l l oca l i zed least-squares f i t t o t h e modal da t a and input s lopes and de f l ec t ions d i r e c t l y a t t h e one-quarter-chord and three-quarter-chord po in t s of t he aerodynamic boxes. This e s s e n t i a l l y bypassed t h e global least-squares f i t rou t ine i n t h e standard program input format. A s l i g h t gain i n computational accuracy i s an t i c ipa t ed by t h i s procedure. This is f u r t h e r confirmed i n f i g u r e 10 f o r a s l i g h t l y d i f f e r e n t sweep configuration. The math model is thought t o accura te ly represent t h e f l u t t e r c h a r a c t e r i s t i c s of t h e AFFDL wind-tunnel f l u t t e r model described i n re ference 2. The present ana lys i s d i f f e r s By employing a N i s s i m form of con t ro l l a w and parameter optimization tech- niques, a f l u t t e r suppression system evolved employing an a c t i v e s t a b i l a t o r con t ro l t h a t increased t h e system f l u t t e r speed above t h a t of t he i s o l a t e d wing. This i s i l l u s t r a t e d i n f i g u r e s 11 and 12 . A s ind ica ted i n f igu re 11, t h i s could be accomplished by employing only two motion sensors, one on the wing t i p and a second on t h e t i p of t he s t a b i l a t o r . It i s f u r t h e r ind ica ted he re t h a t no s i g n i f i c a n t d i f f e rence would be obtained even i f a l l t h e generalized coordinates were measured. Figure 13 i l l u s t r a t e s t h a t fu r the r gains i n f l u t t e r margin could be achieved f o r this configuration i f an active a i l e r o n con t ro l w e r e employed i n place of a s t a b i l a t o r . 1 4 . when employing t h e same a i l e r o n f o r a c t i v e con t ro l of t h e i so l a t ed wing t o gain add i t iona l f l u t t e r margin. configuration. A l l these preliminary s t u d i e s w e r e f e l t t o be p o s i t i v e enough t o warrant t h e design of an experimental wind-tunnel f l u t t e r program t h a t would check the accuracy of the f l u t t e r suppression system design and lend a degree of confidence t o t h e math modeling. This a i l e r o n configuration is i l l u s t r a t e d i n f igu re F l u t t e r margins were again improved beyond t h a t of t h e i s o l a t e d wing even S i m i l a r f e a t u r e s were found f o r the 45" sweep FINALIZED WIND-TUNNEL MODEL DESIGN A s mentioned earlier, t h e bas ic model employed i n t h i s study is a varia- t i o n on the AFFDL wing-tail f l u t t e r model designed by t h e A i r Force F l igh t Dynamics Laboratory and discussed i n re ference 2. d e t a i l s w e r e modified by personnel a t The University of Texas a t Austin t o include an active s t a b i l a t o r cont ro l i n p i t c h and a remote cont ro l of the wing sweep angle. This model and i t s i n s t a l l a t i o n i n the 7 f t by 10 f t wind tunnel a t Wichita State University i s i l l u s t r a t e d i n f igu re 15. The model degrees of freedom include a r i g i d body r o l l mode, wing root bending and t o r s i o n a l f l e x i - b i l i t i e s , fuse lage t o r s i o n a l f l e x i b i l i t y , and f u l l y f l e x i b l e wing and s t a b i l a t o r modes. Some of t h e model design I n add i t ion , the s t a b i l a t o r could be remotely pitched by means of a 218 hydraulic ac tua to r t o provide a s t i f f cont ro l degree of freedom, a l s o be remotely swept with a hydraulic ac tua to r t o simulate various as w e l l as r ap id ly convert t he f l u t t e r model t o a s t a b l e configuration by quickly sweeping t h e wing forward, r a i s i n g t h e system's f l u t t e r speed. la t ter f ea tu re w a s added with t h e hope t h a t i n some cases i t could suppress undesirable model responses t h a t may occur during cri t ical f l u t t e r conditions. The wing could This A schematic of t he model's hydraulic con t ro l supply system, employed t o activate both wing sweep and s t a b i l a t o r motions, is i l l u s t r a t e d i n f i g u r e 16. This con t ro l system is comprised of t h ree major assemblies: t h e hydraulic power supply module, t h e servo con t ro l module, and t h e model hydraul ic ac tua to r system designated r e spec t ive ly as ( a ) , (b), and (c) i n t h e schematic. These components are a l s o i l l u s t r a t e d i n f igu re 1 7 . around an Everpac Model PA-101 air driven hydraulic pump obtained without charge from government surp lus . (0.467 in3/sec) a t 690 N/cm2 (1000 p s i ) which i s the normal working pressure of the system. v o i r within the pump, an add i t iona l reservoi r w a s i n s t a l l e d i n t h e hydraulic r e t u r n l i n e . sweep system and the s t a b f l a t o r sweep system, backup accumulators charged t o 345 N/cm2 (500 p s i ) with nitrogen. a t t enua te f luc tua t ions i n l i n e pressure caused by pulsa t ions of t he pump o r head pressure. The hydraulic power supply module is b u i l t The pump provides a flow of 7.647 cm3/sec Due t o t h e r e l a t i v e l y small capac i ty of t he self-contained reser- The hydraulic power supply module a l s o provides, t o both t h e wing These accumulators f u r t h e r serve t o The servo con t ro l modules are mounted a top and outs ide t h e wind tunnel next t o the model t o minimize l i n e l a g e f f e c t s t o the model con t ro l ac tua to r s . This module provides terminal po in t s f o r t h e servovalve e l ec t ron ic s and houses two surp lus Moog Model 971A servovalves r a t ed a t 18.03 cm3/sec (1.1 in3 / sec ) a t 8 mA. These servovalves are employed t o activate two Clippard Minimatic 7DD-1 double-acting ac tua to r s d r iv ing the wing sweep and s t a b i l a t o r motions. One end of t he ac tua to r rDds is attached t o a l i n e a r va r i ab le d i f f e r e n t i a l transformer (LVDT) which provides f o r prec ise cont ro l of t h e s t a b i l a t o r p i t c h and wing sweep angle while t h e o ther end d r ives t h e l inkage motion. t o t h e wing sweep servoamplifier include t h e wing sweep con t ro l s i g n a l , posi- t i o n feedback from t h e wing sweep LVDT, and a d i t h e r s i g n a l t o keep t h e valve f r e e of sediment and improve t r a n s i e n t response. Signals t o the s t a b i l a t o r p i t c h servoamplifier include t h e conditioned transducer s i g n a l s , pos i t i on feedback from t h e s t a b i l a t o r p i t c h LVDT, and t h e d i t h e r s igna l . S igna ls The cont ro l feedback av ionics , developed as a p a r t of t h e f l u t t e r suppres- s ion system, are i l l u s t r a t e d i n f i g u r e 18. An analog con t ro l w a s developed due t o the expense and complexity of d i g i t a l systems. The avionics f o r t h e s t a b i l a t o r p i t c h con t ro l include pr in ted c i r c u i t modules f o r input con t ro l and ampl i f ica t ion , i n t eg ra t ion , and phase s h i f t i n g . It allows f o r up t o t h r e e channels of output which can command up t o t h r e e separate aerodynamic surfaces. The u n i t can monitor s igna l s from accelerometers, ve loc i ty pickups, and/or s t r a i n gages mounted a t select pos i t i ons on t h e model and blend these according t o a preselected con t ro l l a w . i n t h i s manner permits t he programing of a v a r i e t y of con t ro l l a w s . The modular grouping of t h e d i f f e r e n t c i r c u i t s Chains of inexpensive high-input impedance opera t iona l ampl i f ie rs , which 219 constitute the basic elements of analog computers, were put together to perform the required control functions, into functio formance. Co was adopted replacement of defective circuits fits of modular construction were realized including ease in circuit modifica- tion and construction, as well as circuit substitution if desired. This system's approach to circuit design is di extends the capabilities of the design en the active control technology area. VIBRATION AND FLUTTER STUDIES In an attempt to obtain the most accurate math modeling for the study, experimental inputs were utilized in the analysis whenever practical. This included measurements of vibration modes, frequencies, and generalized masses for the first five modes of the system. the first five modal frequencies measured on the present model at a 60" sweep configuration with one of the models described in reference 2. Attempts were also made to measure the model's first five generalized masses following the procedures outlined in reference 7. in figure 19. measurements that can hopefully be correlated with these data. mass data appear reasonable except possibly for the third mode which was difficult to excite in a clean responsive manner. progress to completely define the structural dynamic characteristics of the model as accurately as practical for several sweep configurations. Table I illustrates a comparison of The results of this study are illustrated An alternate study is currently in progress to make direct mass The generalized Further studies are in By mid-December 1974 the basic model design and fabrication had been completed to the point that an uncontrolled two-day flutter test was possible. These initial tests wele conducted at the Walter H. Beech Memorial Wind Tunnel on the campus of Wichita State University, Wichita, Kansas. The test program provided basically a checkout of the model instrumentation and structural integrity in addition to a flutter data point that could be correlated with the computed flutter point provided by our math model. fluttered spontaneously at 70 meters'per second (230 ft/sec) at a frequency of 8 Hz in the classical wing-tail flutter mode, whereas the model of reference 2 had a flutter speed of approximately 39 meters per second (230 ft/sec). Flutter was suppressed without damage to the model by a reduction of dynamic pressure in the wind tunnel. These results confirmed that the frequency range of unstable model responses lies well within the 0 to 15 Hz levels for which satisfactory preliminary checkouts have been made on the model control system. checkouts are currently being made on the model's overall control response characteristics to define completely the control transfer function. The uncontrolled model Finalized 220 CONCLUDING REMARKS The preliminary findings obtained from the current study indicate that an active aerodynamic control in the form of a stabilator or aileron can be highly effective in suppressing subsonic wing-tail interference flutter. Flutter margins can be restored to at least that of the isolated wing by employing con- trol gains and phasings utilizing parameter optimization techniques. doublet lattice lifting surface theory was found to be adequate for predicting this flutter phenomenon as observed in the wind tunnel. Additional wind-tunnel studies are needed on the modified AFFDL wing-tail flutter model, however, to accurately assess themath modeling techniques employed in the present study for designing flutter suppression systems. the near future. uncontrolled flutter model developed in the present study. fied the structural integrity of the model for the more advanced testing programs and provided a checkout of the instrumentation and a data point for correlation with our math model. both analog and digital modular devices at extremely low costs have brought many of the problem solutions in the active control technology area to within both the technical and economical grasp of the academic researcher as well as the alert designer. The One such test program is planned for Preliminary wind-tunnel studies have been carried out on the The results veri- Recent electronic developments in the form of REFERENCES 1. 2. 3. 4. 5. 6. 7. Topp, L.J., Rowe, W.S., and Shattuck, A.W.: Aeroelastic Considerations in the Design of Variable Sweep Wing Airplanes. ICAS/IPAES, Sept. 1966, pp.1-25. Mykytow, W.J., Noll, T.E., Huttsell, L.J., and Shirk, M.H.: Investigations Concerning the Coupled Wing-Fuselage-Tail Flutter Phenomenon. Journal of Aircraft, V o l . 9, No. 1, Jan. 1972, pp. 48-54. Shelton, J.D., Tucker, P.D., and Davis, J.C.: Wing-Tail Interaction Flutter of Moderately Spaced Tandem Airfoils. AIM Paper No. 69-57, AIAA 7th Aerospace Sciences Meeting, New York, Jan. 20, 1969. Nissim, E.: of Aerodynamic Energy. NASA TN D-6199, 1971. Flutter Suppression Using Active Controls Based on the Concept Cwach, E., and Stearman, R.: Suppression of Flutter on Interfering Lifting Surfaces by the Use of Active Controls. AIM Paper No. 74-404, AIM/ASME/ SAE 15th Structures, Structural Dynamics and Materials Conference, April 17-19, 1974. Sheingold, D.H.: Nonlinear Circuits Handbook. Analogue Devices Inc., Norwood, Massachusetts, 1974. Able, I.: Static Stability and Control Characteristics of Flexible Aircraft. A Wind Tunnel Evaluation of Analytical Techniques for Predicting NASA TN D-6656, 1972. 22 1 TABLE I MODE NUMBER MODAL FREQUENCIES 60' SWEEP CONFIGURATIONS AFFDL MODEL REF. 2 Hz 0.90 3.9 8.1 13.9 17 .1 MODIFIED AFFDL MODEL PRESENT STUDY Hz 1.46 3.82 7.89 16.93 21.90 222 1.4 1.2 1 .o 0.8 0.6 0.4 0.2 0.0 - Low Wing Swrrp s w rep 0 10 20 30 40 50 60 70 80 Wing leading-edge sweep, degrees Figure 1 .- Composite f lu t te r boundary i l lustrating cr i t ical interference f lu t te r condition for large sweep angles. (From reference 1 .) 223 W S a 224 3 4 m w n W x d 0 r4 4 i3 n S 0 C, u aJ m *P F (d 0 P h C, .r 0 C, In % (d (d L *I- F P aJ W 0 E L aJ c, *, 3 ;5 ? .r m *, I tn S 3 L -r c z 6: W aJ c I 0 S 0 C, u aJ m (d V P >s I- .I- F I M a, L S m L L 0 7 225 * 9) L 0 -. c, V rd IC 9) P n .f - 0 5 n - .2 Flutter speed .1 0 .l .f -.2 - .3 N I n 3 n Veloci ty , V , m/sec Figure 4.- Semir igid wing- ta i l model. Uncontrol led f lutter speeds (open 1 oop) . chord sepa ra t ion d i s t a n c e between wing and t a i l ; M = 0; sea- leve l condi t ions . 60" sweep conf igu ra t ion and approximately 1 /4 wing 226 Im 9 2 1 I 1 I inary Displacement and Phase Point on Wing Tip Real - * Q3 - - - - _ Displacement and Phase Point on Horizontal Tail q1 r ig id body roll q2 f i r s t flexible mode q3 second flexible mode Figure 5.- Computed displacement and phase relationships i n open loop f l u t t e r mode o f semirigid wing-tail model. approximately a 1/4 w i n g chord separation distance between wing and t a i l ; M = 0; sea-level conditions. 60° sweep configuration and 227 Imz .nary Displacement of Horizontal Tail Figure 6*- Computed phase r e l a t ionsh ips between wing, t a i l , and control sur face f o r control led semir ig id wing-tail model ( sensor 1 ocated on horizontal t a i 1 ) e approximately a 1/4 wing chord separa t ion d is tance between wing and t a i l ; M 0; sea-1 eve1 condi t ions e 60° sweep configurat ion and 2228 \ -. 3 I ' 4 N I n 3 n ' 3 2 E: a, 3 0- LL 6 12 18 24 30 36 42 0 0 Velocity, V , m/sec Figure 7. - Semirigid wing-tai 1 model control l ed and uncontroll ed f lutter speeds (experimental and computed). approximately a 1/4 wing chord separa t ion d i s t ance between wing and tail; M = 0; sea- level condi t ions. 60" sweep configurat ion and 229 I *Ir- Sensor on T a i l Sensor on Wing m a L 0 c, 0 a5 rc n h n 5 -. I I (Control Laws D o Not Vary with k) t 4 N I 3 n n L " 0 6 12 18 24 30 36 42 Velocity, V, m/sec Figure 8.- Comparison of semirigid controlled model flutter results with sensor mounted on tail and wing. M * 0; sea-level conditions. 230 N I 3 n n 3 2 S a, 3 0- LL t 0 I I I 1 1 I 0 12 24 36 48 60 72 a4 Velocity, V, r n k c Figure 9. AFFDL model. Uncontrolled flutter speed; 60" wing sweep; M = 0; sea-level conditions. 231 16 N I 12 n 3 3 8 C 0- L L . 4 n 3 2 0 12 24 36 48 60 72 84 0 Velocity, V , m/sec Figure 10. AFFDL model. Uncontrolled f lu t te r speed; 45" wing sweep; conditions. M = 0; sea-level 232 Using Gen. Coor. 0, "Using 2 Sensors (Control Laws Do Not V a r y with k) I rn n 12 N L m 8 3 n 3 S 3 0- Q) L LL Q ) 4 0 0 12 24 36 48 60 72 84 Velocity, V , m/sec Figure 11. Comparison of f l u t t e r speeds on AFFDL model when u s i n g generalized coordinates and two sensors i n control law (one sensor located near the outer wing t i p t ra i l ing edge and one near the s tabi l ator t i p 1 eading edge). 60" sweep configuration; act ive s tab i la tor control; M = 0; sea-level conditions. 233 N = 12 n 3 3 8 S W 3 0- W n L -. L 4 A. % Q 0 12 24 36 48 60 72 84 Velocity, V , m/sec Figure 12.- Increase i n f lutter speed o f isolated wing o f AFFDL model. 60' sweep configuration; aileron i s active control using generalized coordinates i n control law; M = 0; sea-level conditions. 234 m L 0 n G e n e ~ a ~ i z e d Coordinates 2 Sensors - -- -- 'f N I 3 >, V S 0) 3 0- e, L LL h n 0 12 24 36 48 60 72 84 0 Velocity, V , m/sec Figure 13.- Comparison of f l u t t e r speeds of AFFDL model us ing generalized coordinates and two sensors i n control law ( b o t h sensors located on w i n g a t 35% of local wing chord, one near the t i o and one a t the root chord). 60" sweep configuration; active aileron control ; M = 0; sea-level conditions. 235 Figure 1.4. - Aerod namic model ing for a i leron on AFfDL model with 60" sweep. 236 Figure.15.- Installation of modified AFFDL wing-tail flutter model in 7 ft by 10 ft subsonic wind tunnel. 237 u a, z .C u 0 E 238 1--1 I- I b-+r ---- I I 1 1 V I-% t 7 I I n l-0 v 1 4 Servoval ves Hydraulic power supply Figure 170- Hydraulic power supply and servovalves f o r modified AFFDL wing-tail model. 239 240 241 CORRELATION WITH FLIGHT OF SOME AEROELASTIC MODEL STUDIES I N THE NASA LANGLEY TRANSONIC DYNAMICS TUNNEL* W i l m e r H. Reed I11 NASA Langley Research Center SUMMARY The NASA Langley transonic dynamics tunnel, which has a v a r i a b l e dens i ty During the 15 years Freon-12 (or air) test medium, w a s designed s p e c i f i c a l l y f o r t h e study of dynamics and a e r o e l a s t i c problems of aerospace vehic les . of operation of t h i s f a c i l i t y , t h e r e have been var ious oppor tuni t ies t o compare wind-tunnel and f l i g h t - t e s t r e s u l t s . Some of t hese oppor tuni t ies arise from rou t ine f l i g h t checks of the prototype; o thers , from c a r e f u l l y designed compara- t i v e wind-tunnel and f l i g h t experiments. This paper br ings together i n one p lace a c o l l e c t i o n of such d a t a obtained from various published and unpublished sources. The top ic s covered are: gus t and b u f f e t response, con t ro l su r f ace e f fec t iveness , f l u t t e r , and active cont ro l of a e r o e l a s t i c e f f e c t s . Some bene- f i t s and shortcomings of Freon-12 as a test medium are a l s o discussed. Although areas of uncer ta in ty are evident and there is a continuing need f o r improvements i n model simulation and t e s t i n g techniques, t h e r e s u l t s presented here in indi- cate t h a t pred ic t ions from a e r o e l a s t i c model tests are, i n general , subs tan t i - a ted by f u l l - s c a l e f l i g h t tests. INTRODUCTION A t t h e time t h e forerunner of t h i s symposium (Symposium on F l igh t F l u t t e r Testing held i n Washington, D.C. , May 1958) w a s held 1 7 years ago, a new tran- sonic wind tunnel w a s nearing completion a t NASA Langley Research Center. Designated the Langley transonic dynamics tunnel (TDT), i t has served, s ince becoming opera t iona l i n 1960, as a National f a c i l i t y devoted exclusively t o work on dynamics and a e r o e l a s t i c i t y problems of a i r c r a f t and space veh ic l e s i n the transonic speed range. An e s s e n t i a l d i f f e rence between the TDT and wind tunnels employed primarily i n steady-state aerodynamic inves t iga t ions s t e m s from t h e sca l ing requirements which must be s a t i s f i e d i n a e r o e l a s t i c model s tud ie s . For example, i n aqd i t ion t o t h e need f o r adequate simulation of t he aerodynamic flow f i e l d about t h e model, i t is a l s o necessary t h a t t h e model s t i f f n e s s , m a s s , and i n e r t i a proper- t ies simulate those of t he f u l l - s c a l e s t r u c t u r e and t h a t t h e r a t i o of s t r u c t u r a l *This paper is e s s e n t i a l l y t h e same as a presenta t ion e n t i t l e d "Comparison of F l i g h t Measurements With Predic t ions From Aeroe las t ic Models i n t h e NASA Langley Transonic Dynamics Tunnel," by W i l m e r H. Reed 111, presented a t the 46th AGARD F l i g h t Mechanics Panel Symposium on Flight/Ground F a c i l i t y Correlation, Va l lo i r e , France, June 9-12, 1975. 243 dens i ty t o test-medium dens i ty be t h e same f o r model and f u l l scale, To a i d i n s a t i s f y i n g these requirements, t h e TDT uses a variable-d e i t h e r air o r Freon-12, The primary test medium, Freon-12, is four times as dense as a i r and has a speed of sound about one-half t h a t of air; thus heavier and less expensive models m&y be used and t h e tunnel power requirements reduced. Some main f e a t u r e s of t he f a c i l i t y are indicated i n f i g u r e 1. Experlmental a e r o e l a s t i c research a l s o imposes demanding requirements f o r spec ia l ized t e s t i n g techniques. A review of such t e s t i n g techniques developed by the s t a f f of t h e Langley transonic dynamics tunnel f o r use i n s t u d i e s of var ious s t a b i l i t y , cont ro l , and response c h a r a c t e r i s t i c s of elastic a i r c r a f t is given i n re ference 1. From time t o time during the 15-year period of operation of t h i s f a c i l i t y , t he re have been various oppor tuni t ies t o compare the r e s u l t s from wind-tunnel and f l i g h t tests. Some of t hese oppor tuni t ies arise from rou t ine f l i g h t checks of t h e prototype, o thers from ca re fu l ly designed comparative wind-tunnel and f l i g h t experiments. This paper brings together i n one place a c o l l e c t i o n of such da ta , gleaned from var ious published and unpublished sources, f o r t he purpose of addressing the question: models, t e s t ed i n a Freon-12 wind-tunnel environment, p r e d i c t t h e behavior of t h e i r fu l l - s ca l e counterparts i n f l i g h t ? To t h i s end, some advantages and shortcomings of Freon-12 as a wind-tunnel test medium are considered and then se lec ted comparisons between wind-tunnel and f l i g h t tests i n areas r e l a t i n g to dynamic response, s t a t i c a e r o e l a s t i c i t y , f l u t t e r , and active-controls research are presented e How w e l l can dynamically scaled a e r o e l a s t i c AIR-FREON COMPARISONS Before comparing test r e s u l t s obtained i n the Langley t ransonic dynamics tunnel with f l i g h t da ta , a few comments are i n order on air-Freon d a t a compari- sons since, by f a r , most of t he tests conducted i n t h i s f a c i l i t y make use of a Freon-12 test medium. (Air can a l s o be used as a test medium.) Freon-12 has seve ra l c h a r a c t e r i s t i c s which make i t a very a t t r a c t i v e test medium f o r scaled dynamic model s tud ies . pressure and temperature are compared with those of air i n t a b l e I. The most advantageous c h a r a c t e r i s t i c s are the high dens i ty and low speed of sound of Freon-12 r e l a t i v e to air a t t h e same pressure and temperature. The r e l a t i v e l y low speed of sound is s i g n i f i c a n t f o r s eve ra l reasons. i n which the reduced-frequency sca l ing parameter wb/V must be s a t i s f i e d , t he lower Gunnel speed f o r a given Mach number reduces d i r e c t l y a l l pe r t inen t f re - quencies and, consequently, s imp l i f i e s instrumentation problems and reduces i n e r t i a loads. For tests involving r o t a t i n g he l icopter blades where model and fu l l - sca l e t i p Mach numbers must be t h e s a m e , the stresses and hence t h e d i f f i c u l t i e s of f ab r i ca t ion are reduced. For f l u t t e r and other dynamic tests, where the r a t i o of s t ruc tura l -dens i ty t o test-medium dens i ty must be t h e same f o r t he model as the a i rp l ane , t he more dense Freon-12 permits heavier models t o be constructed. This is a d i s t i n c t advantage when the d i f f i c u l t y of fabr i - ca t ing models l i g h t enough t o simulate t h e m a s s c h a r a c t e r i s t i c s of a i r c r a f t designs with composite s t r u c t u r e s and active con t ro l s operating a t high speeds Some of t h e more important p rope r t i e s a t atmospheric For dynamic model tests 244 and low a l t i t u d e s is considered. The use of Freon-12 as a test medium allows t h e simultaneous s a t i s f a c t i o n of both Mach number and Froude number f o r those ins tances where both compressibil i ty and e must be For Froude number s i m i l a r i t y , a n approximately 1/5-scale model is required. add i t iona l b e n e f i t is t h a t , f o r a given model s i z e , test conditions of equal Mach number and s tagnat ion pressure produce a Reynolds number i n Freon-12 approximately t h r e e times t h a t i n air. F ina l ly , s ince t h e power required to opera te a wind tunnel a t a given Mach number varies d i r e c t l y as the cube of t he ve loc i ty , t h e u s e of Freon-12 o f f e r s a considerable savings i n power. An The p r inc ipa l uncer ta in ty associated wi th t h e use of Freon-12 as a test medium is the f a c t t h a t i ts s p e c i f i c heat r a t i o y is not t h e same as t h a t f o r a i r (1.13 as compared with 1.4), so t h a t q u a n t i t a t i v e d i f f e rences e x i s t between t h e compressibil i ty r e l a t i o n s f o r air and Freon. There have been numerous s t u d i e s of t he degree t o which d a t a obtained from tests i n Freon-12 can be u t i l i z e d t o p r e d i c t flow c h a r a c t e r i s t i c s , s t r u c t u r a l response, o r s t a b i l i t y i n a i r ( r e f s . 2 t o 5 ) . For example, i n re ferences 2 and 3 , t h e s ign i f i cance of t h i s d i f f e rence i n gas c h a r a c t e r i s t i c s on s ta t ic aerodynamic coe f f i c i en t s w a s s tud ied extensively, and means f o r converting Freon-12 d a t a t o equivalent air values were evaluated. These s t u d i e s ind ica ted t h a t a t subsonic and low super- sonic Mach numbers t h e required cor rec t ions w e r e s m a l l and t h a t the d i f f e rence between the converted r e s u l t s by two co r rec t ion methods, t h e "transonic similar- i t y rule" and t h e "streamline s i m i l a r i t y ru l e , " were very s m a l l . r e p o r t s t he r e s u l t s of an experimental subsonic and t ransonic f l u t t e r inves t i - ga t ion of a 45" sweptback wing planform t h a t w a s t es ted i n a i r and i n Freon-12 i n t h e TDT. Comparisons of d a t a i n a i r and i n Freon-12 indicated t h a t f o r sub- sonic and t ransonic Mach numbers, t h e f l u t t e r speed obtained i n Freon-12 may be in t e rp re t ed d i r e c t l y as f l u t t e r speed i n a i r a t the s a m e m a s s r a t i o and Mach number. Without t h e Freon-12 and air cor rec t ions , t he Freon-12 data.would r e s u l t i n a s l i g h t l y conservative estimate of t h e f l u t t e r speed. Reference 5 Although one might i n f e r from these f l u t t e r da t a comparisons t h a t t he e f f e c t of d i f f e r e n t r a t i o s of s p e c i f i c hea t f o r air and Freon-12 are i n s i g n i f i - can t f o r unsteady aerodynamic fo rces up t o low supersonic speeds, t h e e f f e c t on d e t a i l e d unsteady pressure d i s t r i b u t i o n s has only r ecen t ly been demonstrated ana ly t i ca l ly . of t h e pressure d i s t r i b u t i o n on an NACA 648006 a i r f o i l i n air and i n Freon-12. The a i r f o i l is o s c i l l a t i n g i n p i t c h about t h e midchord a t a low reduced f re - quency (k = 0.06); t h e Mach number is 0.9. S m a l l o s c i l l a t i o n s about a nonuni- form mean flow f i e l d were considered i n t h e ca l cu la t ion which y i e l d s a l i n e a r p o t e n t i a l flow equation with v a r i a b l e c o e f f i c i e n t s t h a t depend on t h e steady flow f i e l d . (See r e f . 6.) The s t a t i c pressure c o e f f i c i e n t Ct and t h e ampli- tude and phase angle of t he o s c i l l a t i n g pressure , lACpl are shown i n f i g u r e 2 as a func t ion of chordwise loca t ion . The rap id change i n t h e steady pressure c o e f f i c i e n t near t h e 65-percent chord loca t ion indi- cates a shock. The p r inc ipa l d i f f e rence between the Freon-12 and a i r d a t a is seen t o be t h e loca t ions of t h e peak unsteady pressures of t h e phase ang le 4 i n t h e v i c i n i t y of t h e shock. Inasmuch as shock waves and r e l a t e d t ransonic e f f e c t s tend t o be less severe f o r three-dimensional than f o r two-dimensional flow, t h e e f f e c t s of y on three-dimensional configurations may be correspondingly milder than those ind ica ted here. needed t o f u r t h e r eva lua te these e f f e c t s i n unsteady flow. Figure 2 presents some r e s u l t s of a f in i t e -d i f f e rence ca l cu la t ion and , respec t ive ly , Cp lACpl and t h e values Additional study is 245 An experimental study t h a t w i l l p a r t i a l l y f u l f i l l t h i s need is planned f o r t h e near fu tu re , The study w i l l involve t h e measur es s d i s t r i b u t i o n s on a cropped-tip d e l t a wing o s c i l l a t i n g i n a p i tch ing and a flap- ping mode i n air and i n Freon-12 a t comparable Reynolds numbers through the transonic speed range, The model w i l l a l s o have o s c i l l a t i n g leading- and trail ing-edge con t ro l sur faces This study should provide needed experimental d a t a f o r evaluating advanced transonic unsteady aerodynamic theor ies and f o r evaluating t h e unsteady flow c h a r a c t e r i s t i c s of air and Freon-12. WIND-TUNNEL AND FLIGHT COMPARISONS This s e c t i o n of the paper presents s e l ec t ed examples showing comparisons of r e s u l t s obtained i n the TDT and i n f l i g h t tests. used as a test medium, and t h e models w e r e dynamically and a e r o e l a s t i c a l l y scaled t o s u i t a b l y match f u l l - s c a l e conditions. The following top ic s are covered herein: I n a l l cases Freon-12 w a s (1) Gust response (2) Buffet response (3) S t a b i l i t y de r iva t ive ex t r ac t ion ( 4 ) F l u t t e r (5) Active con t ro l of a e r o e l a s t i c e f f e c t s Gust Response The response of an a i r c r a f t t o atmospheric turbulence is an important design consideration from t h e standpoint of loads, s t r u c t u r a l f a t igue , and r i d e qua l i t y . The need f o r an experimental c a p a b i l i t y f o r - t h e study of a i r p l a n e response t o gus t loads l ed t o t h e development of a technique f o r generating s inusoida l gus t s i n the test sec t ion of t h e TDT. This technique, described i n re ference 7 , involves measuring t h e response of an a e r o e l a s t i c a l l y sca led model i n simulated f r e e f l i g h t t o a s inusoida l vertical gus t f i e l d generated by o s c i l l a t i n g vanes located upstream of t h e test section. Some key f ea tu res of t h e system are i l l u s t r a t e d i n f i g u r e 3. The model is suspended i n t h e wind-tunnel test sec t ion by a two-cable mount system, which allows lateral and v e r t i c a l t r a n s l a t i o n of t h e model as w e l l as angular rota- t i o n about a l l th ree axes. (See r e f . 8.) The airstream o s c i l l a t o r cons i s t s of two sets of b ip lane vanes mounted on each s i d e of t h e tes t - sec t ion entrance. The vanes are o s c i l l a t e d s inuso ida l ly i n p i t ch about a zero mean angle of a t t a c k a t frequencies up t o 20 he r t z . T ra i l i ng v o r t i c e s from the vane t i p s , passing downstream near t h e s idewal l s of t h e test sec t ion , induce a ve r t i ca l -ve loc i ty component i n the flow f i e l d near t h e center of t h e test sec t ion . A t yp ica l v a r i a t i o n of t h e v e r t i c a l gus t flow angle wi th frequency and lateral d i s t ance from the center of t he test sec t ion is shown i n f i g u r e 4 i n 246 t he form of a three-dimensional p l o t , Note t h a t the gus t angle decreases r ap id ly with increas ing frequency, and the re are v a r i a t i o n s i n the flow angle across t h e tunnel, I n i t i a l a n a l y t i c a l and experimental s t u d i e s i n re ferences 1 and 7 indicated t h e f e a s i b i l i t y of t he airstream o s c i l l a t o r technique. On t h e bas i s of these encouraging s igns , a comparative wind-tunnel, f l i g h t , and ana lys i s study w a s undertaken i n l a te 1960 t h a t used t h e B-52E a i r c r a f t as t h e test art icle. The wind-tunnel program involved a 1/30-size dynamically scaled a e r o e l a s t i c model of the B-52E. (See f i g . 5.) I n order t o achieve reasonable simulation of t h e short-period mode on t h e model, i t w a s necessary t o u s e a v a r i a t i o n of t he two-cable mount system shown i n f i g u r e 3 . I n t h i s case, t h e cables w e r e pinned t o t h e model a t a poin t near t h e center of g rav i ty and t h e pulleys w e r e mounted a t t h e tunnel w a l l r a t h e r than wi th in the contours of t h e model fuselage. This mount configuration has a very low r o t a t i o n a l s t i f f n e s s i n p i t c h and provides adequate simulation of the short-period f r e e - f l i g h t mode. Figure 6 shows a sample of some unpublished r e s u l t s obtained by L. T. Redd and J. Gilman, Jr., of NASA Langley Research Center. Frequency response p l o t s of a nondimensional c o e f f i c i e n t of bending moment a t t h e midwing span per degree of s inusoida l v e r t i c a l gust angle are shown f o r t h ree cases: (1) wind-tunnel- model tests using the airstream o s c i l l a t o r , (2) a n a l y t i c a l p red ic t ions f o r t he cable-mounted model, and (3) f l i g h t tests using s p e c t r a l measurements of atmos- pher ic turbulence and the assoc ia ted response of t he a i rp l ane . These d a t a w e r e produced with t h e a i d of The Boeing Company, Wichita Division, under con t r ac t i n a cooperative program by NASA Langley Research Center and t h e U.S. A i r Force F l i g h t Dynamics Laboratory. With re ference t o f i g u r e 6, i t should be noted t h a t a t very low reduced frequencies (k = 0.01, where k i s the reduced frequency based on t h e mean aerodynamic semichord), t h e model response i s af fec ted by a mount system mode and t h e a i rp l ane response by spurious pilot-induced motions; a t higher reduced frequencies (k = 0.14), the low gus t input level produced by t h e airstream o s c i l l a t o r ( s ee f i g . 4 ) leads t o measurement inaccuracies. The o v e r a l l corre- l a t i o n s between wind-tunnel, f l i g h t , and a n a l y t i c a l p red ic t ions appear t o be good, however, and ind ica t e t h e airstream o s c i l l a t o r t o be a usefu l and v a l i d wind-tunnel technique fo r a i r p l a n e gust loads research. ( I n t h e o r a l vers ion of t he paper a movie c l i p w a s used t o i l l u s t r a t e gust response of t h e model and t h e a i rp lane . ) Buffet Response When b u f f e t response and load predic t ions of complete a i r c r a f t are required, a dynamically scaled a e r o e l a s t i c model test would seem t o o f f e r t he b e s t hopes of obtaining s u i t a b l e data. Since viscous flow phenomena, including boundary- l a y e r separation, are influenced i n varying degrees by t h e va lue of t h e Reynolds number, t h i s parameter would appear t o be somewhat more s i g n i f i c a n t f o r bu f fe t s t u d i e s than f o r f l u t t e r tests. Although t h e loca t ions of l o c a l shocks and commencement of l o c a l separated flow may be Reynolds number dependent i n varying degrees, depending on the p a r t i c u l a r aerodynamic configuration, t he re i s some 247 experimental evidence t o suggest t h a t t he in tegra ted e f f e c t s on the s t r u c t u r a l response and even on t o t a l l i f t may be s m a l l r e l a t i v e t o o ther f t h e accuracy of bu f fe t loads. bu f fe t loads has been evaluated i n re ference 9 by c g the normal-force coe f f i c i en t s and t h e scaled bu f fe t bending moments on a 1/8-scale f l u t t e r model of a variable-sweep f i g h t e r a i rp l ane wi th measured i n a fl ight-buffet-research program. (See r e f . l o . ) The model w a s "flown" on t h e bas i c cable-mount system described earlier with a l i f t balancing device ( see f i g . 3 and r e f . 9) which counteract s of t h e model weight and thus allowed t h e model t o be f s simulating high load f a c t o r s ( i n e r t i a and p i tch- ra te e f f e c t s being neglected, of course). Figure 7 compares the model and fu l l - sca l e v a r i a t i o n of normal-force coef- The a e r o e l a s t i c mode f i c i e n t angles of sweep. The model CN w a s obtained from a load cel l on t h e l i f t balancing cable , whereas t h e a i r p l a n e w a s obtained from an accelerometer located near t h e center of grav i ty . The model Reynolds number range w a s from 0.87 x 106 t o 1.33 x 106 compared with f l i g h t values of 20 x 106 t o 28 x 106. The Mach numbers indicated are model values. The a i r p l a n e Mach number varied from s l i g h t l y above the model va lue of t h e start of t h e maneuver t o s l i g h t l y below t h e model va lue a t t h e end of t he maneuver (high angle of a t t a c k ) . The var iance w a s l a r g e r a t the higher sweep angles. The model and a i r p l a n e values of CN are seen t o agree reasonably w e l l . CN with angle of a t t a c k w e l l beyond t h e b u f f e t boundary f o r t h ree CN Figure 8 compares the a i r p l a n e bu f fe t response with model-predicted values of wing and ho r i zon ta l - t a i l root-mean-square (rms) bending moments and r m s acce le ra t ions a t the center of grav i ty . The d a t a are t y p i c a l i n t h a t t h e f u l l - scale-buffet bending moments on the wing and hor izonta l t a i l s and t h e center-of- g rav i ty buf fe t acce le ra t ions predicted from t h e model d a t a agreed w e l l with a i r p l a n e values a t a l l Mach numbers a t a wing sweep angle of 26". shown here, a t a wing sweep angle of 50" t h e agreement w a s reasonably good a t a l l Mach numbers t e s t ed f o r t h e wing bending moments, but t h e c o r r e l a t i o n of t h e model and a i r p l a n e center-of-gravity acce le ra t ions and ho r i zon ta l - t a i l bend- ing moments w a s not so good a t t h e higher Mach numbers. a i r p l a n e and model response w e r e low and made evaluation of t he technique d i f f i c u l t . Although not A t 72" sweep, both the S t a b i l i t y Derivative Ext rac t ion From Cable-Mounted Wind-Tunnel Model T e s t s Procedures f o r determining a i rp l ane s t a b i l i t y and c o n t r o l de r iva t ives from f l i g h t - t e s t measurements havebeen under development s i n c e t h e ea r ly days of aviation. I n r ecen t years, however, a widespread surge of i n t e r e s t i n t h i s area has been t r iggered by t h e a v a i l a b i l i t y of highly automated d a t a acqu i s i t i on systems and advances i n optimal estimation theory. The cu r ren t s t a t u s and pros- pec t s f o r the f u t u r e of t h i s technology w e r e top ics of a recent s p e c i a l i s t m e e t - ing on methods of parameter i d e n t i f i c a t i o n i n a i r c r a f t f l i g h t t e s t ing . r e f . 11.) (See Pa ra l l e l ing t h i s focus on f l i g h t - t e s t i n g techniques is an i n t e r e s t i n applying similar procedures f o r t h e ex t r ac t ion of s t a b i l i t y and c o n t r o l 248 der iva t ives from "f ree-f lying" a e r o e l a s t i c a l l y scaled wind-tunnel models Pre- liminary ind ica t ions from t h e o r e t i c a l s tud ie s and companion wind-tunnel experi- ments are encouraging, of a cable-mounted model t o known input d i s turbances such as control-surface de f l ec t ions or ex te rna l fo rces applied through t h e suspension cables. The sta- b i l i t y de r iva t ives are then ex t rac ted from equations of motion f o r t he model and t h e suspension system using a maximum-likelihood parameter-estimation algo- rithm (based on ref.. 12) which is being developed under con t r ac t by NASA Langley Research Center. (p i t ch , r o l l , yaw, v e r t i c a l t r a n s l a t i o n , and lateral t r a n s l a t i o n ) wherein t h e model is t r ea t ed as an equivalent r i g i d body. t i v e s therefore r ep resen t quas i - s t a t i c elastic de r iva t ives . Deformation e f f e c t s associated with g r a v i t y forces are neglected. However, by u s e of t h e l i f t bal- ance mentioned earlier, high-angle-of-attack nonlinear aerodynamic c o e f f i c i e n t s may be determined. The proposed procedure involves measuring The equations of motion represent f i v e degrees of freedom The derived aerodynamic deriva- The procedures described above are, i n theory, capable of deducing the aerodynamic c o e f f i c i e n t s assoc ia ted with whatever motions of t h e model are excited by the known ex te rna l disturbances. Numerical experiments using simu- l a t e d "noisy" wind-tunnel d a t a show promise t h a t most aerodynamic de r iva t ives can be determined wi th acceptable accuracy. Further assessment of t he method w i l l be made i n upcoming wind-tunnel model tests. I n a previous study a s i m p l i - f i e d vers ion of such a technique w a s applied t o determine ro l l - con t ro l e f fec t ive- ness f o r a cable-mounted a e r o e l a s t i c model ( r e f s . 1 and 13) . The technique and some comparisons between wind-tunnel and f l i g h t r e s u l t s are summarized below. The approach i s based on t h e assumption t h a t t h e dynamic response of a cable-mounted model t o s inusoida l a i l e r o n d e f l e c t i o n can be represented by a single-degree-of-freedom system i n r o l l . The r o l l i n e r t i a of t he model, t h e spr ing r e s t r a i n t of t h e mount system, and t h e wind-tunnel test conditions are assumed t o be known; t h e r o l l damping c o e f f i c i e n t C and a i l e r o n e f f ec t ive - ness coe f f i c i en t Cz6 are t h e unknowns t o be determined. The amplitude and phase of t he model-roll response t o a s inusoida l a i l e r o n d e f l e c t i o n are measured over a range of d i s c r e t e frequencies. These measurements, when subs t i t u t ed in to t h e equation of motion, produce a set of redundant a lgebra ic equations which are solved by a least-squares procedure t o g ive the unknown aerodynamics deriva- t i v e s C and C l 6 . The r a t i o of these c o e f f i c i e n t s i s proportional t o t h e f r ee - f l i gh t c o n t r o l e f fec t iveness which i s normally expressed i n t e r m s of the wing-tip he l ix angle, pb/2V; where p is r o l l rate; b, wing span; and V , airspeed. l P IP A comparison of t h e a i l e r o n ef fec t iveness measured i n f l i g h t with wind- tunnel model p red ic t ion is shown i n f i g u r e 9. These r e s u l t s are f o r a l a r g e cargo t ranspor t a i r c r a f t a t a Mach number of 0.75. The model da t a w e r e obtained on a Mach scaled a e r o e l a s t i c model used previously i n f l u t t e r s tud ies . t he a i l e r o n s become i n e f f e c t i v e as t h e a i l e r o n reversal po in t is approached, r o l l t r i m of t h e model w a s provided mechanically by d i f f e r e n t i a l d e f l e c t i o n of t he hor izonta l rear cables as shown i n f i g u r e 3 . sons shown i n f i g u r e 9 ind ica t e t h a t t h i s r e l a t i v e l y simple test technique can Since The model and f l i g h t compari- 249 provide s a t i s f a c t o r y estimates of not only t h e r eve r sa l boundaries, but a l s o the a i l e r o n ef fec t iveness of t h e a i rp l ane as a function of Mach number and dynamic pressure. F l u t t e r During high-alt i tude f l i g h t tests of a l a r g e cargo t ranspor t a i rp l ane , a f lu t t e r - type i n s t a b i l i t y w a s encountered on t h e ho r i zon ta l - t a i l su r f ace of t h e T - t a i l empennage. The i n s t a b i l i t y occurred a t a Mach number near 0.8 but only during maneuvering f l i g h t when t h e e leva tor w a s def lec ted more than about 8" i n e i t h e r d i r ec t ion . o s c i l l a t i o n involving coupling between e l eva to r rotat.ion and s t a b i l i z e r to rs ion at a frequency of about 24 h e r t z . two types of con t ro l sur face i n s t a b i l i t i e s , f l u t t e r and buzz, i t has been re fer red t o as "fluzz.") P r i o r t o the inc iden t , f l i g h t f l u t t e r tests and analyses, which w e r e f o r s m a l l e leva tor de f l ec t ions , ind ica ted no f l u t t e r problems within t h e a i rp l ane ' s operating envelope. inves t iga t ions of various proposed so lu t ions , such as vor tex generators, dampers, and e l eva to r m a s s balance, l ed t o t h e s e l e c t i o n of increased e leva tor mass balance as t h e most promising solution. (See r e f . 14.) The problem w a s characterized by a l imi ted amplitude (Since t h e phenomenon had the earmarks of Subsequent f l i g h t Because the re w a s l i t t l e o r no information a v a i l a b l e i n the l i t e r a t u r e a t t h e t i m e on i n s t a b i l i t i e s i n i t i a t e d by l a r g e con t ro l su r f ace de f l ec t ions , an experimental study w a s undertaken i n t h e TDT t o explore t h e phenomenon fu r the r . (See r e f . 15.) Results from t h e study are summarized i n f i g u r e 10. It w a s found t h a t t h e bas i c i n s t a b i l i t y phenomenon encountered on the a i r p l a n e i n f l i g h t tests w a s reproduced i n t h e wind tunnel although a t higher predicted speeds. Whereas i n f l i g h t , t h e i n s t a b i l i t y occurred when t h e e leva tor deflec- t i o n exceeded 8" i n e i t h e r d i r e c t i o n , i t occurred i n t h e wind tunnel only when t h e de f l ec t ion exceeded 8" i n one d i r ec t ion , t h a t is, t r a i l i n g edge down. The reason f o r t h i s behavior may have been due t o increased bearing f r i c t i o n i n the model e leva tor associated with bending of t h e t a i l under s t a t i c loads. F ina l ly , i t should be noted t h a t t h e e leva tor m a s s balancing used as a so lu t ion t o the a i rp l ane f l u t t e r problem a l s o eliminated f l u t t e r on t h e model. Active Control of Aeroe las t ic E f fec t s Active c o n t r o l system technology today is adding a new dimension t o air- plane design. Through app l i ca t ion of a c t i v e con t ro l concepts, o r what has become known as CCV (Control Configured Vehicles), t h e designer can reap such bene f i t s as weight savings, performance improvements, and b e t t e r r i d e qua l i t y . Four such app l i ca t ions and associated p o t e n t i a l bene f i t s are (1) reduced s ta t ic s t a b i l i t y leading t o decreased drag and smaller t a i l s i z e , (2) gu and maneuver load a l l e v i a t i o n leading t o increased f a t i g u e l i f e and/or s t r u c t u r a l weight savings, (3) r i d e qua l i t y con t ro l leading t o improved crew and passenger comfort, and (4) f l u t t e r suppression leading t o weight savings o r increased f l u t t e r placard speeds. tests, and f l i g h t tests. (See r e f s . 16 and 17.) Wind-tunnel and f l i g h t compari- sons f o r two such appl ica t ions - f l u t t e r suppression and load a l l e v i a t i o n - are discussed i n t h e remaining sec t ions of t h e paper. A l l the above have been demonstrated by ana lys i s , wind-tunnel 250 Active f l u t t e r suppression.- To demonstrate t he f e a s i b i l i t y of va r ious a c t i v e con t ro l conceptsg the U , S - A i r Force F l i g h t Dynamics Laboratory h i t i a t e d a f l i g h t program wi th The Boeing Company, Wichita Divis ion, t o study Control Configured Vehicle concepts us ing t h e B-52E a i rp l ane . (See r e f . 18.) Included i n the concepts s tud ied by ana lyses and f l i g h t tests w a s active f l u t t e r suppres- s i o n o r , i n o ther words, f l u t t e r mode cont ro l . I n p a r a l l e l wi th the CCV f l i g h t program, a companion wind-tunnel-model research program w a s undertaken j o i n t l y by NASA and the USAF with con t r ac t support by Boeing (Wichita). (See r e f . 19.) The 1/30-size dynamically scaled a e r o e l a s t i c model of t he B-52E, used previously i n gus t research ( f ig . 5 ) , w a s modified t o s imula te the active con t ro l systems of t h e CCV research a i rp lane . Because of t h e eased weight assoc ia ted with the minia ture electromechanical c o n t r o l system ed t o the model, the model could not s imulate the m a s s s c a l i n g f a c t o r f o r t h e nominal-weight CCV a i rp l ane . Therefore, f o r t h e purpose of comparing wind-tunnel and f l i g h t r e s u l t s s p e c i a l heavyweight a i r p l a n e condi t ions w e r e flown which required in - f l i gh t r e fue l ing . Thus, t h e airplane w a s a l t e r e d t o match the wind-tunnel model. The wing-f lut ter mode c o n t r o l on the model, l i k e the a i r p l a n e , involved f laperons and outboard a i l e rons . Vibratory motions of t he wing were sensed by accelerometers. These s igna l s w e r e sen t from t h e model t o a remotely loca ted , general-purpose analog computer on which t h e c o n t r o l l a w s w e r e simulated and then back again t o t h e model as con t ro l su r f ace command s igna l s . Some sample r e s u l t s from t h i s s tudy (taken from r e f . 19) are presented i n f i g u r e 11 which shows the e f f e c t of t he f l u t t e r mode con t ro l system on the s u b c r i t i c a l damping measured i n the wind tunneland i n f l i g h t . Note t h a t t h e f l u t t e r speed of t h e model is wi th in 8 percent of t h e f l u t t e r speed of the a i rp l ane ; damping t rends below t h e f l u t t e r speed are s i m i l a r but t h e damping of t h e model i s higher than f o r t h e a i rp lane . I n view of t h e high degree of complexity involved i n the wind-tunnel model s imulat ion, t h i s agreement i s considered t o be very good. I n f a c t , t h e wind-tunnel model r e s u l t s agree more c lose ly with f l i g h t - t e s t d a t a than ca l cu la t ions do (not shown). This f l i g h t v a l i d a t i o n of wind-tunnel modeling of a c t i v e con t ro l systems thus tends t o e s t a b l i s h the technique as an economical, t imely means of ver i fy- ing t h e performance of Control Configured Vehicles of t h e fu tu re . Active load a l l ev ia t ion . - Another app l i ca t ion of active cont ro ls has been developed f o r t h e C-5A a i rp l ane as a means of reducing wing f a t i g u e damage due t o incremental maneuver and gust-load sources. This system, designated t h e a c t i v e l i f t d i s t r i b u t i o n con t ro l system (ALDCS), is described i n d e t a i l i n re ference 20. Bas ica l ly , t he ALDCS uses accelerometers located i n t h e outer wing t o provide c o n t r o l su r f ace command s i g n a l s , through t h e a i rp l ane s t a b i l i t y augmentation system, to servo a c t u a t o r s on t h e a i l e r o n s and e leva tors . The a i l e r o n s are de f l ec t ed t o r e d i s t r i b u t e the a i r loads on t h e wing so as t o reduce inboard-wing stresses whereas the e l e v a t o r s are de f l ec t ed t o maintain trim. Speci f ic des ign goals f o r t he system are t o reduce t h e incremental wing r o o t bending moment by 30 percent without s i g n i f i c a n t l y a f f e c t i n g t h e perform- ance, f l u t t e r margins, o r handling q u a l i t i e s of t h e C-5A. A s p a r t of t h e ALDCS development program, a wind-tunnel study of a 1/22- s i z e dynamically sca led a e r o e l a s t i c model equipped with proposed a c t i v e con t ro l system w a s undertaken i n the Langley t ransonic dynamics tunnel . The purpose of 251 t h i s program, which w a s a j o i n t e f f o r t of t h e U.S, A i r Force, Lockheed Georgia Company, and t h e Langley Research Center w a s t o gain added confidence i n t h e ALDCS and t o eva lua te i ts poss ib le e f f e c t on f l u t t e r before unde tests, The model is shown i n f i g u r e 12 , Unlike on t h e B-52 model described earlier, the C-SA model con t ro l system w a s powered by an onboard hydraul ic system. The dynamic response c h a r a c t e r i s t i c s (gain and phase lag) of t h i s system matched those of t h e a i rp l ane up t o frequencies of 35 he r t z on t h e model. The wind-tunnel model program included a number of f a c e t s , one being t o eva lua te the e f fec t iveness of t h e ALDCS by measuring t h e wing bending-moment response t o s inusoida l a i l e r o n frequency sweeps. S i m i l a r measurements were obtained i n f l i g h t f o r comparable conditions. Sone t y p i c a l r e s u l t s from wind- tunnel and f l i g h t tests are presented i n f i g u r e 13. This f i g u r e shows the v a r i a t i o n with a i l e r o n frequency of t h e wing-root bending moment normalized t o t h e maximum bending moment wi th ALDCS off which occurs a t about 1 h e r t z , t he wing fundamental bending frequency. The o v e r a l l t rends f o r the a i r p l a n e and t h e model are s i m i l a r ; however, t h e a i rp l ane system is apparently more e f f e c t i v e than w a s predicted by the model. c i a t ed with t h e f a c t t h a t t h e a i l e r o n con t ro l e f fec t iveness measured s t a t i c a l l y on the model w a s only about two-thirds of t h a t measured on the a i rp l ane . a i l e rons were sealed on t h e a i r p l a n e but no t on the model.) The cause of t h i s d i f f e rence could be asso- (The A second d i f f e rence t o be noted is t h e peak on t h e model response a t approximately 1 / 2 he r t z (scaled t o a i rp lane) with t h e ALDCS on. believed to be due t o coupling between t h e active con t ro l system and t h e model mount system. Similar coupling e f f e c t s have been observed i n test of t h e B-52 model with a simulated active-ride-control system. Here, the feedback gains of t h e ride-control system had t o be reduced i n order t o avoid an i n s t a b i l i t y a r i s i n g from t h e con t ro l system coupling with mount system modes. improvements i n model mount systems are needed to permit more accura te simula- t i o n of the a c t i v e cont ro l systems designed t o modify t h e a i r p l a n e rigid-body dynamics. This i s Thus, ( In the o r a l vers ion of t he paper a movie c l i p w a s used t o show some e f f e c t s of a c t i v e cont ro ls on a e r o e l a s t i c response of t h e B-52 and 6-5A i n f l i g h t and of models i n t h e wind tunnel.) CONCLUDING REMARKS This paper has attempted t o assess t h e v a l i d i t y of pred ic t ions obtained from dynamically scaled a e r o e l a s t i c models i n t h e Langley transonic dynamics tunnel t ha t uses Freon-12 as a test medium. To t h i s end wind-tunnel and f l i g h t - test r e s u l t s per ta in ing t o var ious a e r o e l a s t i c problem areas w e r e brought together i n one p lace fo r comparative evaluations. These areas include gus t and bu f fe t response, con t ro l sur face e f fec t iveness , f l u t t e r and active cont ro l of a e r o e l a s t i c e f f e c t s . Some bene f i t s and shortcomings of Freon-12 as a test medium were a l s o discussed e 252 Although some u n c e r t a i n t i e s remain, and t h e r e is t h e continuing need f o r improvements i n simulation and t e s t i n g techniques, t he r e s u l t s presented here in i n d i c a t e t h a t t h e pred ic t ions from wind-tunnel s tud ie s are, i n general , sub- s t a n t i a t e d by f u l l - s c a l e f l i g h t measurements. During t h e 15-year period s ince t h e Langley t ransonic dynamics tunnel w a s put i n t o operation, a e r o e l a s t i c s t u d i e s i n t h i s f a c i l i t y have provided a highly e f f e c t i v e means of gaining i n s i g h t i n t o new phenomena, ve r i fy ing a n a l y t i c a l methods, and e s t ab l i sh ing f l i g h t s a f e t y - espec ia l ly i n t h e important transonic range where present a n a l y t i c a l methods are usua l ly inadequate. F ina l ly , i t should be noted t h a t with t h e ex i s t ing c a p a b i l i t i e s of t he Langley transonic dynamics tunnel , it is o f t e n d i f f i c u l t t o f a b r i c a t e models l i g h t enough t o s a t i s f y mass-scaling requirements f o r cu r ren t a i r c r a f t designs. For f u t u r e designs, embodying composite s t r u c t u r e s and a c t i v e con t ro l systems, t h i s d i f f i c u l t y i s l i k e l y t o be compounded many fo ld . emerging problems, p lanning- i s underway t o increase , by 50 percent, t h e maximum power and thus t h e maximum s t agna t ion pressure of t he Langley transonic dynamics tunnel. To a l l e v i a t e t hese 253 REFERENCES 1, 2. 3. 4. 5. 6. 7 . 8. 9. 10. 11 e Rainey, A. Gerald; and Abel, Irving: Wind-Tunnel Techniques f o r t h e Study of Aeroe la s t i c E f fec t s on A i r c r a f t S t a b i l i t y , Control , and Loads. Aeroe las t ic E f f e c t s From a F l igh t Mechanics Standpoint, AGARD CP No. 46, Apr. 1969. Von Doenhoff, Albert E.; Braslow, Alber t L . ; and Schwartzberg, Milton A.: Studies of t h e U s e of Freon-12 as a Wind-Tunnel Tes t ing Medium. NACA TN 3000, 1953. Pozniak, 0. M.: I nves t iga t ion In to t h e U s e of Freon 12 as a Working Medium i n a High-speed Wind-Tunnel. Note No. 72, Col l . Aeronaut., Cransf ie ld (Engl.) , Nov. 1957. Treon, S t u a r t L. ; H o f s t e t t e r , W i l l i a m R.; and Abbott, Frank T . , Jr.: On t h e U s e of Freon-12 f o r Increasing Reynolds Number i n Wind-Tunnel T e s t - ing of Three-Dimensional A i r c r a f t Models a t S u b c r i t i c a l and Supe rc r i t i - ca l Mach Numbers. F a c i l i t i e s and Techniques f o r Aerodynamic Tes t ing a t Transonic Speeds and High Reynolds Number, AGARD CP No. 83, Aug. 1971, pp. 27-1 - 27-8. Yates, E. Carson, Jr.; Land, Norman S. ; and Foughner, Jerome T.: Measured and Calculated Subsonic and Transonic F l u t t e r C h a r a c t e r i s t i c s of a 45" Sweptback Wing Planform i n A i r and i n Freon-12 i n t h e Langley Transonic Dynamics Tunnel. NASA TN D-1616, 1963. Ehlers , F. Edward: A F i n i t e Difference Method f o r t h e Solu t ion of t h e NASA CR-2257, Transonic Flow Around Harmonically O s c i l l a t i n g Wings. 1974. Gilman, Jean, Jr.; and Bennett , Robert M.: A Wind-Tunnel Technique f o r Measuring Frequency-Response Functions f o r Gust Load Analyses. J. Aircraft, vo l . 3, no. 6, Nov.-Dec. 1966, pp. 535-540. Reed, W i l m e r H., 111; and Abbott, Frank T . , Jr.: A New "Free-Flight" Mount System f o r High-speed Wind-Tunnel F l u t t e r Models. Proceedings of Symposium on Aeroe las t ic & Dynamic Modeling Technology, RTD-TDR-63-4197, P t . 1, U.S. A i r Force, Mar. 1964, pp. 169-206. Hanson, Pe r ry W.: The P red ic t ion of S t r u c t u r a l Response t o Buffet Flow: A State-of-the-Art Review. (Munich, Germany), O c t . 1974. (Avai lable as NASA TM X-72627.) 39th AGARD S t r u c t u r a l and Materials Meeting Friend, Edward L.; and Monaghan, Richard C. : F l i g h t Measurements of Buffet C h a r a c t e r i s t i c s of t h e F-111A Variable-Sweep Airplane. NASA TM X-1876, 1969. Methods f o r A i r c r a f t S t a t e and Parameter I d e n t i f i c a t i o n . AGARD CP-172, Nov. 1974. 254 12 D 1 3 e 14. 15. 16. 17. 18. 19 * 20 e Mehra, Raman K,; Stepner , David E . ; and Ty le r , James S.: Maximum Like l i - hood I d e n t i f i c a t i o n of A i r c r a f t S t a b i l i t y and Control Der iva t ives . J. A i r c r a f t , v o l . 11, no, 2, Feb. 1974, pp. 81-89. Abel, I rv ing : Evaluat ion of a Technique f o r Determining Airplane Ai le ron Ef fec t iveness and Rol l R a t e by Using a n A e r o e l a s t i c a l l y Scaled Model. NASA TN D-5538, 1969. McAvoy, J. M. : C-14lA Empennage F l u t t e r S u b s t a n t i a t i o n With Revised E l e - v a t o r Balance Weights. Rep. No. ER-8471, Lockheed Georgia Co., June 15, 1966. Sandford, Maynard C. ; and Ruhlin, Charles L. : Wind-Tunnel Study of Deflected-Elevator F l u t t e r Encountered on a T - T a i l Airplane. NASA TN D-5024, 1969. Holloway, R. 3.: In t roduc t ion of CCV Technology I n t o Airplane Design. Aircraf t Design I n t e g r a t i o n and Optimizat ion, AGARD CP-147, v o l . 1, O c t . 1973. Doggett, Robert V. , Jr.; Abel, I rv ing; and Ruhlin, Char les L.: Some Experiences Using Wind-Tunnel Models i n Active Cont ro l S tudies . Advanced Control Technology and Its P o t e n t i a l f o r Future Transpor t A i r c r a f t , NASA TM X-70240, 1974. Thompson, Glenn 0.; and Arnold, James I.: B-52 Cont ro ls Configured Vehicle System Design. AIAA Paper No. 72-869, Aug. 1972. Redd, L. T . ; Gilman, J., Jr.; Cooley, D. E . ; and Seva r t , F. D. : Wind- Tunnel I n v e s t i g a t i o n of a B-52 Model F l u t t e r Suppression System. J. A i r c r a f t , v o l . 11, no. 11, Nov. 1974, pp. 659-663. Grosser , W. F. ; Hollenbeck, W. W . ; and Eckholdt, D. C l : The C-5A Active Impact of Active Control Technology L i f t D i s t r i b u t i o n Control System. on Airp lane Design, AGARD CP-157, O c t . 1974. TABLE I. COMPARISON OF SELECTED A I R AND FREON-12 PROPERTIES AT ATMOSPHERIC PWSSURE AND TEMPERATURE Proper ty Freon-12 A i r F r eon-l2/air S p e c i f i c h e a t , y 3 Densi ty , p, kg/m 1.13 4.896 1 . 4 0.807 1,226 3.99 Speed of sound, a, m / s e c 152 341 0.446 12.81 x 18.1 x 0.708 Viscos i ty , 1-1, N - s e c / m 2 255 MACH NUMBER: REYNOLDS NUMBER, FREON-12: 0 TO 2.59 x 106/m, (0 TO 8.5 x 106/ft) AIR: 0 TO 0.85 x 106/m, (0 TO 2.8 x 106/ft) TOTAL PRESSURE, abs DYNAMIC PRESSURE,FREON-IZ: 0 TO 16.8 kN/m2 (0 TO 350 lb/ft2t2, , AIR: 0 TO 10.1 kN/m2 (0 TO 210 Ib/ft2) TEST SECTION StZE: 0.69 TO 100 k W m 2 (0.1 TO 14.7 psia) 4.87 m x 4.87 m, (16 ft X 16 ft) Figure 1.- NASA Langley t r a n s o n i c dynamics trunnel. - - -0 - - FREON-12 (y = 1.13) -AIR (y = 1.40) 40r k = 0.06 0 .2 .4 .6 .8 1.0 NACA 64 006 XIC Figure 2.- Calculated p r e s s u r e d i s t r i b u t i o n s f o r o s c i l l a t i n g a i r f o i l i n a i r and i n Freon-12. 256 PNEUMATIC LIFT ALANCING DEVICE Figure 3 . - Some aeroe las t ic model t e s t ing fea tures i n the Langley transonic dynamics tunnel. GUST ANGLE ABSOLUTE VALUE, deg Figure 4.- Typical var ia t ion of gust flow angle with reduced frequency and lateral posi t ion f o r k6" osc i l l a t ing vane angle. c = 0 . 2 3 3 m.) (V = 3 5 . 4 m / s e c and 257 Figure 5.- V i e w of B-52 a e r o e l a s t i c model showing gust-generating vanes. PER d e g 0 .04 .08 .I2 .I6 .20 REDUCED FREQUENCY, k Figure 6 . - Frequency response of B-52 from f l i g h t tests and wind-tunnel model tests using gust- generating vanes * 258 M MODEL AIRPLANE 0.52 - 0 0.80 -- 0 1.17 ---- A cN 0.52 - 0 0.80 -- 0 0.90 ---- A 0.52 - 0 0.76 -- 0 0.81 ---- A 0 4 8 12 16 20 ANGLE OF ATTACK, deg Figure 7.- Comparison of model and a i rp l ane v a r i a t i o n with angle of a t t a c k ( re f . 9 ) . CN 1 . 5 r e AIRPLANE A = 2h0 -_ C. G. 0 MODEL M = 0.76 INDICATED AIRPLANE 6 ACCELERATION, PERCENT DES I GN .5 */ BUFFET ONSET HORIZONTAL TAIL BENDING MOMENT, .% PERCENT DESGIN 0 WING ROOT BENDING MOMENT, .50 PERCENT DES I GN I I I 1 1 1 I 1 0 .4 - .8 1.2 cN Figure 8.- Comparison of b u f f e t response from air- plane and model tests normalized t o a i r p l a n e design loads. M = 0.76; 26" wing sweep ( r e f . 9 ) . 259 .04 .03 ROLL EFFECTIVENESS Pb rad .02 .01 O b DYNAMIC PRESSURE Figure 9.- Comparison of flight measurements and model-predicted aileron effectiveness (ref. 1). - - MODEL PREDICTION C pb ' b 2V Clp bA - FROM - - - \ \ O I I "KEAS ' knots Figure 10.- Comparison of flight measurements and model-predicted flutter of T-tail with deflected elevator (ref. 15). 260 AIRPLANE --- MODEL FMC OFF 0 FMC OFF FMC ON A FMC ON - .32 .24 DAMPING, 9 .I6 .08 - - - - - - - - b Figure 11.- Effect of flutter mode control system on damping of B-52 CCV model and airplane (ref. 19). Figure 12.- Model of C-5A with active lift distribution control system in Langley transonic dynamics tunnel. 261 RESPONSE TO SINUSOIDALAILERON SWEEP INPUT NORMALIZED BENDING MOMENT AIRPLANE AT WING ROOT .6 ~ MODEL 1.0 - .8 - 4 0 1 2 3 4 0 1 2 3 4 FREQUENCY, Hz FREQUENCY, Hz Figure 13 .- Characteristics of C-5A active lift distribution control system determined in wind-tunnel and in flight tests. 262 PANEL DISCUSSION THEORETICAL ANALYSIS VERSUS TESTING - A TRADE-OFF Holt Ashley, Stanford University, Moderator: Good evening. L e t m e welcome t h i s knowledgeable and experienced audience t o our vane1 discussion. Theoretical Analysis Versus Testing - A Trade-off. Now i n view of t h e t i t l e t h a t w a s assigned t o those who serve i n t h i s panel, I th ink it i s probably a good thing t h a t t h e event occurred a t t h i s t i m e and t h i s p lace on t h e program, a f t e r everyone has had a b ig dinner and a couple of drinks. A t least i t might g ive some of u s , above and beyond my f r i end John Houbolt, t h e courage t o take t h e extreme pos i t i ons t h a t w i l l be required f o r success on our p a r t and entertainment f o r you. before I go on, and t h a t is , I would l i k e t o add my congratulations t o t h e o ther remarks t h a t have been made informally and today's var ious speakers. I r e a l l y have t o say t h a t I've been t o seve ra l hundred AIAA meetings of var ious kinds, and I have not heard a more i n t e r e s t i n g and informative group of papers than were presented t h i s afternoon. Furthermore - and t h i s you do not a l l know - t h e r e w a s somehow arranged f o r a s m a l l group of us , a t t h e end of our lunch hour, t h e most dramatic f l i g h t test demonstration tha t has ever been my pleasure t o see. Standing out i n f r o n t of t he hangar we f i r s t s a w the B-1 f l y ing overhead, i n a l l i ts glory on i t s way t o some low-level f l i g h t test. Perhaps Harold Sweet w i l l say something on t h a t later t h i s evening. Shor t ly the rea f t e r , w e watched t h e X-24B drop off a B-52 and perform one of i t s f i n a l dead-stick approach and landing f l i g h t s . t h a t w e watched i t a l l the way from release t o touchdown. It w a s q u i t e a t h r i l l . I f you have read the program, the t i t l e is I do want t o make a semiserious remark The weather w a s so g rea t I don't know what i t has t o do with f l u t t e r , bu t w e apprec ia te it. Now l e t m e begin t o introduce the panel members. S t a r t i n g from your r i g h t a t the end of t h e tab le : Gene Baird - Grumman Aerospace Corporation M. Jonathan Turner - Boeing Commercial Airplane Co. Professor Ed Garrick - The most unre t i red " re t i red" NASA s c i e n t i s t a t Langley Research Center; he a l s o worked a t MIT f o r a year i n the 1950's. Harold S w e e t - B-1 Division, Rockwell In t e rna t iona l David E. Brandt - Vice Pres ident , Engineering, of Enstrom Helicopter Corporation; by t h e way, he got o u t of MIT i n 1960 and made Vice President i n j u s t 15 years; he went t he re j u s t two months ago from Boeing Vertol Company. 263 We welcome you a l l , gentlemen, and w e are looking f o rd t o hear what you have t o say, L e t m e b r i e f l y descr ibe t o you w h a t a criminal i nves t iga to r would c a l l t he M.0, of t h i s panel. Af te r I relieve myself of a few words and remarks, I plan t o c a l l on t h e p a n e l i s t i n a lphabet ica l order, There i s no o ther f a i r way t o do i t except reverse a lphabet ica l order. Now, hopefully, t h e let ter t h a t I wrote t o each p a n e l i s t w i l l have t h e following e f f e c t . expected va lue of t he t i m e used f o r t h e i r t a l k s w i l l be f i v e minutes, with a sigma of not t o exceed two minutes. i n t e r a c t wi th one another i n t h e way of questions and comments f o r however long t h a t takes, perhaps 15 t o 20 minutes. t h e bes t t i m e of a ceremony of t h i s kind - i s fo r questions and comments from t h e audience, That t he Then I s h a l l t r y t o s t imula te them t o Afterwards - t h i s I be l ieve i s always So l e t m e say two things about t h a t : 1, Please s ta r t thinking up your tough questions now 2. When you f i n a l l y have t h e opportunity, please w a i t f o r t h e microphone and i d e n t i f y yourse l f , so t h a t your name and company may be recorded on t h e t a p e W e are recording a l l of t hese comments and questions. up by 9:OO p.m. because your moderator has t o catch a 1 2 : O O f l i g h t from L.A. tonight. Hopefully, we can break Now something about t h e subjec t which we've been asked t o address. A s someone whose cont r ibu t ions have been l a r g e l y t h e o r e t i c a l , you might expect m e t o take t h e t h e o r e t i c a l s i d e of t he i s s u e t h a t w e are t a lk ing about, but ac tua l ly I am not going t o do tha t . be t h e Devil 's Advocate and t a l k about t h e wonders of theory t h a t w e a l l be l ieve in . I hope perhaps Ed Garrick w i l l come and I would l i k e t o point ou t t o you t h a t t h e top ic w e have been given i s iden t i f i ed wi th a trade-off. W e have not been presented with an inexorable choice between two extreme a l t e r n a t i v e s . va l ida t ion o f any new design, by M i l . Specs. o r FAR'S o r whatever, c o n s i s t s of a c lose ly coordinated succession of t h e o r e t i c a l analyses of var ious degrees of complexity wi th wind-tunnel test on models of reasonable soph i s t i ca t ion and f i n a l l y a f l i g h t test program. I th ink t h a t what w e should be addressing tonight, as a func t ion of t h e type of a i r c r a f t , i t s s i z e and in t en t ion , i s what is t h e proper balance among those var ious c l a s ses of a c t i v i t i e s t h a t cont r ibu te t o t h i s a c t i v i t y of f l u t t e r validatiofi . W e heard today a l o t about t he cos t of model t e s t i n g and f l i g h t t e s t ing . I n f a c t , I don't t h ink t h a t t h e argument w a s s e t t l e d on which i s more expensive: t o do a f l i g h t f l u t t e r t e s t i n g program on an a i r p l a n e o r t o bui ld a model and test i t i n t h e TDT. A s you a l l know, the f l u t t e r A t t he same t i m e , I th ink you w i l l agree with m e that our a n a l y t i c a l t o o l s are improving s t e a d i l y and tha t computer cos t s (per cycle o r per operation) are decreasing very rapidly. It may w e l l be t h a t , e i t h e r today o r some t i m e i n t h e fu tu re which w e might attempt t o determine, w e are re ly ing more than i s necessary on t h e experimental p a r t of t h e spectrum I described 264 and not enough on t h e a n a l y t i c a l pa r t . are not aware of i t t h a t Clarence Perish0 had a s o r t mind when he picked our topic, anybody wants t o look a t i t , It is an ar t ic le by Dean Chapman, Hans Mark and M e 1 P i r t l e , e n t i t l e d "Computer vs. Wind Tunnels f o r Aerodynamic Flow Simulations,' ' published i n t h e Apr i l 1975, i s s u e of Astronautics and Aeronautics (a magazine sent out by an obscure aeronaut ica l soc i e ty ) , ar t ic le makes some very con t rove r s i a l statements, t o t h e h i s t o r i c a l examples from b a l l i s t i c s , o r b i t a l mechanics, and thermal neutron f l u x i n moderated r eac to r s , as being places where t h e computer e s s e n t i a l l y took over from experiment or test as the d e f i n i t i v e way of designing and v a l i d a t i n g t h e design of t hese devices. massive leap t o f l u i d mechanics generally, as a so lu t ion t o the Navier-Stokes equations including, God help them, turbulent flow and separation. They state t h e conviction t h a t t h e same process w i l l t ake place i n t h a t area. L e t m e read j u s t th ree quotations from t h i s article: I should mention t o those of you t h a t It happens t h a t I bro That They start out by pointing They then make a I 1 A s computers have improved, aerodynamicists progressively improved approximations t o the f u l l governing equations of motion. This h i s t o r i c a l process should continue, i n general, u n t i l computers y i e l d de t a i l ed so lu t ion of t h e Navier-Stokes equation i n p r a c t i c a l t i m e and cost." [implied a t any Reynolds number.] Two developments w i l l be necessary: 11 a. Accurate turbulence models appl icable t o separated and attached flows. b e Computer c a p a b i l i t i e s two orders of magnitude grea te r than ILIAC IV." is their requirement f o r j u s t g e t t i n g t o t h e po in t where t h e r e is a chance of dupl ica t ing the wind tunnel.] And f i n a l l y , they say t h a t t o d isp lace wind tunnels as t h e p r inc ipa l [This source of flow ca lcu la t ion fo-r a i r c r a f t design, computers must reach t h e speeds of 104 t i m e s t h a t of ILIAC I V . They make t h e argument t h a t i t is poss ib l e tha t i n t h e 1980's o r t h e 1990's w e may indeed see computers of t h i s type. The rest of t h e i r conclusions you can draw f o r yourse l f . L e t m e make t h e point t h a t , when it has t o do with what w e ca l l "classical f l u t t e r , " t h e i r argument may be more va l id f o r our area than it i s f o r t h e one they are ta lk ing about. I w i l l g ive you t h r e e reasons: 1. We are reasonably s u r e about Newton's l a w s of motions, even when they are expressed i n terms of an adequate number of modes of f r e e v i b r a t i o n and the generalized coordinates f o r ca lcu la t ion . 265 2, The s t r u c t u r e s s p e c i a l i s t s , p a r t i c u l a r l y i n t h e area of f i n i t e ele- ments, have been working longer with compu S d mechanics ever have, I would claim w e are a l o t c lose r t o a very e f f e c t i v e descr ip t ion , For example, small per turba t ion analyses are based on t h e f a c t t h a t t he s t r u c t u r e has y i e l d s t r a i n s i n t h e order of 2/10 of 1 p e r cent. Where are you going t o see per turba t ions t h a t s m a l l i n f l u i d mechanics? 3 . I be l i eve w e a r e o f t en j u s t i f i e d i n using small-perturbation gas dynamics, perhaps even i n t h e case B i l l Rodden ca l l ed a t t e n t i o n t o t h i s afternoon. When w e can do that, sure ly w e are i n b e t t e r shape than Chapman and company w i l l be with t h e Navier-Stokes equation i n t h e pred ic t ion of turbulence. So perhaps t h e question i s not whether t h i s theory w i l l be playing a much l a r g e r r o l e i n f l u t t e r , bu t r a t h e r when. Eugene F. Baird, Grumman Aerospace Corporation: The subjec t f o r the panel discussion t h i s evening i s forcing us t o look i n t o the c r y s t a l b a l l . However, looking i n t o the f u t u r e i s a necessary f i r s t s t e p i n planning t h e f u t u r e resources t h a t w i l l be required by t h e Aerospace Industry f o r f l u t t e r prevention. I n response t o the ques t ion as t o whether there is p o t e n t i a l f o r trade- o f f s between ana lys i s and test f o r f l u t t e r prevention, t h e answer i s obviously yes. But as t o whether these trade-offs can be r ea l i zed i n t h e fu tu re , a l l I can do i s make c e r t a i n observations which might help t o i d e n t i f y t h e p re requ i s i t e s f o r t hese trade-offs. The p a r t i c u l a r trade-off which I wish t o consider is a reduction i n t h e c o s t of f l u t t e r prevention procedures through an increased emphasis on analyses and a consequent reduction i n tests while maintaining t h e s a m e degree of assurance of t h e e f fec t iveness of t h e f l u t t e r prevention procedures. The f a c t t h a t ana lys i s i s less c o s t l y than test, using cu r ren t state-of-the-art techniques i n both d i s c i p l i n e s , i s not d i f f i c u l t t o show. We r e a l i z e , however, t h a t the-ana lys i s techniques cur ren t ly being used are not s u f f i c i e n t l y accura te t o permit a reduction i n t h e amount of t e s t i n g and i t s associated cos t s . The use of more sophis t ica ted computer programs which y i e ld accurate f l u t t e r r e s u l t s throughout t h e speed regime w i l l obviously involve an associated increase i n computational require- ments and an increase i n t h e number of computer analyses. I f we ex t r apo la t e t h e trend of computer development and assoc ia ted cos t of performing a given mathematical problem versus t i m e , i t is apparent t h a t t h e cos t s are reducing q u i t e s ign i f i can t ly . The question t h a t w e have t o address, however, is whether t he s i g n i f i c a n t i nc rease i n s i z e of computer programs required t o perform these more sophis t ica ted f l u t t e r analyses as a s u b s t i t u t e f o r test w i l l s t i l l r e s u l t i n a v i a b l e trade-off. A t t h i s po in t , i n order t o put my d iscuss ion i n t o perspective, I would l i k e t o i n d i c a t e t h e ove ra l l f l u t t e r prevention cos t s incurred i n t h e development of t h e F-14 f i g h t e r a i rp l ane ( t ab le 1 ) . Two important f a c t s are 266 apparent i n t h i s t a b l e , TABLE 1,- FLUTTER PREVENTION COSTS FOR F-14 ANALYSIS 29% 27% 7 WIND TUNNEL GVT 19% } 71% FLIGHT TEST 25% J R&D COSTS 0.48% One i s t h a t t h e c o s t of t e s t i n g , without cons ider ing a l a r g e investment i n test equipment and d a t a a c q u i s i t i o n systems, accounted f o r 7 1 percent of t h e t o t a l c o s t . The o t h e r f a c t i s t h a t f l u t t e r prevent ion accounted f o r on ly 0.48 pe rcen t of the t o t a l r e s e a r c h and development cos t s . ha l f a percent of t h e R&D c o s t s t o be almost " i n t h e no i se level". one must recognize the l a r g e r number of d i s c i p l i n e s involved i n aerospace vehicle development. The repercuss ions of each d i s c i p l i n e dec id ing i ts own c o s t s are a l s o " i n t h e n o i s e level". u s t o cons ider how w e can c u t down t h e c o s t s a s soc ia t ed w i t h our own p a r t i c u l a r d i s c i p l i n e e One might cons ider However, There i s obviously a need f o r a l l of There i s one o t h e r f a c e t of the a n a l y s i s v e r s u s test trade-off which I haven ' t d i scussed t o t h i s p o i n t , b u t which I cons ider t o b e ve ry important. T r a d i t i o n a l l y i n my company, and I r m s u r e i n most o the r companies, most t e s t i n g occurs a t a po in t when t h e design i s w e l l def ined . model f l u t t e r t e s t i n g must n e c e s s a r i l y occur a t a t i m e when most of t h e s t r u c t u r a l c h a r a c t e r i s t i c s of t h e a i r p l a n e have been "immortalizedt' i n d e t a i l e d des ign drawings. Consequently, i f a problem is uncovered a t t h a t p o i n t , t h e r e can b e l a r g e c o s t repercuss ions . The f a c t t h a t ana lyses of t h e d e t a i l e d des ign conf igu ra t ion i n e v i t a b l y precede t h e test phase i s an important f a c t o r . I f w e could ana lyze t h e conf igu ra t ion w i t h a g r e a t e r degree of confidence, t h e p o t e n t i a l f o r des ign changes a t a l a t e s t a g e i n development could be s i g n i f i - c a n t l y reduced. I n f a c t , proof Most of what I have s a i d t o t h i s po in t i s somewhat on t h e ph i losoph ica l level, bu t l e t u s now g e t down t o engineer ing f a c t s . An obvious p r e r e q u i s i t e t o increased r e l i a n c e on a n a l y t i c a l techniques is t h e development of more complex mathematical models which address t h e v a r i o u s d i s c i p l i n e s a s soc ia t ed w i t h f l u t t e r ( t h a t is, aerodynamic, s t r u c t u r a l , and c o n t r o l system ana lyses) and which y i e l d r e s u l t s t h a t are cons iderably more accu ra t e than have h i t h e r t o been achieved. has g iven us a p r o j e c t e d requirement of computer resources ve r sus aerody- namic a n a l y s i s c a p a b i l i t y which i n d i c a t e s that t h e t r a n s i t i o n from i n v i s c i d nonl inear t r a n s o n i c aerodynamic ana lyses t o v i s c o u s ana lyses , inc luding s e p a r a t i o n e f f e c t s , w i l l r e q u i r e a n inc rease i n computer c a p a b i l i t y of two I n t h e f i e l d of aerodynamics, Chapman's r ecen t paper 267 orders of magnitude over ILLIAC IV, o s c i l l a t o r y flow associated wi th f l u t t e r i s a n area which has not been w e l l investigated o r quant i f ied , I n view of the s i g n i f i c a n t d i f f e rences i n required computer resources, a va luable i n i t i a l s t e p in minimizing the cos t of develop- ment of r e l i a b l e mathematical techniques f o r pred ic t ion of unsteady aerodynamic fo rces would be t o perform planned series of tests t o a s c e r t a i n t h e types of configuration and t h e f l i g h t conditions f o r which evolving inv i sc id t ransonic aerodynamic ana lyses are appl icable and a l s o t o i d e n t i f y t h e regimes where viscous e f f e c t s are important. t ransonic f l u t t e r , and panel f l u t t e r . Howeverp the r o l e of viscous e f f e c t s i n Such subjec t areas would include buzz, I n t h e s t r u c t u r a l ana lys i s d i s c i p l i n e , finite-element methods are now rou t ine ly used wi th a high confidence level f o r * l i n e a r systems; however ,. t he re have been many examples i n recent years of discrepancies between s t r u c t u r a l ana lys i s and test. This obviously, from a f l u t t e r viewpoint, includes the pred ic t ion of v i b r a t i o n mode shapes and frequencies. r econc i l i a t ion between t h e two has been demonstrated by more de t a i l ed study of some aspec ts of t h e s t ruc tu re . This is p a r t i c u l a r l y t r u e of complex j o i n t s , nonlinear elements (such as t h i n panels c lose t o buckling), o r areas wi th d i f f e r e n t load paths i n tens ion and compression. However, after-the-fact explanation of discrepancies are not s u f f i c i e n t . ana lys i s and test i s t o exist, t h e ana lys i s must be co r rec t t he f i r s t t i m e . I n t h e s t r u c t u r a l ana lys i s d i s c i p l i n e , perhaps we must i nves t iga t e t h e need f o r more complex, t ha t is t o say higher order , s t r u c t u r a l elements o r even nonlinear elements. I n many ins tances , I f a real trade-off between The t h i r d d i s c i p l i n e t o address i n terms of improved mathematical modeling is cont ro l system ana lys is , which is playing an increas ingly important r o l e i n f l u t t e r prevention because of the increased emphasis on a c t i v e con t ro l systems t o enhance a i rp l ane performance. Current problems include t h e pre- d i c t i o n of hydraulic ac tua tor impedance c h a r a c t e r i s t i c s and the p red ic t ion of a c t i v e c o n t r o l system feedback s igna ls . very much i n t e r r e l a t e d wi th t h e accuracy of pred ic t ion of v ib ra t ion modes. This is a highly i n t e r a c t i v e subject area i n which recent a i rp l anes have experienced problems which could conceivably be very c o s t l y i n t h e i r resolu- t i o n unless w e can be assured t h a t we have good aerodynamic, s t r u c t u r a l , and c o n t r o l system modeling. This l a t te r problem i s obviously I n summary, whether s i g n i f i c a n t trade-offs between analyses and test w i l l e x i s t i n t h e f u t u r e remains t o be seen. The f a c t is t h a t t h e earlier w e can i d e n t i f y a problem through enhanced ana lys i s c a p a b i l i t i e s , the less c o s t l y t h e o v e r a l l a i rp l ane procurement program w i l l be. There i s no question t h a t w e should continue t o d i r e c t our e f f o r t s toward more accura te ana lys i s techniques, But, it appears t h a t these techniques w i l l not be a v a i l a b l e u n t i l some t i m e i n t he fu tu re . Un t i l they are a c t u a l l y i n hand, w e must obviously continue t o concentrate on increas ing t h e e f f i c i ency of t e s t i n g , which I be l i eve w i l l maintain i t s v i t a l r o l e i n f l u t t e r prevention. 268 David E. Brandt, Enstrom Helicopter Corporation: I ' m probably t h e only one i n t h i s panel who w i l l address t h e r o t a r y wing f i e l d , barrel ' ' so t o speak, where of course ro to r R & D has always been. I had r e a l l y hoped t o be l a s t on t h e agenda, a t t h e "bottclm of t he The top ic of t h i s panel-discussion, "Theoretical Analysis Versus Testing - A Trade-off" almost leaves m e speechless because i n t h e t echn ica l world of t h e l i f t i n g r o t o r , he l i cop te r , tilt ro to r , and machines of t h i s type, t h e debate of theory versus t e s t i n g f o r t h e o r e t i c a l v e r i f i c a t i o n almost cannot begin without addressing t h e question, "Where is t h e theory?'' Now t h i s is a relative statement, of course. I have t o compare myself t o t h e fixed wing technologis t s who abound here t h i s evening and, t o draw on an analogy appropr ia te f o r an a f t e r dinner speech, who s e l e c t t h e i r a n g l y t i c a l t o o l s from a smorgasbord of t h e most de l ec t ab le gourmet dishes. technologist , on t h e other hand, s e l e c t s h i s d i shes from a skid row garbage dump. My twenty years on skid row, watching t h e f a t c a t of t h e classical f l u t t e r f i e l d f i l i n g poin ts on "T's" i n t h e word " f l u t t e r " t o make it look a l i t t l e sharper, c e r t a i n l y have taught m e t h e i n t e r n a l fu ry i n the word knowing who's r e a l l y having t h e fun. A r o t o r discrimination" and, by t h e same token, t h e b i t te rsweet s a t i s f a c t i o n of I 1 The ser ious aspect of t h i s untenable s i t u a t i o n i s that t h e customer of a r o t a r y wing veh ic l e , who has a job t o do and who wants progress, continues t o reach forward without ever having done h i s homework. of d o l l a r s , i f no t hundreds of mi l l i ons of d o l l a r s , on hardware programs, whereas one percent of these d o l l a r s applied t o fundamental ana lys i s t o understand what he i s dealing wi th would have put him money ahead. wi th a three hundred mi l l ion d o l l a r f i a sco , such as t h e Cheyenne program, which unquestionably has had a long-range impact i nh ib i t i ng t h e development of today's so badly needed l i f t i n g ro t a ry , short-haul vehic les . No wonder t h e indus t ry i s scared t o death t o change more than one l i t t l e screw per decade i n a r o t o r system, when t h e only th ing they know about i t i s w h a t they l e a r n by experience. The fundamentals are not understood; t h e a n a l y t i c a l base t o support him is, f o r t he most p a r t , unverified. H e blows mi l l i ons W e end up The lack i n leadersh ip and v i s ion , t h a t pushed members of my p a r t of t h e aerospace indus t ry i n t o t h i s s i t u a t i o n , c e r t a i n l y has t o be shared by both indus t ry and goyernment agencies a l i k e . It is my opinion, i n p a r t i c u l a r , that t h e blame had t o f a l l heav ie s t on t h e government agencies. It i s one th ing t o r a t i o n a l i z e tha t today's indus t ry leaders grew up i n t h e he l i cop te r indus t ry , i n t h e b icyc le shop days, where they b u i l t hardware and t e s t e d it . Then they would put every c r u t c h they could j a m i n t o t h e shotgun t o t r y t o f i x it, never r e a l l y knowing where t h e successes came from. We can blame i t on them i f w e want t o . But today, when w e f ind the b e s t t echnologis t s i n t h e indus t ry who have grown up and have become program managers doing t h e thing and spending mi l l i ons of d o l l a r s f o r experimental development and not one n i cke l f o r fundamental ana lys i s , you start looking f o r t h e source of t h e problem. 269 Money cons t r a in t s , schedule cons t r a in t s , and competitive constraints-- we've faced these things through a l l of our careersI the re , There is nothing new My question is, "Where is t h e government leadership?" Who is sponsoring research so t h a t t h e industry manager has a t o o l t o l ean on t h a t he can t r u s t and have confidence in? Where is the guy who asked t h e questions that put us a l l t o t h e test i n pro tec t ing t h e public i n t e r e s t and challenged what i s going on? Everyone who i s i n t h i s room w e l l knows t h e team e f f o r t t h a t goes on between t h e guy i n government and t h e guy i n industry and how w e g e t along t o ge t a profess iona l job done. A c l a s s i c scenar io w i l l i l l u s t r a t e t h e many f a c e t s of t h i s teamwork. You have been s t ruggl ing f o r a year t ry ing t o f i x t h e hor izonta l s t a b i l i z e r . I t ' s the one th ing tha t i s i n your mind t h e day you're sent off t o t h e customer on another i s sue , but, of course, t h e first th ing your boss te l ls you is, "Handle t h e problem but don't t a l k about t he hor izonta l s t a b i l i z e r . " g r e e t s you wi th " H i Dave, how i s your wife?" You walk i n t o your counterpar t ' s o f f i c e and he "The problems with t h e hor izonta l s t a b i l i z e r a r e n ' t as bad as you probably hear, Harry." " Y e a , I know; i f you don't understand t h e fundamentals, you don't know youtve r e a l l y fixed i t throughout t h e whole f l i g h t envelope, and you are concerned about f a i l - s a fe implications t o w h a t you have done." guess you are going t o i n s i s t w e go back and use some fundamental ana lys i s , a r e n ' t you?'' "I "Unhuh" is Harry's reply. You g r i t your t ee th and a t home you r e p o r t , "Boy, t h a t Harry is r e a l l y sharp. your old p iece of t a i l doing?' explain what t h e requirements are tha t must be m e t and t h e questions that must be answered. t r y i n g t o do t h e last year. I d i d n ' t even ge t a chance t o s i t before he s a i d , 'Oh Dave, how i s Then h e bore r i g h t down on me." You go on t o Then you proceed t o do t h e fundamental ana lys i s t ha t we've been I It sounds easy? It used t o be, but f o r a t least f i v e years I haven't been a b l e t o f ind anybody t o a sk m e any questions o r write a letter of challenge with some t e e t h i n i t which g e t s t h e management's a t t en t ion . I be l ieve t h e hingeless r o t o r is t o t h e short-haul t r anspor t a t ion of t h i s country what t h e swept-wing j e t w a s t o commercial av ia t ion . Lockheed t r i e d t o make it work (as w e l l as several o thers ) and with providence smiling had some success with XH-51. The Army, f r u s t r a t e d and hungry f o r progress, took the b a i t and t h e r e s u l t w a s almost t h e death of t h e hingeless r o t o r , How can you scale up a successful a i r c r a f t i n t o something d i f f e r e n t when you don't understand the fundamental parameters t h a t a f f e c t the a e r o e l a s t i c s t a b i l i t y ? How can you bui ld an a e r o e l a s t i c a l l y scaled wind-tunnel model i f you don't know even simple f a c t s l i k e whether t h e con t ro l system's s t i f f n e s s i s an important parameter? 270 got burned $300 mi l l i on worth, they responded by c r e a t i n g L which i s probably more than NASA w a s seduced t o b i l i t y Research & Development Lab o ry system, There are e l y 650 people doing r e sea rch i n t h e e n t i r e he l i cop te r i ndus t ry by a s i g n i f i c a n t amount. bed by the Army (or vice versa) ,and f o r t h e f i r s t t i m e i n decades, NASA began t o g ive the appearance of waking up t o i t s r e s p o n s i b i l i t i e s i n the r o t o r wing f i e l d . By now you say , s ince t h i s has a l l happened f i v e years ago, t h e state- of-the-art should r e a l l y be moving along, we ought t o b e doing g r e a t , The f a c t is t h a t t h e h e l i c o p t e r i ndus t ry e f f o r t s d i r e c t e d a t fundamentals are p r a c t i c a l l y a t a s t a n d s t i l l . The indus t ry is being s ta rved t o death. Some of the most competent people i n t h i s business are now working f o r t he Army. They are i n t e r e s t e d i n t h e advancing of t h e s ta te-of- the-ar t , bu t only as long as they can do it themselves. tlYes,'' they say, " those are r e a l l y good ideas , and t h e work needs t o be done. w e don ' t want t o burden ourse lves monitoring your con t r ac t s . else," And that's the way it 's been f o r a long time, We c a n ' t g ive you any support because G e t somebody You know that you are not going t o use an ana lys i s somebody else developed unless you have used i t f o r enough yea r s t o have some confidence i n it. I f you don ' t t r u s t i t , you don't use i t , and you s u r e won't cormnit t o a hardware program unless your management is prepared t o fund a b r u t e f o r c e experimental e f f o r t t o make i t work. Five years ago, t h e Boeing Ver to l Company thought they had learned a l i t t l e b i t about h inge le s s r o t o r s , having had a c l o s e a s soc ia t ion with the "by dumb luck" success fu l BO-105. To s a t i s f y t h e Army's UTTAS program, they s tuck t h e i r necks o u t with not one but two h inge le s s r o t o r s (main and t a i l ) which were of d i s t i n c t i v e l y d i f f e r e n t types. (Phi losophical Note: I f you th ink t h e customer won't be l i eve you when you say you can " leap t a l l bu i ld ings with a s i n g l e bound," t e l l him you can l eap two t a l l bui ld ings with a s i n g l e bound - backwards and bl indfolded.) Today, I a m happy t o r e p o r t t h a t t h e Ver to l UTTAS i s , i n f a c t , a t r u l y superb machine, and I be l i eve t h a t i t w i l l set t h e indus t fy s tandard f o r t h e next two decades. f o r guidance, w i th a l o t of wind-tunnel t e s t i n g on dynamic models, w e managed t o make t h e main r o t o r s t a b l e as predicted. a f t e r solving only seven d i s t i n c t d i f f e r e n t modes of a e r o e l a s t i c i n s t a b i l i t y , i s s t a b l e as a rock today. Three years i n t h e wind tunnel , and I can ' t t e l l you how many m i l l i o n s of d o l l a r s , bu t not two c e n t s f o r fundamental a n a l y s i s t o g ive us some guidance of how t o go. Don't change a screw, don ' t change t h e weight of p a i n t on t h e r o t o r , don ' t use a d i f f e r e n t manufacturing process , and everything w i l l be a l l r i g h t . About midyear, be fo re I l e f t t h i s program, they wanted t o change t h e manufacturing process f o r th is t a i l r o t o r . "How much w i l l i t c o s t t o bu i ld i t , Dave?" I looked him i n the eye and s a i d , "How about a m i l l i o n bucks, Harry?" and he d idn ' t b l ink , s o I s a i d , "This year," and eventua l ly got him t o b l ink . Using the unver i f ied a n a l y s i s drawn from the "garbage p i t " Even t h e t a i l r o t o r , 2 7 1 write a le t ter - a le t ter wi th t t o t h e management and get on t h e "fundamental" job t h a t needed t o be done. I despair t h a t t h e research t h a t provides t h e bas i s f o r tomorrow's developments w i l l continue a t t h e slow, uncoordinated pace that t h e i n t e r n a l government engineers w i l l f i n d comfortable, now I one of t h e management i n my own l i t t l e b icyc le shop, and a l l I can say is, "Oh, WOW! And here I sit before you today, Where is t h e leadership?" I. E. Garrick, NASA Langley Research Center: I remember v i s i t i n g a museum ship near Stockholm - an old s a i l i n g vessel that had been recovered from t h e sea bottom and res tored ; it had capsized on its launching wi th much l o s s of l i f e - i n p a r t i c u l a r , that of the marine engineer who had designed it , H e w a s summarily executed! So a l s o t h e real test of an a i r c r a f t , regard less of a mountain of ground work, i s i t s f l i g h t - worthiness, and we would p r e f e r not t o extend the analogy of the marine engineer t o t h e f l u t t e r engineer. account of t h e h i s t o r y of f l i g h t f l u t t e r t e s t i n g i n t h e 1958 forerunner symposium, where p i l o t s i n e a r l y f l u t t e r tests were reassured when t h e f l u t t e r engineer went along on t h e f l i g h t (and Tolve, who d id accompany many such f l i g h t s , implied t h a t t h e p i l o t had more f a i t h i n him than he had i n himself) . Some of you may recall Leon Tolve's 1 am pleased t o have had a r o l e i n suggesting t h e republ ica t ion of t h e proceedings of t he 1958 symposium - t he document w a s dec l a s s i f i ed only i n 1971. It is a valuable document both by i t s e l f and aga ins t which t o measure 17-1/2 years of change; and perhaps, face t ious ly , t h i s panel provides a unique ee t o eat o r t o repeat our previous words. F l igh t f l u t t e r t e s t i n g i s t h e search f o r exposing poss ib le low damping regions of f l i g h t ; it i s without doubt t h e most sophis t ica ted type of f l i g h t test; and o f t e n i t provides a shakedown of o ther t rouble areas as w e l l . i s obvious t h a t w e would l i k e t o reduce t h e amount of f l i g h t f l u t t e r t e s t i n g required t o a minimum. But consider, f o r example, t h e space s h u t t l e and i t s o r b i t e r where f l i g h t t e s t i n g i n t h e t r a d i t i o n a l sense is not f e a s i b l e . f i r s t f l i g h t test of the o r b i t e r i s scheduled t o take p lace i n 1977 by re leas ing it from i t s c a r r i e r B-747 a i rp lane . which need t o be a t low dynamic pressure r e l a t i v e t o those of e i t h e r the s h u t t l e launch or t h e o r b i t e r reentry, in ferences must be drawn on i t s complete f l i g h t sa fe ty . with model, component, and f u l l vehic le ground tests. Clearly, g r e a t r e l i a n c e is being placed on t h e "math models'' used i n design and development. By math model w e now mean r e a l l y a mathematical engineering model composed of f i n i t e elements r a t h e r than t h e phys ic i s t ' s model of mathematical equations. It The From a few such proof f l i g h t s , Comparisons must be made with many ca l cu la t ions and The complete s h u t t l e vehic le , with i t s l iqu id f u e l tank, twin s o l i d boosters, and o r b i t e r , p resents numerous s t a b i l i t y , loads , and dynamics problems i n i t s ascent configuration and, s imi l a r ly , many cont ro l and 272 s t a b i l i t y problems on i t s o r b i t e r reentry. Analysis involving subs t ruc tur ing methods w i l l play a c e n t r a l r o l e here, too, i n t h e i d e n t i f i c a t i o n and so lu t ion of these problems, as w i l l a l s o t h e use of simulators and model and component ground tests, The uses of f i n i t e element methods i n s t r u c t u r e s and of similar methods i n aerodynamics are two of t h e major changes t h a t have taken place i n t h e pas t 17 years. f l u t t e r test methods may be t raced t o the space program. have, of course, been e s s e n t i a l t o t h e space program with t h e real-time ca lcu la t ion of o r b i t s and con t ro l of spacecraf t ; and, i n t u r n , by feedback, t he space program has l ed t o g rea t ly improved computer hardware and software. Continuous improvements i n both f l igh tborne micro-computers and ground-based computers have profoundly a l t e r e d t h e outlook on t h e balance of test and ana lys i s . Consider t h a t real-time test and d a t a ana lys i s permit t he t i m e dura t ion and t h e number of f l i g h t s i n f l u t t e r t e s t i n g t o be g r e a t l y reduced and t h a t t h e latest generation of computers are capable of more number opera- t i o n s (such as a 64-bit number addi t ion) i n a second than t h e r e are seconds i n a year: Purely numerical methods are rap id ly multiplying throughout aerody- namics and s t ruc tu res . I n March of t h i s year a t t h e NASA Conference on Aero- dynamic Analyses Requiring Advanced Computers a t Langley, so lu t ions t o d i f f i - c u l t problems of flows wi th shock waves, separated flows, transonic flows, and of Navier-Stokes equations were exhibited; though, of course, so lu t ions of t h e turbulen t flows problems are s t i l l "around t h e corner." But perhaps some of t h e g rea t e s t changes t h a t have come about i n Advanced computers - Another change t h a t has come about mainly through t h e influence of t h e space program and which i s bringing an e n t i r e l y new dimension t o aeronautics and t o f l u t t e r t e s t i n g is t h e use of a c t i v e con t ro l s i n con t ro l configured veh ic l e s (CCV). l i t e r a t u r e , U s e of a c t i v e con t ro l s f o r s t a b i l i t y o r load a l l e v i a t i o n must not degrade f l u t t e r c h a r a c t e r i s t i c s . Active con t ro l of f l u t t e r i t s e l f w a s pioneered i n f l i g h t by a modified B-52 a i rp l ane . ba l l a s t ed t i p tank, t hese tests represented r e a l l y a c t i v e con t ro l of wing- s t o r e f l u t t e r . Comparison, i n t h i s case, of f l i g h t , wind-tunnel model tests, and ana lys i s shows common trends; but numerical d i f f e rences i n f l u t t e r speed of t he order of 10 percent i nd ica t e some room f o r improvement. Much has been w r i t t e n on t h i s i n t h e recent and burgeoning A s t h e a i r p l a n e used a Active con t ro l places new emphasis on t h e ana lys i s of nonlinear domains, d i s t i n c t i o n s between mild and v i o l e n t f l u t t e r , and ana lys i s of s u b c r i t i c a l response and i t s co r re l a t ion with e f f e c t i v e damping concepts. i n t e r e s t a t t aches t o t h e behavior of t h e g rad ien t s of t h e eigenvalues of t h e a e r o e l a s t i c equations of motion taken w i t h respec t t o var ious parameters. Special The documented record of obtaining f l u t t e r i n f l i g h t is q u i t e sparse. Hence, i t may be use fu l , I f e e l , t o include i n t h e proceedings of t h i s meeting mention of two such cases. Information f o r the f i r s t of these f o r t h e B-57F a i r p l a n e i s by courtesy of R. P. Peloubet and described i n General D y n a m i c s - For t Worth document FZP-680, April 1965. wing of aspect r a t i o 7.5 experienced f l u t t e r ou ts ide its normal operating The subsonic a i rp l ane having a moderately tapered unswept 273 envelope, and a subsequent f l i g h t i n v e s t i g a t i o n gave r e s u l t s i nd ica t ed i n method, l s o shown are c a l c u l a t e d f l u t t e r speeds by t h e k e r n e l func t ion 60 50 40- 30 20 10- 0- ALTITUDE - X I 0 16 - 12 - 8 - 4 0 20 ED FLUTTER SPEEDS ATE0 OVERSPEED FLUTTER POINT / / / I I 1 100 200 'Sdo 400 500 TRUE AIRSPEED, knots Figure 1.- Measured f l u t t e r r e s u l t s and c a l c u l a t e d va lues by ke rne l method. The second case ( f i g . 2) i s f o r a missile whose canard wings came o f f a t M = 1.7 wi th in t h e opera t ing f l i g h t boundary. Calcu la t ions by R. V. Doggett , Jr., CALCULATED FLIGHT FLUTTER SPEED p 2400 r NEW CONFIGURATION / /- SPAN = 33 cm (13 in. 1 1600 VELOCITY knots ^^. ,GHT 1200 -LCALCULATED FLIGHT FLUTTER SPAN = 41 cm (16 in.) 800 AXIMUM FLIGHT BOUNDARY 4 400 0 1 2 3 MACH NUMBER SPEED Figure 2,- F l u t t e r of m i s s i l e wings a t M = 1.7. 274 and R. W e IIess using p is ton theory agreed w e l l with the f l i g h t test r e s u l t s . A redesigned wing of sho r t e r span performed s a t i s f a c t o r i l y . Before c los ing these remarks, I wish t o remind us a l l t h a t doing calcula- t i o n s f a s t e r does not make them more r e l i a b l e and t h a t t h e r e may always be a res idue of uncer ta in ty i n f l u t t e r ca l cu la t ions and a degree of hazard i n f l i g h t f l u t t e r t e s t ing . Our job i s t o reduce these t o a minimum, And t o c l o s e I repeat my c losu re of 1 7 years ago: "Thus, ' f l u t t e r ' it- s e l f should take on a broader meaning combining cybernetics, dynamic s t a b i l i t y , and a e r o e l a s t i c i t y . from the ex terna l flow i n t o t h e s t r u c t u r e , and feedback con t ro l i n s t a b i l i t i e s are similar processes with i n t e r n a l energy sources. Along with a l l of t h i s t he re must come a l s o b e t t e r phys ica l i n s igh t i n t o the mechanism and phenomena of i n s t a b i l i t y whether through damping, or energy, or analog simulation, o r mathematical t r a c i n g of roots and modes, o r whatnot. F ina l ly , i t i s no t only necessary t o understand but t o understand w e l l and c l e a r l y enough so t h a t those i n research or engineering management who make decisions can a l s o see t h e problems i n t h e i r proper l i gh t . " For f l u t t e r i s a process of pumping energy Harold Sweet , B-1 Division, Rockwell In t e rna t iona l Corporation: L e t m e start by saying t h a t analyses have no legitimate r o l e i n f l u t t e r s a f e t y demonstration and v e r i f i c a t i o n . f l u t t e r speed, but they cannot demonstrate f l u t t e r s a f e t y - Only f l i g h t can do tha t . Now, having re jec ted analyses, then I a l s o r e j e c t f l i g h t f l u t t e r t e s t i n g . My wife , when I t o l d her I w a s coming t o a f l i g h t F l u t t e r T e s t Symposium, sa id , "Well, i f you ge t f l u t t e r i n f l i g h t , i s n ' t i t too l a t e?" I n a l l due respect t o t h e p i l o t t h a t Wilmer Reed reported onL I hope we are not looking f o r f l u t t e r i n f l i g h t . W e should be looking f o r f l u t t e r s a fe ty , as w e test f o r performance and f o r i n l e t compatibil i ty, w e should be t e s t i n g f o r t h e pos i t i ve element of f l u t t e r sa fe ty , not f o r t he negative element f l u t t e r . Analyses can p red ic t a probable J u s t I l i k e t o th ink t h a t t h e r e is a s i m i l a r i t y between the f l u t t e r clearance of an a i rp l ane and t h e spor t of mountaineering. To start with, it takes a c e r t a i n pecul ia r type of ind iv idua l t o have a d e s i r e t o engage i n e i t h e r a c t i v i t y . The summit, o r peak, represents t h e goal of f l u t t e r s a fe ty demon- s t r a t i o n f o r a p a r t i c u l a r a i r c r a f t . There are usua l ly several routes of varying d i f f i c u l t y with d i f f e r i n g exposure o r r i s k f o r reaching the goal. My co r re l a t ion function is a Sierra peak, M t . Conness. A t over 4120 meters i t has an easy route up t h e east r idge . There are approaches from the nor theas t f ace and southwest face . My analogy says t h a t t o t h e nor th and nor theas t of the r idge is t h e chasm of ana lys i s and t o t h e south and southwest i s t h e abyss of experiment. 275 The climb t o the nor theas t f ace from the ana lys i s s i d e goes t o t h e class Mow t h e numerical r a t i n g of climbs means t h e higher the r a t i n g , the 5 climb, more d i f f i c u l t t h e c l The class 5 c i s a considerable s k i l l , This is not a d i r e c t rou te t o summit, You a by an overhand requi r ing a traverse t o ge t around. t h e view of t h e summit and r equ i r e s a devia t ion from a d i r path t o t h e summit i n exac t ly t h e same manner t h a t you cannot ge t d i r e c t l y t o t h e goal of f l u t t e r s a f e t y from an ana lys i s . Only a predicted f l u t t e r speed is poss ib l e from which s a f e r e s t r i c t e d f l i g h t envelopes ( the traverse from t h e overhang) can be spec i f ied , The overhang obs t ruc t s The climb from t h e experiment s ide t o t h i s peak goa l i s not only c l a s s 5 but class 5a, o r class 6 , i f you're of t h e o ld school of u n i t s , d i r e c t a ids where your weight is being supported by a r t i f i c i a l climbing a ids . I rate the d i r e c t approach t o t h e summit from t h e experiment s ide , and unl ike t h e ana lys i s approach, i t goes up a chimney d i r e c t l y t o t h e summit as a more d i f f i c u l t approach than from t h e ana lys i s . Now the ana lys i s w i l l , a t least, have a s a f e margin pred ic t ion that you can move off from. Going d i r e c t l y by t h e experiment rou te i s a real sporty course. It requ i r e s Going up t h e easy east r idge the climb start i s a scree slope. A scree s lope is one t h a t ' s covered wi th loose rock where f o r every s t e p you take up t h e slope, t h e s lope s l i d e s backwards on you two s teps . symbolic of t h e thrashing around t h a t is usua l ly done i n t h e ea r ly design s t ages of an a i r c r a f t . programs. This is where a n a l y s i s w i l l become supreme. Normal f l u t t e r analyses can show a f l u t t e r deficiency, but they cannot g ive an e f f i c i e n t This is s o r t of Recently w e a l l have been working with optimization lightweight so lu t ion . The pathfinding capab i l i t y optimization programs w e are rap id ly ass imi la t ing scree slope. This east ridge, as i t approaches t h e summit meters wide and 100 meters long. Way down t o t h e way down t o t h e l e f t is t h e experiment abyss. A s being provided by t h e can a i d the climb up t h a t narrows t o a sp ine a few r i g h t is t h e ana lys i s chasm; one c rosses the sp ine , he is guided by t h e ana lys i s exposure on one s i d e and experiment exposure on the other. p robab i l i t y of experiment success is obtained. t o guide t h e exposure required i n t h e experimental a s sau l t . are recycled i n t o the analyses t o gain a n a l y t i c a l improvement and improve t h e test condition matching; thus , t h e exposure and l i m i t a t i o n s of t he ana lys i s a s s a u l t are reduced. A s f a r as climbing t h e east r idge is concerned, i t goes as a class 2 climb. This is a l i t t l e more than a t r a i l h ike with some boulder-hopping on the sp ine and summit. In te r fac ing experiment and ana lys i s i s represented by the choice of going around the boulder on the ana lys i s s i d e or on the experiment side. Analyses are used t o design t h e experiment such t h a t the g r e a t e s t The real r o l e of ana lys i s i s The experiments Normally, c o s t and phys ica l cons t r a in t s can be expected t o modify the design. i n t h e S i e r r a and suddenly be on Glacier Park's qua r t z i t e . t o be ro t t en , t h a t i s i t crumbles and doesn't cons is ten t ly provide t h e s o l i d hand/foot holds and p i ton anchors t h a t are inherent wi th gran i te . goal is a t t a i n a b l e providing t h e changed climbing conditions are recognized immediately. 276 To m e t h i s i s somewhat l i k e having planned t o climb on s o l i d g r a n i t e Glac ie r ' s rock tends The summit I n the f i n a l ana lys i s , t r adeof f s between analys s and ~ x p e r ~ m e n t are those which g ive t h e leader of t h e climb, t h e f l u t t e r engineer, the h ighes t confidence i n t h e f l u t t e r s a f e t y of t he a i r c r a f t , M. J. Turner, Boeing Commercial Airplane Company: From my i n i t i a l discussion wi th t h e program chairman I gathered t h a t he wanted m e t o serve here as a member of t h e l a r g e a i r c r a f t f r a t e r n i t y , and from t h a t viewpoint t o present a few comments on t h e outlook f o r cos t reduc- t i o n i n achieving f l u t t e r clearance of new a i r c r a f t , a t t e n t i o n t o l a r g e t ranspor t a i r c r a f t , t h e range of f u t u r e p o s s i b i l i t i e s from long haul supersonic a i r c r a f t t o medium range subsonic t r anspor t s is r a t h e r staggering. o v e r a l l assessment of cos t reduction p o s s i b i l i t i e s but l i m i t my remarks t o a b r i e f review of cur ren t c a p a b i l i t y and research needs t o check the e sca l a t ion of f l i g h t test cos t s . f o r supersonic and subsonic t r anspor t a i r c r a f t is indicated i n f igu re 1.) Undoubtedly my thinking has been colored t o a l a r g e ex ten t by my as soc ia t ion with t h e not-so-recent National SST Program, r e l a t e d follow-on a c t i v i t i e s under DOT con t r ac t , and a cur ren t NASA Contract (NAS1-12287) covering s t r u c t u r a l design s t u d i e s of an arrow-wing supersonic t ranspor t . Even i f w e l i m i t our For t h a t reason I s h a l l not attempt t o make any quan t i t a t ive (The c o n t r a s t i n scope of t h e f l u t t e r clearance problem 200 400 600 800 1000 1200 1400 1600 1800 V T ~ E KNOTS Figure 1.- Fl ight envelopes. VD is design d ive speed, M is Mach number. 1 f t = 0.3048 m e 277 Although dynamic behavior is very configurat ion s e n s i t i v e , l a r g e t rans- po r t a i r c r a f t are genera l ly charac te r ized by r e l a t i v e l y low f r eq t h e reve lan t modes of primary s t r u c t u r e o f t e n with very c l o s e spacing of n a t u r a l f requencies . About 20 na tu ra l modes of primary s t r u c t u r e may be required t o achieve a reasonably adequate f l u t t e r ana lys i s , and a wide range of mass d i s t r i b u t i o n s ( f u e l and payload) must be considered. These c h a r a c t e r i s t i c s tend t o complicate t h e modeling problems--both f o r t h e o r e t i c a l ana lys i s and wind tunnel t e s t i n g . important s t r u c t u r a l design cons idera t ion , as i l l u s t r a t e d i n f i g u r e 2, emphasizing the need f o r e f f i c i e n t and accura te mul t id i sc ip l ine a n a l y t i c a l design t o o l s f o r both preliminary design and d e t a i l design appl ica t ions . F l u t t e r prevention is l i k e l y t o be an LOW SPEED CONTROL LOCKS (AILERON A N D FLAPERON) THICKENED W I N G T I P (SPARS AND COVERS) X 2 STIFFENED FRONT S P A R WEB 7 STIFFENED REGION COVERS) X 5.5 STIFFENED REAR INBD. NACELLE DIFFUSION RIBS-' Figure 2.- Arrow-wing s t r u c t u r a l design study. Contract NAS1-12287. The scheduled cos t s r e f l e c t e d i n the f l i g h t test p lan are pr imar i ly der ived from a r i s k assessment. influenced by ca lcu la ted margins, m u l t i p l i c i t y of p o t e n t i a l l y c r i t i c a l f l u t t e r modes, parametric s e n s i t i v i t y s t u d i e s , c o r r e l a t i o n between wind tunnel model tests and a n a l y s i s , and experience from previous f l i g h t tests. Resul ts of a t y p i c a l model t e s t / a n a l y s i s c o r r e l a t i o n s tudy from t h e National SST Program are shown i n f i g u r e 3. These da t a were der ived from a component study of a semispan wing model; only f l u t t e r speeds (dynamic pressures) and ' f l u t t e r f requencies are compared. The gap i n a n a l y t i c a l c a p a b i l i t y ind ica ted This is a r a t h e r sub jec t ive process , 278 near Mach 1 Is still with us; this is a source of major concern in test planning for high performance aircraft. If the program had survived, similar data for a complete model would have been available to support final flight test p lanning 30C n 2-J Y- . 20c U W LT 3 m m w LT n U Q Z 1 1oc & 0 @ MODEL TEST POINTS a ANALYSIS- MODEL 0 ANALYSIS - PROTOTYPE AIRPLANE * FLUTTER FREQUENCY (H~)/MASS RATIO DYNAMIC PRESSURE AND FLUTTER FREQUENCY IN MODEL SCALE ' 0.6' 0.7 0.8 0.9 1 .o 1 .I 1.2 1.3 MACH NUMBER Figure 3.- Analysis/test comparison; transonic wing model. 1 lb/ft2 = 47.9 N/m2. Significant escalation of flight test costs sometimes occurs when unexpected trends appear during the test. flutter prediction process is obviously the only remedy for that kind of experience, and this capability must provide for future design innovations. Some of the obvious areas of concern for the future are: Improvement in accuracy of the * Unsteady transonic aerodynamics--theoretical, experimental, and empirical correction procedures * Structural modeling criteria 279 e Active con t ro l s * S u p e r c r i t i c a l a i r f o i l s e Wing mounted engines wi th la rge , high bypass r a t i o nace l les As ind ica ted by the papers presented a t t h i s symposium, s i g n i f i c a n t progress has been made i n recent years toward b e t t e r i n t eg ra t ion of ana lys i s , wind tunnel model t e s t ing , ground v ib ra t ion t e s t i n g , and f l i g h t f l u t t e r t e s t ing . s t a n t i a l advances i n t h e following areas: During t h e next decade I be l ieve i t is reasonable t o expect sub- (1) In tegra ted a n a l y t i c a l design t o o l s (2) Three-dimensional, unsteady, nonlinear inv isc id aerodynamic theory (3) Experimental unsteady aerodynamics ( 4 ) S u b c r i t i c a l ana lys i s and s u b c r i t i c a l t e s t i n g techniques (5) Active modal con t ro l technology Progress i n these areas should improve f l u t t e r pred ic t ion capab i l i t y , reduce r i s k , and thereby help t o con t ro l the c o s t of f l i g h t f l u t t e r t e s t ing . However, i t is a l s o reasonably c e r t a i n t h a t new design innovations w i l l cont r ibu te a s u f f i c i e n t element of uncer ta in ty t o j u s t i f y some f l i g h t f l u t t e r t e s t i n g of any new high performance a i r c r a f t . Holt Ashley: I w i l l al low f i v e minutes t o see i f any of the panel members have b r i e f questions and comments. Harold Sweet : Regarding t h e grandiose ana ly t i ca l approaches, thank God I w i l l be r e t i r i n g , I hope, before those computers are b u i l t . I. E. Garrick: Regarding t h e ro to r , which w a s brought up earlier, I want t o ca l l a t ten- t i o n t o the f a c t that the Apr i l 1975 i s sue , I be l ieve t h e Journal of A i r c r a f t had a very f i n e review of t h e problem of propulsion systems, he l icopter r o t o r s , but i n a way I think they were a l l i n t e r e s t i n g , t h e theo re t i ca l , semiempirical procedures t h a t were out l ined i n the var ious papers . These are not 280 David Brandt: I've been wai t ing f o r someone t o suggest t h a t t h e proponents f o r ana lys i s should make the f i r s t f l igh t . , B i l l Bousman, Ames Direc tora te , U. S . Army A i r Mobility R&D Laboratory: It has been a bad night f o r us a t Ames. There have been a l l s o r t s of nas ty things s a i d about Hans Mark. I would l i k e t o defend h i s pos i t ion , but I had a note from t h e computer center a month ago saying t h a t our t i m e s l o t i n the computer w a s c u t by one t h i r d because they were increasing wind-tunnel support time. A l l of us heard about being a combined mountain climber, ae roe la s t i c i an , and f l u t t e r f reak; a t least now I understand why two weeks ago when I t r i e d t o climb by M t . Conness on t h e east s ide I had so much t rouble . experimentalist , and t h a t r s t h e a n a l y t i c a l s i d e . I ' m an I a l s o found out t ha t I ' m i n bed with 2000 NASA employees by working f o r t h e Army. evening. I have sat i n h i s o f f i c e and he ta lked about h i s problems, and I sat t h e r e and mumbled a l l those good words t h a t h e has mentioned. But when i t comes f o r a s o l u t i o n fo r t h e problem, I am p r e t t y much a skeptic. It would be very n i c e i f w e were a l l much smarter so w e could f i x these th ings as they come up, but t h a t w i l l never happen. I a l s o doubt t h a t pouring the government's money i n t o these problem areas w i l l ge t us much i n terms of fundamental understanding. I have a g r e a t d e a l of sympathy wi th what Dave has sa id t h i s I j u s t don't have any answer f o r Dave's problem. Chris Borland, Rockwell I n t e r n a t i o n a l Corporation: Comments t o Holt: The i n i t i a l remarks by D r . Ashley brought ou t comments from j u s t about everybody on t h e Chapman-Mark a r t i c l e . of a t tending t h e second AIAA Computational F lu id Dynamics Conference i n Hartford, Conn., t h i s year, and t h e a r t i c l e was an objec t of extreme con- troversy. I would l i k e t o r e p o r t t o t h i s gathering t h a t the view that t h e computer i s going t o d i sp l ace andlor replace t h e wind tunnel is by no means universa l among t h e people who are involved i n t h e area o r f i e l d of computa- t i o n a l f l u i d dynamics. Some remarks by P a t Roache, who i s one of t h e b iggies i n t h i s business, address t h e po in t t h a t numerical methods under development are probably t h e area where t h e biggest a c t i o n is. ignored by t h e ar t ic le , which s a i d t h a t bigger computer turbulence models were needed t o so lve everything once and f o r a l l . I th ink t h e consensus of f e e l i n g w a s that both t h e wind tunnel and t h e computer w i l l be around f o r a long time, so t h e experimentalist need not look i n t o h i s retirement p lan t o f i g u r e out how soon he can ge t ou t of t h e bus iness , because he's going t o be there f o r q u i t e a while. I had the p r i v i l e g e This w a s completely 281 l s o , I would l i k e t o address some remarks t o M r . Sweet -who happens t o be my boss, has t o say i s t h a t w h a t w e r e a l l y have t o do is tread the narrow path between ana lys i s and experiment, they are sadly mistaken. H e increased my computer budget, so I know that I heard what he Anybody who f a l l s o f f e i t h e r s i d e of t h e mountain, Holt Ashley : Thank you Chris. I t h i n k w e should a l l say a word about that Chapman- Mark article. th ing of a bea t ing on what they sa id ; they are a l l b i g boys you ‘know, and they are q u i t e capable of defending themselves i n t h i s environment. suspect, although I c a n r t prove i t , t h a t they a l l had t h e i r tongues displaced perhaps a few microinches i n t h e d i r e c t i o n of one o r t h e o ther cheek when they wrote t h i s . This i s not t h e only forum from which they have taken some- I s t i l l Harold Sweet: Chris i s doing some f i n i t e element flow f i e l d work, p a r t i c u l a r l y with respec t t o o s c i l l a t i o n i n cavities, which I have some g r e a t hope f o r , except t ha t I can’t a f ford h i s computer b i l l and I a m not s u r e the Bank of America can e i t h e r . Bruce McKeever, Time/Data Corporation: I have a comment t o Jon Turner: I would l i k e t o suggest you modify your stand a l i t t l e b i t on g e t t i n g your algorithm thoroughly developed before you br ing on t h e real test. smart enough t o come up wi th a new technique which could be use fu l a r e n ’ t w i s e enough t o devise any kind of a r t i f i c i a l test t h a t is equal t o one real physical experiment. My awn experience ind ica t e s t h a t people who are M. J. Turner: What I meant t o say is t h a t , i n developing confidence i n ana lys i s , one m u s t . f i r s t of a l l ve r i fy t h e adequacy of t h e bas ic technologies involved - i n our case unsteady aerodynamics, s t r u c t u r a l behavior, and a c t i v e con t ro l dynamics. F ina l ly , I th ink t h e r e are i n t h e p a s t numerous instances where w e overlooked t h e extremely important a d d i t i o n a l requirement of ve r i fy ing t h e in tegra ted a n a l y t i c a l c a p a b i l i t y f o r complex systems having thousands of degrees of freedom. Before a newly developed ana lys i s program is applied t o 282 a design p ro jec t it is e s s e n t i a l t o run some test cases on r ep resen ta t ive systems, with s u f f i c i e n t d e t a i l t o i den t i fy t h e obs tac les t h a t r e s u l t from shear complexity, B i l l Rodden, MacNeal-Schruendler Corporation: I have wr i t t en elsewhere t h a t government is spending much of i ts money i n supporting t h e wrong people t o so lve problems that w e don't have. forthcoming Proceedings of 1500 pages from t h e NASA Conference on Computa- t i o n a l Fluid Dynamics makes m e say "WOW!" When t h e government wants t o so lve real research problems instead of imaginary ones, then we can begin t o th ink about reducing t e s t i n g cos t s , but not u n t i l then. The I. E. Garrick: I happened t o be present a t t h e March Conference a t Langley, and I w a s t r u l y impressed with t h e real understanding and approaches t o numerical methods tha t those people are making. I th ink they are making a darn good beginning. I th ink B i l l Rodden is g e t t i n g too impatient. I r e a l l y th ink i t ' s a good beginning i n t h i s area of work, and w e can r e a l l y expect some g rea t improvements i n the d i r e c t i o n which B i l l Rodden is t a lk ing about, but I don't th ink it w i l l go a l l t h e way. Holt Ashley: I want to add something t o t h e theo re t i c i an ' s defense. I ' v e heard too many cracks here about how w e can do things only after t h e f a c t s , so l e t m e j u s t remind you of one l i t t l e s t o r y , which i s completely ou t of the area of a e r o e l a s t i c i t y so i t is not s e l f serving. You have an a i r p l a n e t h a t you cal l t h e F4H, and you wanted t o ge t t o high a l t i t u d e f a s t . There are a l l s o r t s of ways of doing it. Not a l l are as successful as i t w a s thought they should be. Certainly t h e static-performance approach of keeping the maximum dis - tance between t h e t h r u s t and drag curves with respec t t o a l t i t u d e w i l l do t h e job . approach and an optimum t r a j e c t o r y ca l cu la t ion , and they showed how t o do it r i g h t . through t h e t ransonic range. They gave t h e Navy a rec ipe f o r making t h i s f l i g h t and sa id i t would take 334 seconds t o go from low speed and a l t i t u d e t o level f l i g h t a t Mach 1 and 65000 f e e t . It w a s 2 minutes f a s t e r than t h e Navy had ever been a b l e t o do it , but they went out and d id i t i n 332 seconds. There are a few s t o r i e s l i k e t h a t w e should remind ourselves o f . Now A r t Bryson and a student of h i s d id a s impl i f ied equation They demonstrated the importance of pu t t i ng the nose down while going 283 Clarence Perisho, McDonnell Douglas Corporation: I th ink you touched on something I have been th inking of i n t h e course of l i s t e n i n g t o t h e panel, and t h a t is t h a t nothing i s going t o replace f l u t t e r t e s t i n g f o r the f l i g h t vehicle, f o r ana lys i s i s i n design, bu t I keep hearing the word co r re l a t ion . The question is, do you think t h a t ana lys i s w i l l replace t h e discovery on models of configuration-sensit ive i n t e r a c t i o n f l u t t e r today? b i l i t y t ha t a n a l y s i s w i l l be any b e t t e r than what we have seen i n t h e experiment ? Certainly, a very important p lace Is t h e r e any possi- M. J. Turner: I think t h a t there has been a change i n t h e last two o r t h ree decades i n t h e r o l e of model t e s t i n g , now commonly regarded as a procedure f o r ver i - f i c a t i o n o f t h e a n a l y t i c a l t o o l s t h a t are being used, while ana lys i s i s being used as t h e p r inc ipa l design too l . Analysis i s c e r t a i n l y not going t o replace t e s t i n g completely, but with more extensive app l i ca t ion of a c t i v e cont ro ls I b e l i e v e t h a t t h e f l u t t e r v e r i f i c a t i o n w i l l be more r ead i ly absorbed i n t o t h e f l i g h t test program, with some reduction of t i m e and cos t s . Further- more, with new d a t a processing techniques the re i s an opportunity t o use an on-line computer t o improve our d iagnos t ic capab i l i t y . I f su rp r i se s do occur, w e should then have a b e t t e r capab i l i t y of understanding the s i t u a t i o n . Char l ie Coe, NASA Ames Research Center: I can ' t resist t h e comment t h a t i t almost seems as if the theme of t h e whole'discussion implies t h a t t he re is some t h r e a t t o a l o t of people because of some development of a n a l y t i c a l procedures o r methods t h a t eventually w i l l come down t h e l i n e and th rea t en t h e experimental, o r vice versa, F i r s t , I l i k e Harold Sweet's analogy not necessar i ly so much f o r t h e mountain climbing approach, but I can ' t help but t h ink t h a t , t o a g r e a t ex ten t , i f you want t o g e t from here t o the re you would l i k e t o have a road map of some s o r t t o study t h e b e s t approach t o get t he re . The f a c t that you have been a b l e t o study by some a n a l y t i c a l procedure t h e bes t rou te - the b e s t method and possibly t h e lowest-cost method - t o g e t t o your des t ina t ion , that s t i l l doesn't eliminate t h e need t o g e t there. have t o conduct your experimental test and f l i g h t test o r whatever t o demonstrate t h a t you are there . Perhaps t h e cos t of a c t u a l l y making t h e demonstration can be reduced, but t h e need i s s t i l l the re , opinion that t h e balance i s between a n a l y t i c a l procedures and wind-tunnel t e s t h g techniques; the wind tunnel is j u s t an analog computer. a strong s i m i l a r i t y between t h e a n a l y t i c a l approach by t h e wind tunnel versus numerical techniques o r whatever, and again i t ' s t h e cost breakdown So you s t i l l , as Harold says , It's my personal So t h e r e is 284 t h a t r e a l l y makes t h e d i f fe rence , I th ink t h a t , i n t he end, t h e balance of which way i t w i l l go, of course, depends on c o s t f a c t o r s bu t a l s o on bra ins . That*s t h e o the r thing, i f w e have t h e knowledge, granted t h e developing knowledge f o r reaching our goa ls by a n a l y t i c a l procedures, experimental procedures, o r whatever, I th ink t h a t the balance is going t o come i n propor- t i o n t o the b r a i n power. I s o r t of f e e l t h a t i t is r e a l l y t h e bes t of a l l t hese f ac to r s . 285 E SERIES ANAL FLIGHT FLUTTER TESTING AT THE AIR FORCE FLIGHT TEST CENTER: CONCEPTS AND RESULTS Russe l l W. Lenz A i r Force F l i g h t T e s t Center and Bruce McKeever T i m e / D a t a Corporation SUMMARY Concepts of using d i g i t a l t i m e series a n a l y s i s f o r f l i g h t f l u t t e r t e s t i n g a t t h e A i r Force F l i g h t T e s t Center (AFFTC) are discussed, The AFFTC F l i g h t F l u t t e r F a c i l i t y i s described. U s e of a minicomputer-based t i m e series ana lyzer and a modal a n a l y s i s software package is described, as are the r e s u l t s of s eve ra l eva lua t ions of t h e software package. The reasons fo r employing a minimum phase concept i n analyzing response only s i g n a l s are discussed. The use of a Laplace algorithm i s shown t o be e f f ec - t i ve f o r t h e modal a n a l y s i s of t i m e histories i n f l u t t e r t e s t i n g . Sample r e s u l t s from models and f l i g h t tests are provided. The l i m i t a t i o n s inhe ren t i n t i m e series a n a l y s i s methods are d iscussed , and t h e need f o r e f f e c t i v e noise reduct ion techniques is noted. The use of d i g i t a l t i m e series a n a l y s i s techniques i n f l u t t e r t e s t i n g is shown t o be f a s t , accura te , and cost e f f e c t i v e a t AFFTC. INTRODUCTION A basic mission of t h e A i r Force F l i g h t T e s t Center (AFFTC) i s t h e f l i g h t t e s t i n g of new o r modified a i r c r a f t , The t e s t i n g of t h e s e aircraft and their e x t e r n a l store conf igura t ions has pro- duced the need f o r a support c a p a b i l i t y i n t he area of f l i g h t f l u t t e r c learance , Because of t h e na tu re of t h e AFFTC mission, t h e f l u t t e r t e s t i n g method must m e e t t h e following requirements and be e f f e c t i v e under t h e following circumstances: (1) The a n a l y s i s c a p a b i l i t y must be usable during t h e t e s t i n g of a l l types of a i r c r a f t , and it must be genera l enough t o cover c o n t r a c t o r t e s t i n g requirements. (21 The test engineer may not have complete knowledge of t h e expected f l u t t e r c h a r a c t e r i s t i c s . F l u t t e r p red ic t ion ana lyses , 287 (5 1 newly developed n mu inimize prog am cost and e been analyzing t i m e h i s t o r i e s analog techniques during p o s t f l i g h t l y s i s w a s o f t e n l i m i t e d to s t r i p en t h e a i r c r a f t w a s equipped with eeps were followed by mul t ip l e ob ta in damping, This method f o r t h e engineer t o ob- odes made it impossible ency sweeps w e r e conducted t o uced c o n t r o l su r f ace ristics of he s i n g l e modes i n es A, Long, Yr,, and i o n s are g r a t e f u l l y i m e series ana lyzer and of t h e system, 288 0 l A a = b = c 6 C f g H h j = k m P Q R r S S T t amplitude of f unc t i o UT, per sec the complex frequency response w \I 1 - c 2 , per sec au tocor re l a t ion , v2 derivative of t h e au tocor re l a t ion with respect t o t i m e cons t an t frequency, Hz s t r u c t u r a l damping complex frequency response func t ion impulse response funct ion, ion element number mass, kg (sl real component of t h e frequency response func t ion y componen he frequency response magnitude of t h e res idue , V complex res idue power spectrum, v2 Laplace variable arbi t rary t i m e i n a sample data frame, sec t i m e , sec 289 Y Y@ er spectrum, v2 01 so lu t e damping, per sec A € A t t i m e i n da t a frame pr io r t o taking an FFT, sec 5' viscous damping r a t i o 0 phase of t he r e s idue , deg CJ e damping, 2~01, per sec e lag , sec e response, rad FLIGHT FLUTTER FACILITY The AFFTC F l igh t F l u t t e r F a c i l i t y w a s designed t o permit tes t engineers t o use t r a d i t i o n a l s t r i p c h a r t ana lys i s techniques i n conjunction with advanced d i g i t a l t i m e series ana lys i s methods. Pulse code modulation (PCM) o r frequency modulation (FM/FM) f l i g h t d a t a are converted o analog s igna l s which can be analyzed by prevent a l i a s i n g ( equency foldback) i n t h e d i g i t a l analyses. r technique ( g. 1). The analog f i l t e r s improve t h e s t r i p analyses by ducing noise and i s o l a t i n g modes. They also 290 The alphanumeric/graphics d i sp l ay te rmina l i s t h e primary input / ou tpu t device. u n i t which gene ra t e s a reproducible copy i n 9 seconds. A mul t ip lexer permits t h e simultaneous sampling of up t o 1 6 channels of data. An t i a l i a s ing f i l t e r s (low pass f i l t e r s set a t 30 h e r t z o r 60 h e r t z ) prevent higher f requencies from a l i a s i n g o r fo ld ing back t o lower frequencies during t h e d i g i t a l ana lys i s . The sampled d i g i t a l t i m e h i s tor ies and t h e analyzer s e t u p information are s to red on two 1.2-million-word d i s k u n i t s . One d i s k u n i t permits t h e t i m e h i s t o r y data used i n t h e nea r ly real-time a n a l y s i s of selected data channels t o be s t o r e d p r i o r t o ana lys i s . Mul t ip le a n a l y s i s approaches may be applied t o t h e s t o r e d data. The data d i s k also enables an engineer t o recall a d d i t i o n a l channels of data w h i l e t h e a i rcraf t i s tu rn ing or r e f u e l i n g o r when s t r i p charts i n d i c a t e t h a t a p a r t i c u l a r channel i s of i n t e r e s t . The second d i s k u n i t is reserved f o r s t o r i n g t h e pro- gram software. The s i x tunable bandpass (12 l o w pass o r high pass ) filters improve s t r i p chart ana lyses , permit more f l e x i - b i l i t y i n the s e l e c t i o n of a n t i a l i a s i n g f i l t e r c u t o f f s , and allow bandpass-f i l tered s i g n a l s t o be analyzed d i g i t a l l y without having t o use d i g i t a l filters. A patch panel l i n k s the va r ious system components. N o t shown i n t he photograph are t h e three s t r i p chart recorders and a programmable c a l c u l a t o r w i t h i t s associated terminal . It i s opera ted i n conjunct ion w i t h a hard copy A reduced system can and has been used a t AFFTC during f l u t t e r t e s t i n g . The panel-operated, two-channel spectrum analyzer can be used i n conjunct ion w i t h s t r i p chart analyses , bu t t h i s approach r e q u i r e s more f l i g h t t i m e and r e s u l t s i n less o v e r a l l accuracy than can be obtained by us ing t h e e n t i r e c a p a b i l i t y . The cu r ren t AFFTC conf igura t ion is considered t o be a minimum f a c i l i t y for e f f i c i e n t opera t ion , graphics d i s p l a y te rmina l and selected AFFTC- o r con t r ac to r - w r i t t e n software. The engineer uses one ox more of t h e available a n a l y s i s techniques (described later i n t h e paper) t o gene ra t e t r e n d s of modal frequency, damping, o r amplitude. During AFFTC tests i n which c o n t r o l su r f ace impulse e x c i t a t i o n i s used, a t least t w o response channels are analyzed before t he p i l o t is cleared f o r t he next test condition. For tes t planning purposes, approximately 4 minutes are allowed pe r test p o i n t , a l though t h i s estimate i n c r e a s e s i f t he aircraft is t o be power l i m i t e d dur ing The primary mode of system ope ra t ion uses t h e alphanumeric/ 291 TIME SERIES/LAPLACE ~ ~ Y S I S The d ig i t a l t i m e series a n a l y s i s t e c h n i u t i l i z e t h e FFT t o l i n e a r l y transform a s t h i s t o r y i n t o a complex frequency domain f u p r i s e d of s inuso ids w i t h s p e c i f i c amplitude and phase character- istics. The squared magnitude of a response as a func t ion of frequency (au to power spectrum) can be obta ined as follows: S ( j w ) = Y* ( j w ) .Y ( j w ) (1) YY where Y ( j w ) i s t h e Four ie r t ransform of a response t i m e h i s tory and Y* ( j w ) i s t h e complex conjugate of Y ( j w ) force t i m e h i s t o r y ( x ( t ) ) i s also measured, a c r o s s power spectrum can be computed: I f t h e i n p u t The amplitude and phase r e l a t i o n s h i p between t h e response and a given inpu t i s used t o d e f i n e a system t r a n s f e r func t ion (complex frequency response func t ion) as follows: The use of t he cross spectrum and i n p u t au to spectrum removes removing the effec of n o i s e t h a t is no t c o r r e l a t e d w i t h t h e he need fo r complex d i v i s i o n , and, more important ly , t h e cross pectrum t e n d s t o prove t r a n s f e r func t ion estimates by T h e Four ie r t ransform of the r a n s f e r func he impulse response func t ion , which is a t i m e h i s t o r y comprised of damped t i n d i c a t e s t r u c t u r a l response t o an impulse type e frequency, damping, amplitude, and phase of t h e s inusoids t h a t make up t h e impulse response func t ion (or complex frequency response func t ion) d e f i n e t h e modal characteristics of the s t r u c t u r e a t t h e measured l o c a t i o n f o r a specific f l i g h t condi t ion , 292 input . It is assumed t h a t t h e response i n t h e response only case is c h a r a c t e r i s t i c of a minimum phase system. This impl ies t h a t t h e system is phys ica l ly r e a l i z a b l e , t h a t damping i a l l modes, and t h a t of a l l t h e impulse responses w i au tocor re l a t ion , t h e one selected has t h e most buildup of energy, When t h e s e con t h e Hilber t t ransform can be used of t h e system given only i t s amplitude charac minimum phase c a l c u l a t i o n s are described and t h e more common a u t o c o r r e l a t i o n t e c h n i calculate t h e t r a n s f e r func t ion accura derived minimum phase spectrum, Y8 ( j w ) is made as follows: where X ( j w ) is a co noise , and swept s i n e been proven i n f l i g h t test, I f t h e inpu t i s n o t f l a response may i n d i c a t e high energy a t a l o c a t i o n t h a t corresponds t o a pole of t h e d r i v e func t ion , Th i s p o s s i b i l i t y must be con- s i d e r e d by t h e engineer because it occurs i n a l l techniques of response only ana lys i s , rum is n o t per fec s s m p t i o n s t i l l pro- reasonable accur of t h e technique has 293 ce a n a l y s i s uses t h e concept o f a p a r t i a l f r a c t i o n he complex frequency response func t ion t o d e f i n e if modal parameters f o r each pole, s = s i n t h e Laplace p lane , as follows: - j e i (n/180) jOi(s/180) R . e R . e 1 = ! { s + (2ncti - j2ski) s ' + (2sai -i- j2ski) 3 (5 1 1 + 1 A graph ica l d e s c r i p t i o n of t h e po le s and t h e r e l a t e d modal parameters is given i n f i g u r e 3 . t h e absolu te damping, ai, and t h e frequency l i n e number, ki, of t h e mode. composed of a magnitude, Ri, and a phase, Bie This r e s i d u e de- f i n e s t h e modal e igenvector when measurements are made over an ' e n t i r e s t r u c t u r e . For s t r u c t u r e s with nonproportional damping, t h e residue de f ines a complex mode; bu t f o r modes with propor- t i o n a l damping, t h e phase r e l a t i o n s h i p s of t h e e igenvec tor p o i n t s on ly d i f f e r by approximately 0" o r 180°, The impulse response func t ion i n t h e form der ived by t h e Laplace sof tware demonstrates t h e phys ica l meaning of t h e modal parameters: The pole l o c a t i o n , si, d e f i n e s The numerator i n equat ion ( S ) , ri, is a complex r e s i d u e cos [2nkit + Cli(n/180)] 1 h ( t ) = C {2Rie (-2nai) t i The abso lu te damping t o t h e more f a m i l i a r and frequency, f , as and t h e frequency l i n e number can be r e l a t e d damping r a t i o , 5 , o r s t r u c t u r a l damping, g , fol lows : 1 1 rn ~ = z g = a a f o r lowly damped modes " E (7 1 f = 294 mode genera t ion approach has made it poss ib l e fo r engineers t o gene ra t e known funct ions d i g i t a l l y and t o perform circle checks on t h e modal r e s u l t s c a l c u l a t e d from t h e t r a n s f e r func t ion , The Laplace software conta ins procedures t h a t a t tempt t o i d e n t i f y t h e modes which have the highest spectral energy and t h e lowest damping. A modal energy value is c a l c u l a t e d f o r each pole as a percentage of t o t a l energy i n t he frequency band being analyzed. a selected c u t o f f value and w i t h an a t t e n u a t i o n (absolu te damping) less than a specified cu to f f are included i n t h e mode l i s t p r i n t - out . T h i s procedure e l imina te s long mode l i s t p r i n t o u t s and makes it much easier f o r t h e a n a l y s t t o i d e n t i f y and track t h e modes t h a t are of i n t e r e s t t o him, Only the modes w i t h a percentage energy greater than The accuracy of t h e Laplace algori thm and i t s a b i l i t y t o separate c l o s e l y spaced modes has been i n v e s t i g a t e d a t AFFTC by using d i g i t a l l y generated t r a n s f e r funct ions. S ingle o r b i p o l a r modal parameter l is ts were input , a complex t r a n s f e r func t ion w a s der ived, t h e Laplace r o u t i n e s c a l c u l a t e d the modal parameters, and a comparison w a s made between i n p u t data and the extracted data i n order t o assess program l i m i t a t i o n s , The s i n g l e mode study verified t h a t frequency w a s derived accura t e ly and t h a t damping w a s ca l cu la t ed t o wi th in 1 0 percent of t h e correct value f o r t h e modes w i t h v iscous damping ratios less t h a n 0,10, except for modes near t h e upper c u t o f f frequency, A t y p i c a l error envelope showing the maximum values of damping which r e s u l t e d i n a 10-percent error i n damping is shown i n f i g u r e 4 . The a t t e n u a t i o n curve demonstrates t h a t t he i n t e r f e r e n c e effect of the ends of the data frame can be s i g n i f i c a n t . Knowledge of t h i s effect and t h e r e l a t i o n s h i p between damping r a t io and absolute damping (eq. ( 7 ) ) is used by the a n a l y s t t o i n s u r e t h a t appropriate frame s i z e s and sampling rates are selected i n order t o e x t r a c t t h e modes of i n t e r e s t accu ra t e ly , a parametric v a r i a t i o n of dampinq r a t io and frequency r e s o l u t i o n The bipolar d i g i t a l complex frequency func t ion study used 295 e e r r o r i n he c a l c u l a t i o n of t h e c h a r a c t e r i s t i c s of ion-element i on between modes w a s t h e m i n i m u m 35) w a s less than 1 0 percent , A a i n t h i s accuracy. wo modes converged i n frequency, t h e accuracy of e estimates w a s deg aded, Light ly damped modes ( 5 < 0.035) re eva lua ted accura e l y r e g a r d l e s s of t h e presence zf other imates of c l o s e 1 spaced modes i c h had h igher e i n e r r o r , bu t he accuracy of he estimate improved es were h igh ly d g i t a l s t u d i e s v e r i f i e d a11 s i g n i f i c a n energy and l o w damping uld be accurate ace software er func t ion , (The o AFFTC engineers ce program, When d e s i r e d , w e r e analyzed sepa ra t e ly by using more appropr i a t e The Laplace package software w a s a l s o eva lua ted by using analog compu er models. Table 1 shows t h e r e s u l t s of a four-mode case i n which a pulse e x c i t a t i o n w a s used. These response only cases were analyzed by using t h e m i n i m u m phase algori thm before performing t h e Laplace ana lys i s , The frequency w a s g e n e r a l l y ined f o r w e l l e x c i t e d modes when damping r a t i o s 20. The a n a l y s t used t h e frequency response t o v e r i f y t h e estimates v i s u a l l y , The frequency ermined accu ra t e ly f o r modes t h a t envelope of t h e Laplace sof tware ed modes o f t e n exh ib i t ed low calcu- l a t e d damping d e r of 0.001), although t h i s e r r o r w a s read he engineer by observing t h e t r a n s f e r func p l o t s , The f a l s e modes were a l s o iden- w ene rg ie s and/or l o w r e s idues on t h e 296 and analog simula he Laplace pa f critical mo de e analyzed wi i n advance, and a 1 nonh~ghly s imultaneou~ly wi h good accuracy, only data w a s eva uated well by usin FLIGHT FLUTTER TEST APPLICATIONS f l i g h nd 297 Typical hard copy output f o r a est i n which c o n t r o l sur- face pulses were used is shown i n f i g u r e s 8 and 9 and table 2, The AFFTC software w a s w r i t t e n t o u t i l i z e t h e Laplace software package subrout ines e f f i c i e n t l y during a real-time f l u t t e r ana lys i s , Figure 8 con ta ins a t i m e h i s t o r y of sampled response data for an e l e v a t o r pu l se during a B-52D aircraft/store c e r t i f i c a t i o n program. The dashed l i n e s i n d i c a t e t h e 6,25 seconds of data which w e r e analyzed by using t h e minimum phase assumption, The maximum response peak w a s used as a s t a r t i n g loca t ion because it r e s u l t e d i n more c o n s i s t e n t data t r ends , (The p i l o t i npu t did n o t r e s u l t i n a t r u e sp ike inpu t because t h e dynamics of the c o n t r o l system caused s m a l l overshoot o s c i l l a - t i ons . ) The magnitude of t h e t r a n s f e r .function i s shown i n f i g u r e 9, The engineer could a l s o view t h e co inc ident , quadra- t u r e , o r phase spectrums o r phase plane p l o t s . The v e r t i c a l l i n e s i n f i g u r e 9 were drawn automat ica l ly a t frequencies selected for a n a l y s i s by t h e Laplace software. The a n a l y s t t hen had t h e opportuni ty t o change the frequency a n a l y s i s band, damping (alpha) c u t o f f , and energy threshold?, or he could have the mode l ist (table 2 ) displayed and copied. If t h e i n p u t w a s known, t h e t i m e h i s t o r y would not normally be d isp layed and t h e minimum phase assumption would no t be needed t o d e r i v e t h e t r a n s f e r funct ion; bu t the rest of t h e a n a l y s i s would be t h e same. I n table 2, t h e damping l e v e l s of t h e 4,16-hertz and 5.76-hertz modes would be questioned by t h e a n a l y s t because of low ene rg ie s and r e s idues (poor e x c i t a t i o n ) . I t is s i g n i f i c a n t t h a t t w o high energy, high res idue , c l o s e l y spaced modes were i d e n t i f i e d . The frequency and damping of these modes could no t be determined e a s i l y by using t r a d i t i o n a l s t r i p chart logar i thmic decrement analyses. The t o t a l t i m e required t o perform t h e a n a l y s i s and obta in the hard copy r e s u l t s shown w a s 1.1 minutes, Additional t i m e histories were analyzed from d i s k data as desired. Mult iple data t r ends w e r e p l o t t e d by hand dur ing t h e f l i g h t , b u t mode r e s u l t s s to red on the d i s k w e r e p l o t t e d during p o s t f l i g h t sess ions using t h e graphics d i s p l a y u n i copy device. These hard copy outp 298 i o h ra l ~ e s p o n s e he r e l a t i o n between frequen t i m e frame w a s f i l l t h e no i se level. The response s igna tu re f o r modes w i t h higher damping o r h igher f requencies may be considerably sho the example, and t h e r e s o l u t i o n would end up by being lower, ( I f the frame s i z e is n o t shortened appropr i a t e ly , t h e data appear t o have l o w e r damping because of t h e cont inuously e x c i t e d data i n t he noise l e v e l and s ta t i s t ica l v a r i a b i l i t y , ) As demonstrated i n f i g u r e 10 , t h e reduct ion i n r e s o l u t i o n has seve ra l effects on the data: (1) he d a t a cu rves are smoothed and less noise i s evident ; (2 the a b i l i t y t o separate c l o s e l y spaced modes decreases; and (3) t h e min mum damping l e v e l which can be def ined increases . The last effec as t roph ic i n f l S igna l To Noise R a t i o The resol t h e s i g n a l ra t io i n f l i g h h i s ~ a p p e n s smoothing of t y. However, frequency r e s o l u t i o es, Both h igher force levels and longer sweep t improve t h e signal. t o n o i s e ratio. The c a l c u l a t i o n of t h e t r a n s f e r fun correct measurement of i n u t and output . I e x c i t e d s i g n i f i c a n t l y by urbulence or buff i n p u t i s wrong; therefore is wrong, and t h i s d i s to r I n f i g u r e 11, t h e s i g n a l to no i se ra t io i n he response is poor, speed f ~ u t t e r po in t s , so t h e l i n e a r sweep times were restricted to 7 seconds. The t r a n s f e r func t ion for t h i s t i m e h i s t o r y is shown is f i g u r e 12, Most of t h e energy i n f i g u r e 1 2 is i n a symmetric mode (between t h e dashed l i n e s ) , bu t t h e s t u r e w a s being e x c i t e d a n t i - symmetrically by ae estimate prevented analyzed accu The aircraft w a s power limited a t i t s h ig 299 300 en must be general 301 For c e r t a i n condi t ions , there i s a d e f i n i t e one-to-one re- ionship between the frequency response characteristics P and Q where The amplitude, A b ) , and t h e phase, Cp(w) , are uniquely related to t h e real and imaginary components of t h e t r a n s f e r funct ion: I t can be noted t h a t t h e logarithm of t h e t r a n s f e r func t ion is related t o the log amplitude characteristic and t h e phase characteristic i n t h e same manner t h a t H ( j w ) i s related t o P and Q i n equat ion ( A l ) . I f t h e system is both s t a b l e and causa l , Hi lber t t ransforms can be derived which relate P and Q (ref. 4 ) : Q(u) du u - w (A5 ) The s i m i l a r i t y of equat ions ( A l l and (A41 makes it p o s s i b l e t o c a l c u l a t e e i t h e r t h e amplitude or phase given t h e o t h e r , I n t h i s case, the logarithm of H ( j w ) must have n e i t h e r uns tab le po le s nor zeroes , (A7 I 302 Of more prac ical i n t e r e s he phase i n d i g i t a l t u d i e s is t h e following equat ion, which u t i l i z e s t h e Four ie r ransform ( r e f , 51, where DFT IFT T d i r e c t Four ie r transform, inverse Four ie r transform, and a r b i t r a r y t i m e i n t h e d a t a frame wi th t h e funda- mental Four ie r per iod going from 0 t o T 0 t = o , T T 2, 1 T - U ( t - 2) = The @ ( w ) which is c a l c u l a t e d is known as a minimum phase, and t h e system is a minimum phase system,, The complete frequency response func t ion i s est imated by combining t h e minimum phase w i t h t he square r o o t of t h e autospectrum. The frequency response may then be inverse Four ie r transformed t o give the t r u e impulse response func t ion f o r t h e minimum phase system. Three assumptions must be made about t h e d a t a f o r t h e minimum phase procedure t o be used, F i r s t , it i s assumed t h a t a l l modes have s t a b l e damping. Second, t h e system i s assumed t o be causa l ; t h a t is, t h e impulse response i s considered t o be zero f o r nega t ive t i m e and it is assumed t h a t t h e system cannot respond t o an inpu t before it occurs. Third, of a l l frequency responses with t h e same autospectrum, t h e one s e l e c t e d is assumed t o have t h e smallest t o t a l change i n phase angle from zero t o maximum frequency. This impl ies t h a t , of a l l impulse responses with t h e s a m e au tocorre la - t i o n , t h e one s e l e c t e d has t h e most r a p i d i n i t i a l buildup of energy . The f i r s t t w o criteria would almost c e r t a i n l y be t r u e i n an a i r c r a f t response, The t h i r d c r i t e r i o n i s more d i f f i c u l t t o v e r i f y f o r a p a r t i c u l a r s t r u c t u r a l response, but t h e minimum phase 303 I = cos b 304 0 oca ed i (A161 ollowing au i o n derivative n be obtained: s ev iden t from equat ions (A17) and ( A l 8 ) t h a t w h i l e t h e o s c i l l a t i o n rates of an unknown impulse response ermined without knowing t h e phase by c a l c u l a t i n g ion or t h e d e r i v a t i v e of the a u t o c o r r e l a t i o n , t be determined except for a very l i g h t l y has also been found t h a t the au tocor re l a t ion , of the p a r t i c u l a r impulse response i s n o t always impulse response, he derivation of he system parameters from t h e response as good an answer as can be ob- are Used, However, t h e auto- and the minimum phase approach o f t e n give e estimates of frequency and damping, An ad- he minim^ phase a sumption, when it is appli- mode shape (wi th e except ion of a p o s s i b l e 305 306 FERENCE 1, S 2, Norin, R. S,; and Sloane, E, A,: A New Algo Improving D i g i t a l Random Control System Spee Proceedings of t h e 2 1 s t Annual Technical Mee I n s t i t u t e of Environmental Sciencies, Volume pp. 46-52. 3. C o l e , Henry A, , Jr.: On-Line Fa i lure Detect ion and Damping Measurement of Aerospace S t r u c t u r e s by Random Decrement Signatures . NASA CR-2205, Mar, 1973. 4 . Solodovnikov, V. V. (W, Chrzczonowicz, t rans l . ) : S t a t i s t i c a l Dynamics of Linear Automatic Control Systems, Second ed, Van Nostrand Reinhold CO., 1965. 5, Oppenheim, A l a n V,; and Schafer, Ronald W,: D i g i t a l S igna l Processing. Prent ice-Hal l , Inc., 1975. 6. Houbolt, John C,: S u b c r i t i c a l F l u t t e r Tes t ing and System I d e n t i f i c a t i o n . NASA CR-132480, Aug. 1974. 307 TABLE 2,- AFFTC FLUTTER TEST RESULTS: MODE L I S T PRXNTOUT, (27 ,000 ft = 8239 m) RUN NO. = 18 SPEED = 350.E ALTITUDE = 27000 X-DUCER = 7. SETUP NUMBER = 1 ENRG. THRES. = .01 ALPHA CUTOFF = 25.6 % TOT. ENERGY = .9789 MODE NO: % ENERGY: FRE(1: S-DAMP: RESIDUE: PHASE: 1. 28.73 2.24 .0967 1.511 -79.78 2. 69.15 3.04 .0536 1.756 -76.61 3. 1.038 4.16 .0507 .2792 -58.11 4. 1.072 5.76 .0447 .3597 -134.3 308 FACILITY ? A ~ E ~ Figure 1,- F l a t 309 c i 310 viscous DAIPING RATIO CC) FOURIER DESCRIPTION - - [TRANSFER FUNCTION] U Figure 3.- Transfer function parameters. .3 .2 1 .l 7 10 7.5 5 2.5 0 32 64 $$ 12# 160 192 224 258 RESOLUTION ELENENT HUNBER (FREQUENCY DOMAIN l%lAMESiZE = 256) Figure 4 .= Ten-pexcent' exror limitation plot . 311 10. -10. 0. 8.0 TIME Figure 5.- Truncation of data frames. 16.0 Figure 6,- T h e ave 3 1.2 FREQUENCY 2 . 5 6 3 34 8.79 14 74 22.27 45.00 Figure 7 . - Analysis of model data using swept sine input. STRUCTURAL DAMPING .04Q . l o 3 .119 03 2 ,119 .204 313 10. REALS [VOLTS) -10. RUN NO. = 18 X-DUCER = 7. SPEED = 350.E ALT = 27000. START NO. = 94 Figure 8.- AFFTC flutter test results: t i m e history select ion. (27 ,000 f t = 8230 rn) 1.0 MAGN 0 0 FREQUENCY [HZ] 19.84 - RUN NO. = 18 X-DUCER = 7. SPEED = 350.E ALT = 27000. Figure 9.- AFFTC flutter test results: transfer function magnitude. (27,000 f t = 8230 rn) 314 I . 1 1 . . I I . 1 I O r CI e ui a z c3 U ui 5 0 315 Figure 11.- Forced response i n t h e presence of noise. 0. FREQUENCY 30. Figure 1 2 , - Magnitude of t h e ion f o r a forced response i n t h e presence of noise , 316 N t= P 0 m 31 7 FLIGHT FLUTTER TESTING TECHNOLOGY AT G R W H. J. Perangelo Grumman Data Systems Corporation F. W. Milordi Grumman Aerospace Corporation SUMMARY The stringent requirements for flutter testing modern-day aircraft have led Grumman to develop new analysis techniques to be used in its Automated Telemetry Station for on-line data reduction. The initial technique developed by Grumman utilized a least-squares difference-equation linear-systems ident- ification approach to extract resonant frequency and damping coefficient information from digitally filtered input and response data. This technique was successfully used on the F-14A flutter program starting in 1971, provid- ing a quantum increase in capability relative to previously used techniques. The main advantages of the approach are (1) Multimodal (highly coupled) analysis capability (2) Quantitive answers for highly damped modes (3) Ability to handle fast shaker sweeps (2 to 70 Hz in 15 sec) These advantages, coupled with the computational and data storage capacity of the ATS, reduced test time, saved fuel, and significantly increased flight test efficiency. Grumman has since expanded its flutter data reduction capability to encompass correlation, random decrement, and spectral techniques which are used in conjunction with its least-squares difference-equation identification approach to determine modal characteristics of response signals excited either by deterministic or random means. ing techniques have exhibited superior noise rejection characteristics relative to the digital filtering approach initially employed; however, the proper utilization of these techniques generally requires an increase in data record length or sweep time. This is particularly evident when response signals are of a bimodal nature or contain low frequency modes ( = displacement response ( a t some s t r u c t u r a l loca t ion) x ( t ) = s t r u c t u r a l d r iv ing function &,em = constant c o e f f i c i e n t s (with dN = 1.0) N, M = p o s i t i v e in t ege r constants (M and x ( t ) Equation (8) states that t h e f i l t e r e d response and dr iv ing function s i g n a l s are dynamically r e l a t ed t o each other through the same system t r a n s f e r function as t h e u n f i l t e r e d s igna l s . Thus, i n t h e a n a l y s i s of system response t o a known d r iv ing function, i d e n t i c a l l y f i l t e r e d measurements of system input and output data can be used without masking dynamic behavior. f i l t e r i n g p lays an important r o l e i n minimizing noise e f f e c t s . This Certain well-known cross-correlation and cross-spectral r e l a t ionsh ips can be e a s i l y es tab l i shed along c l a s s i c a l l i n e s s t a r t i n g with e i t h e r equation (6) o r (7) . The development here w i l l emphasize those i t e m s considered s i g n i f i c a n t i n the computation of these functions f o r systems i d e n t i f i c a t i o n purposes. F i r s t consider t h e ca lcu la t ion of the c ross -cor re la t ion of some a r b i t r a r y s i g n a l w(t) with y ( t ) and x ( t ) over t h e f i n i t e i n t e r v a l of time ranging from tl t o t seconds as denoted by 2 t w( t )y( t + T)dt @ w y ( T ) - 1 t -t r 2 1 tl t2 2 1 tl (P,(T) = S w( t )x ( t + .r)dt t -t 340 Subs t i t u t ing y ( t ) from equation (6) i n t o equation (9) r e s u l t s i n t h e following cross-correlation convolution i n t e g r a l : x(t+.r-a)h(a)do CpWy(d - 1 t -t 2 1 tl t2 --m 2 1 tl so0 = .t h ( , , [ ~ 1 w(t)x(t+T-o)dt -I- I f t h e system is assumed t o be i n i t i a l l y a t rest,it follows that both Cp (T) Wy and $I equation (11) can be changed from +oo t o t +T. Because t h e lower l i m i t of i n t eg ra t ion can be set t o zero, due t o system causa l i t y , t h e r e s u l t a n t com- puta t ion i s f i n i t e . The majority of test s i t u a t i o n s involve t h e ana lys i s of d a t a from a s t a b l e system exc i ted by a f i n i t e duration input s igna l . Under such conditions t h e co r re l a t ion functions computed v i a equations (9) and (10) w i l l tend t o zero as T increases i n magnitude and thus represent func t ions whose Fourier transforms e x i s t . Taking the Fourier transform of equation (11) r e s u l t s i n the following cross-spectral re la t ionship : (T) are zero f o r ‘t<-t2 and t h a t t h e upper l i m i t of i n t eg ra t ion i n wx 2 Cp (iw) = H(iw)Cpwx(iw) wy where Cp (iw), Cp (iw) = Fourier transforms of Cp (T) and C~,(T) Wy wx Wy Comparing equation (11) with (6) and equation (12) with (7) reveals t h a t Thus, t h e c ross -cor re la t ion and s p e c t r a l functions involved are mathematically r e l a t e d i n the s a m e manner as a c t u a l system input and output var iab les . an algorithm attempting t o i d e n t i f y system resonant frequencies and damping c o e f f i c i e n t s from measured response and d r iv ing function s i g n a l s can use cross-correlation o r c ross -spec t ra l techniques t o reduce t h e da t a without 341 disguis ing system c h a r a c t e r i s t i c s . It should be noted t h a t t h e above mentioned r e l a t ionsh ips hold regard less of t he interval between tl and t2" Obviously as t h i s time i n t e r v a l increases , no ise r e j e c t i o n improves and t h e ca lcu la ted functions @=(T) and @ (T) become b e t t e r approxha t ions t o t h e i r classical cross-correlation functions. spec t r a l techniques are slower from a computational po in t of view, they are more powerful i n suppressing noise e f f e c t s than simple f i l t e r i n g . Wy Although cross-cor re la t ion and Autocorrelation and au tospec t ra l ca l cu la t ions , requi r ing only response s igna l measurements, can prove of value i n analyzing f l u t t e r response da ta obtained from an a i r c r a f t excited by a dr iv ing func t ion possessing an impul- sive autocorre la t ion function. Random exc i t a t ion having e i t h e r a spectrum which is broadband-flat o r one which can be considered as the output of a l i n e a r system which is dr iven by a broadband-flat random input s a t i s f y t h i s requirement. source such as atmospheric turbulence o r a r t i f i c a l l y via random shakers. Deterministic s igna l s such as a broadband s i n e wave sweep, a narrow spike, o r function such as s i n e (wt)/(wt), where w i s somewhat l a r g e r than t h e h igh- est s i g n i f i c a n t frequency i n t h e response da ta , a l s o s a t i s f y t h e impulsive au tocorre la t ion function requirements. This random exc i t a t ion can be obtained e i t h e r n a t u r a l l y from a The mathematical s ign i f i cance underlying the au tocorre la t ion approach can be evolved from e i t h e r equation (6) o r (7) . S t a r t i n g from equation (7), multiplying both s ides of t h i s equation by i t s complex conjugate r e s u l t s i n Y (-iw)Y(iw) = H(-iw)H(iw)X(-iw)X(io) or 2 @ (iw) = ]H(iw) I @ (io) YY xx I f @ (iw) i s broadband-flat then xx @ ( i w ) 2 IH(iu)I2 = H(-iw)H(iw) YY Taking t h e inverse Fourier transform of equation ( 1 4 ) r e s u l t s in 342 +m Qyy(t) = .f h(.r)h(t + .r)dT -m 4- = 1 h(-T)h(t - T)dT -m Equation (15) i n d i c a t e s t h a t t h e function (p ( t ) , which i s e s s e n t i a l l y equiv- a l e n t t o t h e au tocorre la t ion func t ion of y ( t ) , i s equal t o a similar r e l a t ion - sh ip r ep resen ta t ive of t he au tocorre la t ion func t ion of h ( t ) . This equation a l s o ind ica t e s t h a t $I ( t ) i s equivalent t o t h e system output response re- s u l t i n g from t h e input dr iv ing func t ion equaf t o t h e impulse response func t ion folded about t h e t = O axis. For values of t > O it follows t h a t $I ( t ) i s a c t u a l l y t h e f r e e decay of t h e system t o t h e aforementioned input. YY YY YY Another method f o r analyzing randomly exc i ted response da ta , t h a t has This method e s s e n t i a l l y averages fixed-duration segments of emerged i n recent years, i s t h e random decrement s igna ture method. (See reference 5.) a random response record t o ob ta in what i s termed a random decrement signa- tu re . The p a r t i c u l a r segments t o be se lec ted and averaged from a given random response record are determined on t h e b a s i s of s i g n a l l eve l . i a l l y , a predetermined l e v e l is es tab l i shed . Every t i m e t h e amplitude of t h e response s igna l rises pas t o r s inks below t h i s level a fixed-duration segment of da t a , s t a r t i n g a t t h e time t h e level i s crossed, i s averaged with previous- l y accumulated segments. It can be reasoned t h a t as t h e number of averaged segments increase t h e r e s u l t a n t random decrement s igna ture w i l l approach the f r e e decay of t h e system from an i n i t i a l displacement equal t o t h e pre- determined s igna tu re l e v e l . I n some respec ts t h e random decrement s igna tu re is s i m i l a r t o an au tocor re l a t ion function i n t h a t both r e l a t ionsh ips represent f r e e decay information. equivalent s ince they represent d i f f e r e n t f r e e decay problems. Essent- However these r e l a t ionsh ips are not Difference-Equation/Z-Transform Modeling Approximation Grumman f l u t t e r ana lys i s software uses what has been termed a model- matching method as a primary means of ex t r ac t ing resonant frequency and damping c o e f f i c i e n t information from test da ta . Actually, t h e process i s a least-squares equation-error parameter i d e n t i f i c a t i o n technique. essence, c o e f f i c i e n t s o r parameters of a dynamic model are a n a l y t i c a l l y manipulated t o obta in t h e bes t f i t , i n a least-squares sense, t o t h e test da ta . The dynamic model used i n t h e i d e n t i f i c a t i o n process takes t h e form of a f in i t e -d i f f e rence equation. This difference-equation model i s a d i s c r e t e version of equation (1) which i s w e l l su i ted f o r u se i n a d i g i t a l computer where sampled values of test da ta must be d e a l t with. A d e t a i l e d I n 343 der iva t ion of t h i s difference-equation model, accomplished through t h e use of Z-transform mathematics and sample-data system theory, i s contained i n reference 1, A somewhat abbreviated de r iva t ion is set f o r t h below f o r t h e convenience of t h e reader. The essence of t h e de r iva t iona l approach is t o model t h e continuous system with an open-loop sample-data system so t h a t t h e synchronously sampled input and output s i g n a l s of t h e modeled system approximately agree with t h e i r corresponding continuous system counterpar t s a t t h e sampling in s t an t s . This i s accomplished by assuming a sampled system model contain- ing the continuous system t r a n s f e r func t ion H(s), as defined i n equation (2), preceeded by a da ta recons t ruc t ion element possessing a polygonal hold c h a r a c t e r i s t i c . (See chapter 11, reference 6 . ) In t h e opera t iona l ' r ~ l ' nota t ion of t h e Laplace transform, t h e t r a n s f e r func t ion f o r a polygonal hold recons t ruc t ion element i s defined by where T = t i m e increment between sampled da ta po in t s This da ta recons t ruc t ion element converts t h e sampled input t o t h e model i n t o a continuous s igna l constructed by connecting t h e sampled input po in ts with s t r a i g h t l i n e s . Driving the continuous system dynamics with t h i s approximation t o t h e a c t u a l input s i g n a l genera l ly r e s u l t s i n an output s igna l t h a t agrees w e l l wi th t h e a c t u a l system response s igna l , provided t h e sampling frequency is at least 5 times t h e upper pass-band l i m i t of t h e continuous system and of a s u f f i c i e n t rate t o in su re a r e l a t i v e l y smooth reconstructed input s igna l . The r e s u l t a n t t r a n s f e r func t ion f o r t h e model- ed plant dynamics is P ( s ) = D(s)H(s) where 1 Ts H1(s) = - 2 H(s) 344 The ana lys i s of sample-data systems is generally accomplished through the use of the Z-transform i n much t h e same manner as continuous systems ana lys i s is t i e d together through t h e use of e i t h e r the Laplace o r Fourier transforms. sampled t i m e functions. relates the Z-transforms of sampled system output t o sampled system input and is simply converted t o a t i m e domain d i f f e rence equation between sampled system input and output quan t i t i e s . The Z-transfer function r e l a t ionsh ip f o r t h e modeled sample-data system is defined by The Z-transform represents a convenient means f o r handling The Z-transfer function of a sample d a t a system * where R(Z) = Z-transform of X(Z) = Z-transform of sampled model output sampled input s i g n a l P(Z) = Z-transfer function of sampled d a t a model Ts Z = e Using the t i m e s h i f t i n g theorem,it follows from equation (17) t h a t -1 2 P(Z) = - Hl(Z) Z - l ’ Now s ince H (s) is express ib le as a f i n i t e r a t i o of polynomZals i n s, whose denominator polynomial is of nigher order than t h a t of i t s numerator, i t i s poss ib le t o compute H (Z) from H (s) i n accordance with t h e following i n t e g r a l d e f i n i t i o n of t h e Z-transform: 1 1 1 Equation (20) expresses H (Z) i n t e r m s of a sum of residues f o r t h e bracketed expression over t he poles of H ( s ) . The r e s u l t is t h a t H1(Z) is express ib le as a f i n i t e r a t i o of polynomials i n Z. Subs t i t u t ing equation (20) i n t o (19) and car ry ing out t h e indicate.d a n a l y t i c a l manipulations, f o r t h e given form of H1(s)’ r e s u l t s i n t h e following expression f o r P(Z): 1 1 345 EJ N C bnZen C bnZmn N N (l-ePnTz-l) c anZmn n=l n= 0 - n=O - n=O P(Z) = Equation (21) shows t h a t t h e Z-transfer func t ion of t h e modeled sampled- da ta system is a f i n i t e r a t i o of polynomials i n Z. numerator and denominator are both equal t o N, which corresponds t o t h e order of t h e denominator polynomial of H ( s ) , d a t a recons t ruc t ion device used and t h e assumed form of H ( s ) . (18) and ( 2 1 ) it follows t h a t The order of t h e This i s a consequence of t h e From equation N N n = l n= 0 R(Z) = -1 anZ-nR(Z) + C bnZ-nX(Z) Taking t h e inverse Z-transform of equation ( 2 2 ) r e s u l t s i n t h e following d i f fe rence equation re la t ionship : N N n = l n= 0 r ( t ) = -1 anr(t-nT) + C bnx(t-nT) where r ( t ) = t h e inverse 2-transform of R(Z) Equation ( 2 3 ) represents t h e dynamic difference-equation r e l a t ionsh ip between t h e modeled sample-data systems response r ( t ) and sampled values of t h e a c t u a l system input x ( t ) e system response is approximately equal t o t h e a c t u a l response of t h e continuous system a t d i s c r e t e sampling increments, t h i s d i f f e rence equation r e l a t ionsh ip is more appropr ia te ly w r i t t e n as Since i t is assumed t h a t t h e modeled N N n= l n=O Y (kT) = -c any(kT-nT) + C bnx (kT-nT) 346 where k = a p o s i t i v e in t ege r constant y(kT), x(kT) = values of y ( t ) and x( t ) at t=kT a b = constant d i f f e rence equation c o e f f i c i e n t s corresponding t o demonimator and numerator Z-transfer func t ion polynomial c o e f f i c i e n t s n” n The a poles p of t h e system t r a n s f e r function H ( s ) as indicated i n equation (21) . System resonant frequencies and damping c o e f f i c i e n t s are determined from t h e poles of H ( s ) through t h e r e l a t ionsh ips defined i n equations (3a) and (3b). difference-equation c o e f f i c i e n t s i n equation ( 2 4 ) are r e l a t e d t o t h e n n It follows from equation (8) t h a t f i l t e r e d system response and d r iv ing func t ion data, y,(t) and x f ( t ) , are r e l a t e d by t h e same general difference- equation re la t ionship . Thus, N N Yf(kT) = - anyf(kT - nT) + C bnxf(kT - nT) n=l n=O From equations (9) t o (12), it obviously follows t h a t t h e c ross -cor re la t ion functions + ( t ) and +,(t) are r e l a t e d i n a s i m i l a r fashion, r e s u l t i n g i n Wy N N +w(kT) = - C a + (kT - nT) + C b n w x $I (kT - nT) n= 0 n w y n=l I f t h e system is excited by an input s igna l having a broadband-flat s p e c t r m , t h e au tocorre la t ion func t ion of system response Q, representa t ive of t h e f r e e decay of t h e system f o r values of t grea te r than zero. I n t h i s case , the following difference-equation r e l a t ionsh ip is implied : ( t ) w i l l be YY N +yy(kT) = -1 a 4 (kT - nT) nYY n=l 347 When dealing wi th response s i g n a l s represent ing t h e f r e e decay of t h e system, it follows from equation ( 2 4 ) t h a t N It a l s o follows t h a t N w(jT)y(jT + kT) = -1 a w(jT)y(jT + kT - nT) n n = l where j = a pos i t i ve in t ege r constant w(t) = an a r b i t r a r y function of time and, t he re fo re , J J N C w(jT)y(kT + j T ) = -C C anw(jT)y(jT + kT - nT) j =O j=O n = l o r t h a t , f o r t h e free decay problem,the following cross-cor re la t ion d i f f e rence equation app l i e s : N +wy(kT) = -C a (kT - nT) n w y n= l Equations (25) t o (28) represent those fundamental d i f f erence-equation r e l a t ionsh ips u t i l i z e d by Grumman's on-line software f o r t h e purpose of ident i fy ing system resonant frequency and damping c o e f f i c i e n t information. Resonant Frequency/Damping Coefficient I d e n t i f i c a t i o n Equation ( 2 4 ) def ines t h e basic d i f f erence-equation r e l a t ionsh ip used This equation w i l l be used i n t h e following a n a l y t i c a l d e s c r i p t i o n by Grumman's least-squares equation-error parameter i d e n t i f i c a t i o n algo- rithm. of t h e technique alebough it should be understood that any of t h e d i f f e r - ence equations represented by equations ( 2 5 ) t o (28) could be used, as d i c t a t ed by t h e manner i n which t h e measured test d a t a are i n i t i a l l y processed. 348 Analy t ica l ly , t h e least-squares equation-error i d e n t i f i c a t i o n technique minimizes t h e va lue of t he func t ion J shown below: where kl, k2 = in teger cons tan ts def in ing t h e da ta set over which J yk = y(kT) = t h e system response quant i ty a t time kT yk = y(kT) = t h e system response quant i ty estimated by t h e is t o be minimized - - d i f f e rence equation a t t i m e kT I n p a r t i c u l a r yk = -C a y + C bnxk-n n k-n n=O n=l where - - a b = estimates of t h e a and b c o e f f i c i e n t s contained i n equation ( 2 4 ) which minimize t h e func t ion J x(kT) n 9 n n n = xk = t h e system input quan t i ty a t t i m e kT I f t h e system response s igna l is t h e only quan t i ty required i n da t a ana lys i s , t h e second summation on the right-hand s i d e of equation ( 3 0 ) is dropped. The procedure f o r minimizing J c o n s i s t s of s u b s t i t u t i n g equation ( 3 0 ) i n t o equation (29) and tak ing t h e p a r t i a l de r iva t ives of t h e r e s u l t i n g expression with respec t t o t h e H and 6 c o e f f i c i e n t s , s e t t i n g the express- n n ions thus obtained t o zero. which are t o be solved f o r t h e des i red c o e f f i c i e n t information over t h e e n t i r e da t a set. The so lu t ion of t hese simultaneous l i n e a r equations, t o ob ta in t h e des i r ed es t imates f o r difference-equation c o e f f i c i e n t s , can be expressed i n t h e following m a t r i x form: This r e s u l t s i n 2N+1 equations i n 2N+1 unknowns ( 3 1 ) 349 where C = Dl = .I .I 'k2-l . . . 'k2-N Xk2 . . X k2-N (34 1 Equation (31) mathematically def ines t h e i d e n t i f i c a t i o n process used i n determining difference-equation coe f f i c i en t s . s c r i p t s T and -1 denote t h e respec t ive matrix transpose and inverse oper- a t ions a I n t h i s equation t h e super- Once t h e i d e n t i f i c a t i o n algorithm determines t h e a c o e f f i c i e n t s , as n elements of t h e estimated Z-transfer function P (2) are computed. (21) t ha t t h e r o o t s of t h i s polynomial are r e l a t e d t o t h e estimated poles of vec tor , t h e roo t s of t h e denominator polynomial of t h e It follows from equation H ( s ) by 350 where - y = t h e n t h root of t h e estimated Z-transfer func t ion denominator - polynomial 'n = t h e estimated n t h pole of H ( s ) It can be seen from equation (35) t h a t estimates f o r t h e real poles of H ( s ) are defined by From equations (3) and (35) it follows t h a t estimates f o r t h e complex conjugate poles of H ( s ) are defined by and it follows t h a t k k V - = - I [arc t a n (-1 'k T U I (38) (39) The real and imaginary p a r t s of t h e complex conjugate poles of H ( s ) are' computed i n accordance with equations (38) and (39 ) . The real poles of H ( s ) are computed from (36) . System damped n a t u r a l frequencies and damping c o e f f i c i e n t s are ca lcu la ted from t h e real and imaginary p a r t s of t h e complex conjugate poles of H ( s ) using t h e r e l a t ionsh ips shown i n equations ( 4 ) and (5) * 351 RESO SYSTEM IDENTIFICATIOM PROBLEM The example problem described i n t h i s appendix d e p i c t s t h e app l i ca t ion of t h e response-error modeling technique t o t h e i d e n t i f i c a t i o n of a s impl i f ied nonlinear resonant system roblem, The technique can be applied t o t h e ana lys i s of l i n e a r as w e l l as nonlinear systems although i t genera l ly requi res more computation t i m e than t h e d i f f e rence equation-error technique cur ren t ly used by Grumman i n t h e ana lys i s of l f n e a r da t a , of response-error modeling techniques t o l i n e a r and nonlinear system ident i - f i c a t i o n problems is cu r ren t ly undergoing extensive inves t iga t ion , covering The u t i l i z a t i o n f s c i e n t i f i c and engineering appl ica t ions . Spec i f ic algorithms i t y y , genera l ly depending on t h e manner i n which model parameters described here in is t o apply t h e concept, i n y s i s of resonant system phenomena t y p i c a l of t e r ed i n t h e ana lys i s of f l u t t e r response data. The d%scussion set f o r t h below fs ‘broken down i n t o t h r e e sec t ions . These sections respec t ive ly cover a statement of t h e example problem, a descrip- t i o n of t h e a n a l y t i c a l approach t o be used i n i t s so lu t ion and a discussion of some p ~ e l i m i ~ a ~ y r e s u l t s obtained, Problem Statement The problem addressed here concerns i t s e l f with t h e i d e n t i f i c a t i o n of a nonlinear (hard-spring) resonant system defined by t h e following d i f f e ren t - i a l equation: e * Y (t ) KO; (t ) +KoY ( t ) +% sgn [ Y ( t ) ] Y ( t ) = F ( t ) (40) where Co KO, K1 = const an t parameters Y(t) = system displacement response F ( t ) = system forcing func t ion sgn[Y(t)] = +1 i f Y(t) i s p o s i t i v e o r -1 i f Y(t) is negative and K determine t h e dynamic behavior of 0 9 1 The constant parameters C t h e system. Therefore, t h e i d e n t i f i c a t i o n process c o n s i s t s of def in ing t h e value of t h e s e parameters from measured da ta , It is assumed t h a t r e l a t i v e l y 352 c lean measurements of system v e l o c i t y response and forcing function are ava i lab le . It is f u r t h e r assumed t h a t t h e system i s i n i t i a l l y at rest and that t h e forcing func t ion is a swept frequency s i n e wave whose frequency i s var ied from some point below t o some o ther point above t h e apparent resonant frequency of t h e system. The least-squares response-error modeling technique i s t o be used as t h e method f o r achieving system identification., This technique e s s e n t i a l l y assumes t h a t t h e form of the dynamics are known, thus allowing t h e e s t ab l i sh - ment of a dynamic system model. The i d e n t i f i c a t i o n process i s implemented by varying the c o e f f i c i e n t s i n t h e model so as t o minimize t h e mean-square- e r r o r between t h e measured v e l o c i t y response of t h e a c t u a l system and t h e corresponding v e l o c i t y response of t h e assumed model, Underlying Analytical Approach Since knowledge of t he a c t u a l system's form i s assumed, t h e following equation def ines t h e system model : The lower-case nomenclature used i n equation (41) d i s t i ngu i shes modeled system q u a n t i t i e s from those of t h e ac tua l system, as defined by equation (40) . Sta r t ing wi th i n i t i a l estimates f o r c measured values of system d r iv ing function, equation (41) is solved t o ob ta in i t s ve loc i ty response over some i n t e r v a l of i n t e r e s t . meters are incremented, from run t o run, so as t o minimize t h e following mean square e r r o r function: k ,and kl, along with 0' 0 Model para- T 2 3 = 1 E ( t ) d t 0 where T = t i m e duration of ana lys i s E(t) = i ( t ) - ; ( t ) 353 In order t o a n a l y t i c a l l y compute t h e parameter changes required t o miniaize J it i s necessary t o express i ( t ) as a func t ion of t hese quan t i t i e s . For a given forc ing function, $ ( t ) can be considered t o be a function of i t s current parameter va lues ( i e e e 9 c k ,and k ) and t i m e . The form of ? ( t ) f o r some o the r set of parameter va lues ( i e e e , c k 4- Ak ) can be simply approximated from t h e f i r s t o rder terms of the Taylor series expansion f o r y ( t> as indica ted i n t h e following equatbon: o 9 0 1 + Ace, ko + Ako and 0 1 1 where - - YO ia - Ac0 + - Ak, + - akO ( 4 3 ) The pa r t i a l de r iva t ives of t h e right-hand s i d e of equation ( 4 3 ) are t i m e varying s e n s i t i v i t y c o e f f i c i e n t s which are so lu t ions t o s e n s i t i v i t y d i f f e r e n t i a l equations, These d i f f e r e n t i a l equations are e a s i l y derived from equation ( 4 1 ) by tak ing t h e pa r t i a l de r iva t ive of t h i s lat ter equation wi th respect t o each parameter as indicated below: which can be w r i t t e n as 354 where I n a l i k e manner t h e s e n s i t i v i t y equations f o r k and k 0 1 are defined by .. where ayO ayO s3 = - akl s = - 2 8k 0 Equations ( 4 4 ) , (45) , and (46 ) are l inea r , second-order, d i f f e r e n t i a l equations with t i m e varying s t i f f n e s s c o e f f i c i e n t s t h a t are a func t ion of t h e modeled system's displacement s igna l . d i f f e r e n t i a l equations are a function of t he ve loc i ty o r displacement response of t h e modeled system. The time varying s e n s i t i v i t y c o e f f i c i e n t s required i n equation ( 4 3 ) are obtained by solving equations (44 ) t o ( 4 6 ) along with equation (41) . The exc i t a t ion s igna l s d r iv ing t h e s e n s i t i v i t y Now t h a t a l l t h e elements i n equation ( 4 3 ) are defined, it can be subs t i t u t ed i n t o equation (42) r e s u l t i n g i n ( 4 7 ) T . , 2 J = 1 0 [Y - yo - SIAco - S Ak - S3Akl] d t 2 0 The function J is minimized by tak ing its p a r t i a l de r iva t ive with respec t t o each of t h e incremental parameter changes and s e t t i n g t h e result ir lg expressions t o zero. The so lu t ion of t he t h r e e simultaneous l i n e a r equations, 355 t o obtain t h e three incremental parameter changes, can be expressed i n the following m a t r i x form: where T 0 V - r T 0 [SI = J- P = [Sl-lv r I S I 2 d t . . s1s2 s; . . '3'2 " 2 I:i s3 d t The elements of the P vector, computed by multiplying t h e inverse S matrix by the V vector, express t h e parameter changes resu l t ing from a given pass through t h e data. The process i s generally repeated u n t i l the parameter changes become small o r t he calculated value of J f a l l s below some pre- scribed leve l . Example Problem Results A digital-computer algorithm using the defined ana ly t ica l approach w a s designed f o r t he purposes of making a preliminary evaluation of t h e technique. a t numerical values of 3948 and 394 .8 , -with the value of C I n t h i s evaluation the KO and K system parameters w e r e set 1 being varied 0 356 between 3.142 and 12-57. would have a resonant na tu ra l frequency of LO Nz and s t r u c t u r a l d ~ p ~ g c o e f f i c i e n t s ranging from 0,05 t o 0 .2 , The apparent resonant frequency of t h e a c t u a l nonlinear (hard-spring) system is gen her than 10 Hz increas ing with t h e magnitude of system displacemen i n turn, is a function of t he system's inherent damping and the magnitude of t h e d r function. The assumed form of t h e dr iv ing func t ion w a s an exponentia swept frequency sine wave covering t h e 6 t o 20 Ez frequency range in approzr- imately 6 secondso The amplitude of the d r iv ing f u n c t i w a s held a t a constant amplitude which w a s numerically equfvalent t o I n i t i a l runs ind ica ted t h a t convergence of t h e algorithm w a s depen on having reasonable i n i t i a l estimates f o r system parameters. good estimates are not always ava i lab le . Rather than increaslng the analyt- i c a l complexity of t h e c o e f f i c i e n t updating technique, which w a s considered outs ide t h e scope of t h i s preliminary inves t iga t ion , i t w a s decided t o adopt a s t r a t e g y t h a t could be applied i n prac t ice , with s u i t a b l e cons t r a in t s , t o generally insure convergence. information contained i n the test d a t a and t h e user ' s presumed knowledge f o r t h e form of the system's dynamics. i n i t i a l value of k w a s set t o zero, with t h e i n i t i a l value of k taken as the squared value of t h e apparent resonant frequency of t h e response data. This frequency is simply determined by measuring the period of t h e response s igna l i n the v i c i n i t y of its peak value. se lec ted a t a t e n t h of t h e square roo t of koe nominal s t r u c t u r a l damping c o e f f i c i e n t of 0.1 i f t h e system w e r e l i n e a r . A l i n e a r system with these values f o r C and go 0 In p r a c t i c e The s t r a t e g y adopted w a s based on t h e inherent I n accordance with t h i s s t r a t egy , t h e 1 0 The i n i t i a l value f o r co w a s This would correspond t o a Algorithm parameter updating w a s constrained so t h a t kl would be set was prevented from f a l l i n g below a ten th of back t o zero i f i t s value went negative o r became g rea t e r than t h e cur ren t value of ko. its i n i t i a l value, F ina l ly , t h e parameter changes from run t o run were constrained so that. t h e change i n k could not exceed t h e i n i t i a l value of ko and t h a t t h e change i n kl could not exceed a t e n t h of t h e i n i t i a l va lue of koe ponding l i m i t s a l l parameter changes were uniformly attenuated by a f a c t o r (not t o be less than a tenth) in an attempt t o prevent any parameter change from exceeding its l i m i t . are considered loose and were determined empir ica l ly with no attempt being made t o r e f i n e them i n an optimal sense. The value of k 0 0 I f e i t h e r o r both of t hese parameter changes exceed t h e i r corres- For t h e problem a t hand, t h e above cons t r a in t s Using t h i s s t r a t egy , r e s u l t s w e r e obtained i n analyzing d a t a from systems having C damptng t e r m s of 12.57$ 6.283, and 3.141. The s t i f f n e s s 0 357 c o e f f i c i e n t s KO and K1 were he ld a t cons tan t va lu The r e s u l t s l i s t e d below r e f l e c t t h e a b i l i t y of t h e approach t o converge on t h e t r u e c o e f f i c i e n t va lues with t h e inherent c h a r a c t e r i s t i c of r equ i r ing more i t e r a t i o n s as damping decreases . of 3948 and 394.8, Ana 1 ys is Model Parameter For C = 12.57 0 For C = 6.283 0 For Co = 3.141 Pass 0 1 2 3 4 5 6 0 1 2 3 4 5 6 7 8 9 1 0 0 1 2 3 4 5 6 7 8 9 10 11 1 2 13 C 0 6.911 11.70 14.32 12.87 12.67 12.57 12.57 7.540 10.51 6.423 8.113 8.337 6.139 6.832 6.458 6.294 6.282 6.283 8.796 5.727 5.960 4.738 2.967 3.244 3 280 3.284 3.306 3.281 3.171 3.137 3.140 3.141 k 4777. 4724. 4411. 3843. 3977. 3947. 3948. 5685. 4644. 4618. 4914. 5136. 4151. 4482. 4157. 3943. 3948. 3948. 7738 5803. 4981. 6064. 5557. 5630. 5359. 5066. 4745. 4300. 3979. 3954. 3949. 3948. 0 kl 0.0 35.56 217.4 439.6 386.2 395.2 394.8 0.0 323.6 391.0 387.5 262.5 394.0 343.3 368.3 397.5 394.7 394.8 0.0 474.2 605.8 260.7 235.6 234.8 263.3 293.7 328.0 372.9 396.1 394.1 394.6 394.8 358 1. Waisanen, P,R,, and Perangelo, H.J,: Real Time Flight Flutter Testing via Z-Transform Analysis Technique. AIM Paper No, 72-784, 1972, 2. Baird, E.F,, and Clark, W.B.: Recent Developments in Flight Flutter Testing in the United States. AGARD Structures and Materials Panel, Lyngby, Denmark, April 1972. Paper presented at 34th meeting of 3. Taylor, Lawrence W.,Jr., and Iliff, Kenneth W.: Systems Identifica- tion using a Modified Newton-Raphson Method - A FORTRAN Program. NASA TN D-6734, May 1972. 4. Grove, Randell D., Bowles, Roland L., and Maybew, Stanley C.: A Procedure for Estimating Stability and Control Parameters from Flight Test Data by using Maximum Likelihood Methods Employing a Real-Time Digital System. fiJASA TN D-6735, May 1972. 5. Cole, Henry A., Jr.: On-Line Failure Detection and Damping Measure- ment of Aerospace structures by Random Decrement Signatures. CR-2205, March 1973. NASA 6. Ragazzini, J.F., and Franklin, G.F.: Sampled-Data Control Systems. McGraw-Hill Book Company, Inc., New York, 1958. 359 Table 1,- System command opt ions I t e m Maneuver mode P l o t menu S t a r t maneuver S t a r t event Stop event Stop maneuver Recall mode P lo t recall U t i l i t y opt ion * Input types: Input * KB LK, LP LK LK LK LK KB, LK KB, LP KB, LP Function Applicat ion program s e l e c t i o n Selects p l o t s and/or t a b s f o r d i sp l ay I n i t i a t e s real t i m e d a t a t r a n s f e r t o d i sk I n i t i a t e s processing and tagging of d a t a Tags end of da t a slice t o be processed Ends d i s k recording and processing Allows intermaneuver d i s k da t a processing Allows d i sp lay of previous a n a l y s i s r e s u l t s Enables access t o f i l e s f o r purposes of changing p l o t scales, da t a s c a l i n g and c e r t a i n program a n a l y s i s v a r i a b l e s KB - Keyboard type-ins LK - Latchkey push but ton s e l e c t i o n LP - Display l i g h t pen s e l e c t i o n Table 2.- Overview of major a n a l y s i s program opt ions ~ Model a n a l y s i s order Multiple a n a l y s i s order Data preprocessing F i l t e r i n g con t ro l Corre la t ion l a g range Transform s i z e Data window Transducer s e l e c t i o n Data sample rate Analysis op t ions Model order can be var ied from 2 up t o 1 4 f o r each response t ransducer Multiple ordered ana lys i s models can be spec i f i ed f o r use on response d a t a y ie ld ing sepa ra t e r e s u l t s Recusive d i g i t a l f i l t e r i n g , c ross -cor re la t ion ana lys i s , au tocor re l a t ion ana lys i s , o r random decrement s igna tu re processing Spec i f ica t ion of pass-band and rol l -off character- ist ics (up t o 36 dB p e r octave) Se lec t ion of co r re l a t ion func t ion p o s i t i v e and negat ive l a g range Fas t Fourier transform s i z e up t o 2048 po in t s Spec i f ica t ion of t i m e dura t ion o r frequency range Analysis of 1 t o 28 measurements a t 500 samples per second 500, 250,or 100 samples per second 360 Table 3. - Summary of TLEFAD r e s u l t s on simulated swept frequency response d a t a 41.8 52.1 TLEFAD pre- processing option Direct 22.0 HZ 19.0 Hz .198 41.5k.239 .203+.011 26.0 t o 33.0 t o .050 52.1rt.048 .050rt.002 62.0 Hz 67.0 Hz Cross- o r r e l a t i o n Auto- o r r e l a t i o n 361 Table 4. - Summary of r e s u l t s on simulated randomly exc i ted response da ta Program TLEFAD RES I D 0 Option Auto- c o r r e l a t i o n Auto- co r re l a t ion Random decrement T i m e dura t ion (seconds) 90 90 90 18 0 Number of runs 11 1 3 1 3 6 'rue _I fd - 2.00 3.00 8.00 16.0 42.0 52.0 2.00 3.00 8.00 16.0 42.0 52.0 2.00 3.00 8.00 16.0 42.0 52.0 2.00 3.00 8.00 16.0 42.0 52.0 - I_ - s u l t t g . loo ,050 .075 .030 200 .050 .loo .050 .075 .030 .200 .050 .loo .050 .075 ,030 ,200 .050 . loo .050 .075 .030 .200 .050 - - Analysis f d -t l o 2 e OO+ ,042 3 - OO+ .024 8.01+. 055 16 .O+. 060 41.621.03 52.1+. 149 2.01+. 034 3. 012. 017 8. Ol?. 052 16.0+. 055 4 2 . 1 ~ 380 52.2t.168 2.00+. 037 3.00+ .029 8.022. 060 16 .02. 073 42.6+. 526 53.4+. 307 2. oo+. 021 3.01+. 018 8.03+ 051 16. O+ .049 42.5k.407 52 e 32.157 e s u l t s g + l o .084+. 019 .041+. 011 .063+. 017 .031+. 006 .182+. 029 .0512. 004 .068+. 015 .041+. 012 .067+. 016 .025+_. 004 e 186+. 024 .052+. 006 e 068+. 023 .041+_. 015 .059+ a 017 .027C. 005 .194+. 044 .055+. 007 .076+. 009 .045+. 010 .058+. 011 .027+. 002 .185+. 026 .053+ e 006 362 Table 5. - Summary of f l i g h t test da ta r e s u l t s \ Mode AWlB SWlB SW2B g U fd fd I d d U U f d Analysis ~ TLEFAD 6.15 .089 5.26 -134 15.2 ,097 d i r e c t ,097 .011 .080 .022 .197 .008 TLEFAD 6.15 .095 5.24 .139 15.2 -103 crOss-cor~ ,035 1 .007 1 -055 1 .014 1 .155 1 .009 RESID0 6.14 .086 - - 15.1 ,082 FLAPR W~B/STRP I I 363 \ RF Demodulator Discriminator I BANKA, I Discriminator I ;IANKB 1 1 I I 1 Manual Patch Analog - Digital Converter 1-11 Preprocessor Tables Figure 1. - Block diagram of Automated Telemetry S ta t ion . 364 Modal characteristics: freq.= 2.00 - 3.00 - 8.00 - 16.0 - 42.0 - 52.0 damp.= .lo0 - .OS0 - .075 - .030 - .200 - .050 Figure 2.- Simulated flutter response data. 365 SE ER EYE F- -2 KEAS U: 71 0 0 5 n 0 I E 0 x . 1 1 1 1 2 2 S S A A A A 2. DO - 3.003 2.97 - 0.050 - f .50 0. 0s - 1 * 5 . ' . @ O 1.2C4 0 . O f O 1.00 - 12.2 3 . 5 6 1 15.9 - 0.029 4 . . 0. 02 - 1 . a o 40.1 - o . rii 0.00 -1.10 51.9- 0.052 from no i sy sweep i n f i g u r e 2. 0. 009 590.3 3.9s 151S.2 0. I U D 391.5 a. 93 '511.2 5. o o a 591. 5 E. 9s !5!5.2 1. DOE 590.5 :. 9s ?5!S.2 9. C O ~ ~ 9.6040 9.5040 9.6040 15.112 15. 112 23.03c 20.096 21.900 2?. 931 2:. 931 27.9D1 Flgure 3. - Annotated primary output t a b u l a t i o n from TLEFAD program. m2t 0 O f !5 n 7 . S¶# - A U l O l O 8039 !.49 I910 7 5 2 I5 11 2. 566-4 1.CSD-6 00 s2 J. n mws o s I. 19 7 . eo-6 5. crt-1 0121 11.9 W20 0 1 15 n :. 101-c 00000 3019 s4. ¶ Figure 4 . - Val ida t ion output t a b u l a t i o n from TLEFAD program. EVENT TI%IE ACTUAL FB 1.50 1 0 . 0 20. t $9.0 Figure 5. - Shaker frequency p l o t from TLEFAD program. 366 1.008 . . . . . . . . . . . . . . . . . . . . . . . . I l 1 0 0 . . . . . . . . . . . . . . . . . . . . . , . . . . . . . . . . . . . . -1.08 -1.m I O 0 0 1.000 2.000 LAGS (NORMALIZED) Figure 6 . - Input s i g n a l c ross -cor re la t ion funct ion from TLEFAD program. LAGS (NORMALIZED) Figure 7. - Response signal cross -cor re la t ion funct ion from TLEFAD program. 367 FREQUENCY Figure 8, - Power s p e c t r a l d e n s i t y p l o t from APSD program. FREQUENCY F igure 9 , - Frequency response func t ion ampl i tude from COQUAD program. 368 FREQUENCY Figure 10. - Frequency response phase a n g l e from COQUAD program. . 3 0 -. H '1.1 1. n 11.) FREQUENCY " 11. - Annotated in-phase spectrum from COQUAD program. 369 .so -1.1 1.11 11.4 1 FREQUENCY 121 Figure 12. - Annotated quadrature spectrum from COQUAD program. D A W . - (FREQ2/FREQl)' - 1 - (FREQP/FREQI)' + 1 XDUCER-CMK 05 05 05 RES. FKO. 3.027 12.01 e. 007 DARING COEF. .os .097 . l M ;REO 1 2.832 7.61 7 10.93 FREO2 "' J. 125 e. we is . t e Figure 13. - Annotated output tabulation from COQUAD program. 370 FREQUENCY Figure 14. - Calcula ted frequency response f u n c t i o n ampl i tude from ENERGY program. 01 @9 01 0) 42 6Y 42 0) 01 I Y 61 00 01 #Y 42 09 42 0) op #Y RES#IAllT FIWNCY 16.02 $2.11 IC. 00 52.04 I . t i 0 S.#@I 7. no 1 . n 9 5. b@1 1. no . OS04 .os25 .om2 .04YO .I145 . 0% 1 . (741 . t¶?S .#4YO . o n 2 l .c57*0 4.319-1 1 . 5 m o 4 . 3 m I 2 . w - 1 ¶. w- I 1.s.-1 2. m- 1 9. ¶IS- I 1.4%-1 .021 .020 .610 . 0 1 0 .020 .020 .021 . O f 0 .011 .01l . 2 U l . 2 U l ,2441 . 2 u 1 . W C .640C .WOC .04oc . U O C .E406 13.2 20.5 n. 1 57.0 12.4 22.9 31.7 57.0 1.50 2.21 2.2s 4. u c. u ¶. 6c 5. w c 30 10 .6 1*5. . 5 . I.% Figure 15 . - Primary ou tpu t t a b u l a t i o n from ENERGY program. 371 01 01 09 09 95 09 09 09 09 01 09 01 05 01 OS 01 0s 01 QS 02 09 09 09 02 09 02 09 09 05 2 ?I I 17.5C 16.01 41.71 52.04 -. 147 . 0 029 1. ¶?6 3.001 2.153 5.6% 7. 990 1.999 3.081 7.990 . D44C e. 215 _1c .2027 . I496 -1.00 -1.00 . t 043 . 151 1 .IO6 .074O .os75 . O W . 0 5 2 -1 .00 .4we 2.741-4 1.57% 0 I . 763-2 4 .17 - I 01111 01111 2.601-1 9. s.5- 1 3.354-2 1.nr-3 1.300-1 1..t32-2 2.995- 1 9.915-1 1.476-1 OOOOO .02# e1 .020 02 020 02 .r)l@ 02 .01 02 . O f 0 03 .010 03 .010 33 , D10 83 * 020 01 .02O 03 .020 03 .021 83 .020 D l . @ l o 03 . O l O 0 3 .OlO 0 3 . 0 1 0 02 .b10 02 .z 20. . I 57. 55. I 57.0 12.4 22.9 12.4 22.9 SI.? 57.0 31.7 57.0 31.7 57.0 31.7 57.0 1. so 2.21 2.2s 4.60 2.2s 4.60 2.2s 4 .60 6. u 9.66 I . so 5.56 1. se 5.56 I . 59 5.56 6.30 1 0 . 9 6. 30 1 0 . 6 L Diagnost ic f o r real d i f f e r e n c e equat ion roo t . F igure 16. - Annotated secondary ou tpu t t a b u l a t i o n from ENERGY program. FREQUENCY Figure 1 7 . - Reconstructed frequency response f u n c t i o n ampli tude from ENERGY program. 372 Figure 18.- Flight test f lut ter response data e 373 Figure 18. - Concluded. 3 74 1.8 1.4 0.6 1.4 0.2 0 2 4 6 8 10 12 14 ANALYSIS PASS Figure 19. - Parameter convergence f o r nonlinear model. 375 TBE APPLICATION O F DIGITAL COMPUTERS TO NEAR-REAL-TIME PROCESSING OF FLUTTER TEST DATA S. R. Hurley Lockheed-California Company SUMMARY A description o f procedures used i n monitoring, analyzing, and displaying f l i g h t and ground f l u t t e r t es t data is presented. These procedures include three d i g i t a l computer programs developed t o process s t ruc tu ra l response data i n near real t i m e . Qual i ta t ive and quant i ta t ive modal s t a b i l i t y data are derived from t i m e h i s to ry response data resu l t ing from rapid sinusoidal f re- quency sweep forcing functions ¶ tuned-mode quick stops and pilot-induced control pulses. The techniques have been applied t o both fixed- and rotary- wing a i r c r a f t f l u t t e r model t e s t s . during f l i g h t y whirl tower ro tor systems tests ¶ and wind tunnel An hydraulically driven osc i l l a to ry aerodynamic vane exc i ta t ion system is described. This system was recent ly u t i l i z e d during the f l i g h t f l u t t e r tes t programs accomplished during Lockheed L-1011 and S-3A development. INTRODUCTION The present day costs of prototype/development f l i g h t vehicles and over- a l l demands on f l i g h t t e s t i n g t i m e require t h e f l u t t e r engineer t o minimize both f l i g h t and calendar time associated with f lu t te r substant ia t ion and f l i g h t envelope clearance. This objective must be accomplished while maximum safe ty of f l i g h t t o t h e f l i g h t crew and vehicle i s maintained. Test and data analysis procedures must a l so be developed t o minimize the r i s k of s t ruc tu ra l damage and/or loss o f the high cos t , dynamically scaled wind tunnel f l u t t e r models normally used during the pre-prototype phase of a f l i g h t vehicle devel- opment program. test program which u t i l i z e s r e l i a b l e procedures o f instrumentation, s igna l conditioning, exc i ta t ion technique, ,and data transmittal/storage/retrieval/ display .) properly integrated and compatible with the pa r t i cu la r charac te r i s t ics of t he test vehicle. These objectives can be a t ta ined only by a well-coordinated The i n s t a l l a t i o n of special sinusoidal exc i ta t ion devices ¶ although desir- able, can be j u s t i f i e d only f o r those cases where t h e s t a b i l i t y of a number o f f lu t te r - s igni f icant modes must be monitored, or f o r those cases where a l t e rna te o r more economical exci ta t ion techniques, such as control pulses do not adequately exci te t h e modes o f i n t e r e s t . In invest igat ing the e f f ec t o f ” 377 r e l a t ive ly minor design changes which arise during t h e operational phase of an a i r c r a f t such as control system changes external s to re additions and s igni f icant m a s s or s t i f f n e s s var ia t ions , a l te rna te exc i ta t ion methods which do not demand special purpose hardware in s t a l l a t ions may be used. These methods include t h e well-known control pulse (manual or e l e c t r i c a l ) f o r l o w frequency modes generally less than 10 Hz, as w e l l as recent developments i n computerized data analysis techniques applied t o t urbulence-induced s t ruc tu ra l response data. The l a t t e r methods r e l y primarily on various Fourier trans- forms and spec t r a l analysis procedures t o determine modal frequency and damp- ing charac te r i s t ics . Examples of such techniques are described i n references 1, 2 , and 3. This paper b r i e f l y describes the various f l u t t e r t e s t i n g techniques u t i l i z e d at t h e Lockheed-California Company i n recent years as applied t o several major f l i g h t vehicle programs. online data monitoring capab i l i t i e s made possible by the a v a i l a b i l i t y of modern computerized data handling systems. Primary emphasis i s placed upon the Proper acknowledgement should be given t o several associates at the Lockheed-California Company who were instrumental i n developing , and making operationally p r a c t i c a l , t he techniques described i n t h i s paper. Ed.mund A. Bartsch and Darrow Richardson developed the real-time decay program and the real-time response program. B i l l Kobayashi developed the peak p lo t analysis with contributions made by Joe Bu t t i t t o , B u r t McCorkle, Bridget Shycoff, and Erick Sturcke. MODAL EXCITATION So t h a t t h e f lu t te r - s igni f icant modes of t he Lockheed L-1011 a i r c r a f t could be properly evaluated , an hydraulically driven osc i l l a to ry aerodynamic vane exc i ta t ion system w a s developed and in s t a l l ed on the wingtips and s t a b i l i z e r t i p s . being mounted on the a f t fuselage. Industr ies , Santa Ana, Cal i fornia . fabr icated at Lockheed by using he l icopter ro tor blade design and fabricat ion techniques , which provided the required s t ruc tu ra l capabi l i ty t o withstand the extreme i n e r t i a l and aerodynamic loadings imposed on t h e vanes at the required frequencies. are shown i n f igures 1 and 2. The same system w a s l a te r used during t h e S-3A f l u t t e r tes ts , The vane actuators w e r e developed by Royal The aerodynamic vanes were designed and Photographs o f the vane i n s t a l l a t i o n and control un i t s Sal ient features of t he exci ta t ion system are : A. It provides constant and se lec tab le s inusoidal force over t h e frequency range of from 0.5 t o 25 Hz f o r L-1011 application and 2.5 t o 50 Hz f o r S-3A application. 378 B. It u t i l i z e s an automatic l i n e a r per iod frequency sweep function. Sweep time/rate i s s e l e c t a b l e , The sweep rate u t i l i z e d during t h e L-1011 program optimized modal response minimized sweep t i m e il and optimized frequency s h i f t due t o sweep rate. optimized response amplitude /t e s t t i m e e The S-3A sweep rate C . D. The i n s t a l l e d un i t weight i s approximately 46 ki.lograms. me a i r f o i l used w a s symmetrical with 53-cm span and 46-cm chord. The vane w a s mass balanced with center o f g rav i ty at t h e ax i s of r o t a t i o n (20% chord). The aerodynamic cen te r , as determined by wind tunne l t e s t s , w a s approximately 1 .25 cm af t of t h e ax is of r o t a t i o n , minimizing ac tua to r force requiremenw . Blunt t r a i l i n g edges were added t o t h e vanes t o ensure a zero l i f t t ra i l s t a b i l i t y when unpowered. E. The vane fo rce capab i l i t y w a s +lo00 newtons at 200 KEAS with propor- t i o n a l l y higher forces ava i lab le a t h igher speeds. The maximum vane o s c i l l a t o r y angle of a t t a c k was -115 . The force on each vane w a s ind iv idua l ly se l ec t ab le . 0 F. Automatic f a i l - s a fe f ea tu res were designed in to the ac tua tor cont ro l system t o l i m i t vane fo rce , vane amplitude, and/or a i r c r a f t s t ruc- t u r a l response. G. There were provisions for manually tuning p a r t i c u l a r modes of i n t e r e s t and s top vanes at zero l i f t pos i t ion wi th in l e s s than 1 cycle. The vanes can be driven e i t h e r i n phase o r 180° out of phase as required t o exc i t e symmetric or antisymmetric a i rp l ane modes. H. In addi t ion t o t h e use of t h e o s c i l l a t o r y vanes t o provide modal exc i ta - t i o n , c e r t a i n modes were inves t iga ted by using cont ro l pulses or e l e c t r i c a l l y commanded symmetric a i l e ron impulses. In t h e case of c e r t a i n wind tunnel f l u t - t e r model tests, modal damping c h a r a c t e r i s t i c s have been determined by applying the peak p l o t da ta ana lys i s method t o model response t l m e h i s t o r i e s exc i t ed by e x i s t i n g wind tunne l turbulence. The choice of exc i t a t ion i s based on the s p e c i f i c modes of i n t e r e s t , cost considerations, and da ta ana lys i s procedure t o be used. DATA ANALYSIS METHODS Real-Time Decay Analysis The real-time decay ana lys i s program w a s developed t o analyze telemetered f l i g h t f l u t t e r t e s t da ta by use of an online computer and t o he lp make a r ap id determination of t h e damping of s t r u c t u r a l modes exc i ted e i t h e r by con t ro l pulses or by tuning with s inusoida l forcing devices and quick-stopping t h e e x c i t a t i o n input . 379 The decay analysis program is based on the well-known a t i o n t h a t the decay t i m e h i s to ry of t h e free osc i l l a t ion following a pulse or quick stop i s an exponential function. A p lo t of t he log magnitude of the decay versus t i m e i s therefore , a s t r a igh t l i n e . The output of the red-time decay program i s a p lo t of t h e log of t he successive half-cycle amplitudes versus number of ha l f cycles, which i s proportional t o t i m e i f constant frequency of decay i s assumed. i n i t i a t e d f l a g s igna l j u s t p r i o r t o t h e control pulse input or by a f l ag s igna l automatically generated j u s t p r io r t o the osc i l l a to ry vane stop e l e c t r i c a l command. When the compute mode i s t r iggered , the computer processes the t i m e h i s tory data as follows: The compute mode of t he program i s t r iggered by a p i lo t - or ground- It searches f o r extreme values, maxima and minima, i n such a w a y t h a t each successive extreme value Y i s determined It calculates t h e double amplitude D fo r each ha l f equation : i i and s tored (fig. 3). cycle, by the where i = 1,2 , . . . . N-1 , with N 5 40, a p rac t i ca l maximum number of ha l f cycles. The logarithm of the double amplitude D i s calculated and normal- ized t o 1 . 0 f o r t h e maximum value as follows: i A high-speed l i n e p r in t e r i s u t i l i z e d t o rapidly plot t h e normalized logarithm LD. versus i , the number of ha l f cycles. A t y p i c a l example of t he pr inted output i s shown i n f igure 4. In previous appl icat ions, up t o nine response parameters have been simultaneously analyzed and p lo t t ed within 30 t o 40 seconds after the control pulse or quick stop. Using engineering judgment, t h e engineer can f a i r a s t r a igh t l i n e through the p lo t t ed data and rapidly determine a quant i ta t ive damp- ing value using a transparent overlay. As noted i n f igure 4, the pr intout format serves as a convenient data-keeping device by ident i fying the following : 1 (1) tes t number ( 2 ) f l i g h t number ( 3 ) date (4) run code number ( 5 ) response parameter number/identification (6) equivalent airspeed, Mach number, and pressure a l t i t ude at the t i m e of pulse calculated from telemetered pressure measurements type of s igna l conditioning ( f i l t e r i n g ) u t i l i z e d ( 7 ) 380 (8) a pr intout o f least-squares l i n e a r curve f i t o f t he function LD. versus i between the f irst maximum LD iden t i f i ed as S , and a number of consecutive ha l f cycles ( N ) . The calculated value of s t ruc tu ra l damping ( g ) percent e r r o r ( E % ) , and the average frequency (FM) over the computer-selected decay region are a l so pr inted 1 i3 If the computer-selected decay region agrees with the f lu t te r engineer 's judgment, the damping and frequency can be taken d i r ec t ly from the pr intout . In addi t ion, these computer-calculated values of g and FM can be d i g i t a l l y displ-ayod i n the data-monitoring area during f l i g h t . Before the response t i m e h i s to ry s ignals are used as input t o the real- time decay analysis program, t h e telemetered data are f i l t e r e d through analog f i l t e rs selected t o i so l a t e t h e ant ic ipated modes of i n t e r e s t , depending on proximity and response amplitude of adjacent modes. The uni t s used are se lec tab le as low pass , high pass , or band pass filters, and they r e l i ab ly con- d i t i on exponentially decaying s igna ls having s t ruc tu ra l damping rates of up t o 25%. compatible format at a r a t e o f 500 samples per second p r i o r t o processing. A t yp ica l f low chart o f a PCM data acquis i t ion and monitoring configuration is shown i n figure 5 . The analog s igna ls , af ter proper f i l t e r i n g , are d ig i t i zed i n computer- This analysis method i s applicable f o r modal response cases where the mode i s excited t o an i n i t i a l l e v e l of approximately three times the average l e v e l of response t o random and atmospheric turbulence forcing levels. In addition , the technique relies heavily on engineering judgment i n se lec t ing the proper t i m e s l i c e s . t i m e and manual p lo t t i ng e f f o r t previously required i n analyzing f ree decay response data The computer program does, however, minimize t h e Real-Time Response Analysis The real-time response program w a s developed primarily t o provide rap id evaluation of t h e s t a b i l i t y trends re la t ive t o a large number of modes as a function of airspeed. This technique is u t i l i z e d when s inusoidal frequency sweep forcing devices are avai lable on the t e s t a i r c r a f t . Again, computer- processed data are available within approximately 30 seconds after the end of t he sweep exci ta t ion. range of 3.0 t o 50 Hz. The sweep function used, though not a requirement, was a l i n e a r period sweep defined by the relat ionship Typical sweep t i m e s are 40 t o 60 seconds for a frequency 0 F F ( t ) = l + a F t 0 where F ( t ) = frequency at t i m e t - Hz = frequency at time t = 0 - Hz *O 381 t = t i m e = s e e a = dimensionless sweep rate This func t ion w a s s e l e c t e d as t h e b e s t compromise between response ampli- tude , frequency s h i f t , and t i m e required t o sweep through t h e des i r ed frequency range. The respQnse c h a r a c t e r i s t i c s r e s u l t i n g from a l i n e a r per iod sweep were based on a s tudy conducted by Edmund A. Bartsch and contained i n Lockheed Report LR 16484, "Flight F l u t t e r Testing Method." Typically, nine response parameters are processed simultaneously. The response ana lys i s i s based on t h e assumption t h a t t h e response r a t i o var ies inverse ly as t h e modal damping r a t e . P l o t s are maintained t o t r a c k r e l a t i v e response versus equivalent airspeed (see figure 6 as a t y p i c a l example). The response time h i s t o r y s igna l s of each parameter a re preconditioned, p r i o r t o being used as input t o the computer program, through constant band- width ( k 2 . 5 Hz) t r ack ing f i l t e rs t o minimize extraneous responses and high frequency no i se . The t r ack ing f i l t e r cen ter frequency i s con t ro l l ed by the telemetered function generator s igna l which drives t h e o s c i l l a t o r y aerodynamic e x c i t e r vanes. The analog outputs of t h e t racking f i l t e r s are then d i g i t i z e d at a r a t e of 500 samples p e r second and converted t o engineering u n i t s f o r processing. Flag s igna ls are used t o t r i g g e r sweep-start and sweep-stop t i m e i n t he computer. The sweep-stop s igna l causes the computer t o s t o p receiving da ta , complete ca l cu la t ions , and start p r i n t i n g results. A t y p i c a l real-time response ana lys i s p r in tou t i s shown i n f igu re 7. The computer program processes the, time h i s to ry da t a as follows: It determines inpu t and response amplitudes. The input function i s t h e output of a s t r a i n gage bridge on t h e o s c i l l a t i n g vane which i s c a l i b r a t e d t o measure vane normal force . Input frequency a t time of maximum response i s ca l cu la t ed from the average period of t h e three previous and t h e th ree subsequent cycles o f t h e input function. It determines t h e time at which maximum and minimum response ampli- tudes occur, e l imina t ing minor or t r a n s i e n t f l uc tua t ions by a minima c r i t e r i a i d e n t i f i e d as a "window," r e t a in ing and p r i n t i n g out only t h e s i g n i f i c a n t response m a x i m a and minima. The results of t h e real-time program are presented i n tabular form ( f i g u r e 7 ) . A separa te sheet i s p r in t ed f o r each response parameter of i n t e r e s t . A s noted i n f igu re 7, t h e following data are p r i n t e d ou t versus elapsed time from sweep-start f o r all response maxima and minima which satis% the "window" c r i t e r i a s p e c i f i e d wi th in the swept frequency range. 382 Time of input peak i n seconds (time of max. and min. response) Input period i n seconds Input frequency i n Hz Vane input amplitude i n pounds Response amplitude i n engineering uni ts ( i .e. , l b , in-lb , acceleration ( g ) ) Response r a t i o i n engineering un i t s In addition t o the response r a t i o , and general t e s t i den t i f i ca t ion , the following information i s a l so pr in ted : S t a r t and stop t i m e of sweep Indi cat e d a i rspe e d Equivalent airspeed Alti tude Mach number The ident i f ica t ion of modal maxima is made by the f l u t t e r engineer, based on frequency and relat ionship t o response data at previous airspeeds. symmetric and antisymmetric sweeps a re normally made t o evaluate a l l per t inent modes. Both Peak Plo t Data Analysis Program The peak p l o t data analysis program w a s developed at the Lockheed- California Company and i s described i n d e t a i l i n Lockheed Report 25111, "Fourier Transform Analysis," dated March 31, 1972. used a t Lockheed t o obtain modal frequency and damping data from t i m e h i s tory da ta obtained from r o t o r system whir l tower tests, wind tunnel f l u t t e r model tests, and L-1011 and S-3A f l i g h t f l u t t e r tests. This method i s u t i l i z e d for those pa r t i cu la r modes where the modal data of i n t e r e s t have a high level of s igna l contamination or extraneous response of adjacent modes. The peak plot program i s avai lable t o the f lut ter engineer as an in te rac t ive computer graphics program which allows nearly instantaneous i t e r a t i v e solu- t i ons t o be obtained. da ta p lo t t ing and solut ion displays. Hard copies of desired data p l o t s are e a s i l y obtdned. This technique has been Simple l i g h t pen commands can be used t o optimize 383 L The peak p l o t method may be b r i e f l y described as follows: The Cooley-Tukey fast Fourier transform (FFT) algorithm i s applied t o t h e d i g i t i z e d time h i s t o r y test d a t a sample i n order t o generate a p l o t o f t he l o g of t h e Fourier transform, l o g F ( o ) , as a function of the l o g o f t h e f re - quency, l o g (0 ) . displayed by t h e l i g h t pen detecting t h e ind ica ted frequency peak( s ) on the screen displayed p l o t . The frequency of t h e mode or modes o f i n t e r e s t i s llcoarsely'l Figure 8 i l l u s t r a t e s an example o f such a p l o t . A f t e r s e l e c t i n g t h e mode and frequency of i n t e re s t . , t he program then uses a d i r ec t computation of t h e d i sc re t e Fourier transform given by N-1 F ( w k ) = A t f (ti) [cosuk ti -j Sine k ti] i = O wheye cc, i n g i n t e r v a l , N i s t h e number of da ta po in t s i n t h e block being transformed, t. i s t h e ith t i m e po in t , and j i s is t h e frequency o f t h e mode t o be analyzed, At i s t h e d a t a sampl- k fl 1 Since 'w i s an approximate frequency, procedures have been programmed t o k i t e r a t e t o a near ly t r u e w by ad jus t ing t h e harmonic number, k , and number of d a t a p o i n t s , N , used i n t h e transform. The next s t e p i n t h e method generates a t i m e h i s t o r y of t h e function The t i m e dependence o f t h e function G( 7 ) is obtained by computing t h e f o r a sequence o f da t a blocks where G( 7 ) i s computed function I n F( uk)l by using t h e tes t da ta f ( t ) f o r the t i m e i n t e r v a l T < t < 7 + ( N - 1 ) ; 7 i s t h e t i m e of f i r s t d a t a poin t i n t h e block being transformed. A running Fourier transform i s used f o r computing e f f i c i ency . The da ta f o r each block i s e f f i c i e n t l y transformed by a recursive formula which uses the results from t h e previous block. A f t e r t h e first block., t he result f o r sub- sequent blocks i s obtained by a s ing le de l e t ion of a term, and t h e addition of a new t e r m t o the result of the previous block. The basis f o r t he peak p l o t method i s t h a t t h e t r a n s i e n t response is c lose ly approximated by an exponentially damped sinusoid. i s a p l o t o f I n F (o ) versus t h e t i m e corresponding t o t h e first d a t a The a c t u a l peak p l o t - I k l 384 point f o r the sequence of data blocks. A measure of the d a q i n g i s obtained ce o f noise cedure i n some applications, bu t primarily as a pos t f l igh t or pos t t e s t data analysis too l . CONCLUDING REMARKS Each of t h e flutter t e s t i n g methods described has ce r t a in advantages and disadvantages such as cost , ease of use, spec i f i c exc i ta t ion requirements, and appl icabi l i ty t o spec i f i c test objectives and is used ind iv i combination as judged necessary. None of t h e methods descr i conclusive s t a b i l i t y data under cer ta in flight conditions such as heavy Mach or transonic buf fe t conditions for higher damped modes. r e l y heavily on t h e engineer-in-the-loop approach fo r f i n a l judgement. All methods described The a v a i l a b i l i t y of high-speed/capacity computers has provided t h e neces- sary t o o l fo r developing advanced data analysis methods which more f u l l y s a t i s f y the desired objectives of f l u t t e r t e s t i n g at economically feasible l eve l s . Current development studies within the aerospace industry and govern- m n t agencies are contributing t o more sa t i s f ac to ry solut ions of the problem. REFERENCES 1. Newman, K. W . ; Skingle, C . W . ; and Gaukroger, D. R. : The Development of Rapid - Testing Techniques f o r F lu t t e r Experiments. 1974. C . P. No. 1274, 2 - Soovere , Jaak ; Turbulence Excited Frequency Domain Damping Measurement and Truncation Effects Oct. 1975. (Paper No. 5 o f t h i s compilation.) NASA Symposium of Flutter Testing Techniques , 3. Mackenzie, Alexander: Application of t h e Fast Fourier Transform t o Ground Vibration Testing, and Fl ight F lu t t e r Testing. Proceedings of t h e F i f t h Annual Symposium of The Society of Fl ight T e s t Engineers, Anaheim, Cal i fornia , August 7-9, 1974. 385 Figure 1. Photographs of f l u t t e r vane instal led on a f t fuselage. 386 Figure 2. Photographs of the flight f l u t t e r t e s t vane excitation control units. 387 .- Y F 4- m c 388 + + + + + + b & 6 + + + 4 33s - r v __ > L O C > P C -N. 3- r + + + + + + 0 + + + z8: .-.-I ( 0 - 1 00) Nr I ~ m w j 4- + + + + + + + + + 3(oC v o c vmr Q) Q J e a 4 DCDC 8%:: N N C ~ 389 I I 4 I___) cd a %3 cd %I 0 -!J k cd 6 rl k rl cd 0 .r( 8 390 N w I t; G ZI z 2 w 3 U U. m J 0 8 c . al 2 0 I- 2 12 w 0 z v) w U w > F 4 w U 26 24 22 20 18 1 .0VL .4 .5 .6 .7 .8 .9 1 .0VL AIRSPEED V/VL 1 POUND = 4.448 NEWTONS Figure 6 . Typical frequency and response r a t i o vs. equivalent airspeed from real-time response analysis. 391 G c U 5 C < 5 C ! < < 1 I ! P- 392 --.a00 -.160E 01 MAG. - L 01 -.240E -.320E -.400E FOURIER TRANSFORM CASE 100, VAR. 1 -LT STABTIP, NZ O 1 t 01 .OW .400E 01 .800E 01 .120E 0 2 .160E 02 .200E 02 m FREQ I .5120E 03 I NUMBERPTS. TIME HISTORY ,zTK- ~ .5700E 01 INPUT DATA EXIT FREQ = .9760E- 01 Figure 8. Typical Fourier transform display plot. 393 -.300E ' 01 -.400E 01 -.500E 01 -.600E 01 -.700E 01 -.800E 01 .500E 01 MAG. .Ooo ,000 TIME HISTORY I PEAKPLOT 1 FFT INPUT DATA EXIT .zoo FREQUENCY START TIME STOP TIME NUMBER PIS. I DISPLAY I .400 ,600 .500 .100E 01 TIME .9760E01 .5700E01 .6700E01 .5120E03 FREQ = 9.7760 DAMP = .I8371 NPTS = 982 Figure 9 . Ty-pical peak p lo t display. 394 THE APPLICATION OF RECENT TECHNIQUES IN FLIGHT FLUTTER TESTING M. A. Abla Gates Learjet Corporation SUMMARY A f l i g h t t e s t program is ins t i tu ted i n order t o evaluate the appl icabi l i ty of two recent f l i g h t f l u t t e r tes t ing methods. These methods a re the random decrement (randomdec) and autocorrelation techniques each method are based on analyzing response data obtained by sinusoidal and random excitation. A parameter identification d ig i ta l program, usinq l eas t squares approach, i s devel oped to determine the aeroel asti c character is t ics of a two mode system. have been obtained primarily by the randomdec method. is limited t o discussions and recommendations based on these resul ts . The relat ive merits of To date, the f inal resul ts of the two types of excitation Therefore, this paper INTRODUCTION The Gates Learjet Corporation ( G L C ) , a re la t ive newcomer t o the general aviation f ie ld , has consistently upgraded the f l i g h t f l u t t e r testing techni- ques used d u r i n g a i r c r a f t cer t i f ica t ion . For instance, sinusoidal excitation of the control surfaces has replaced the p i l o t impulse technique; application of the shake and stop approach has produced decay responses of better quali ty; and additional s tabi 1 i ty c r i t e r i a such as the amp1 i tude response and f l u t t e r margin ( r e f . 1) , have become possible. Further improvements have recently been made feasible by the acquisition of new computer equipment. I t is anticipated that the f a c i l i t y improvement wil l f a c i l i t a t e implementation of recent data reduction techniques resulting i n reduced program costs and time delays. A survey of the available l i t e r a tu re was made i n order t o c lassi fy the various approaches which have been used o r proposed. The autocorrelation and randomdec methods showed the greatest promise fo r possible implementation. a resu l t , a program was in i t i a t ed to investigate the re la t ive merits of these two methods. T h i s comparative investigation was to be based on actual random and sinusoidal f l i g h t response data o b t a i n e d on a Learjet Model 25; the u l t i - mate objective being to recommend a particular technique fo r use i n future f l i g h t f l u t te r tes ti ngs. As Most of the analysis has been done using the randomdec approach. Therefore, the major portion of this paper is devoted to discussions, evaluations, and recommendations based on these resu l t s . along w i t h the problems encountered. T h i s paper presents these discussions 395 T h i s section of the paper presents an overall description of the f l i g h t F l i g h t Test Program test program, computer program, and data reduction procedure, F l i g h t testing was planned w i t h two objectives i n mind. The f i r s t objec- t ive was to obtain actual f l i g h t test data f o r this program. The second objec- t i ve was t o gain i n s i g h t regarding the re la t ive merits of sinusoidal excitation versus random atmospheric turbulence. Briefly, this model is a small, h i g h performance business j e t w i t h a speed envelope o f 350 knots and Mach .86. led on the a f t fuselage, and two large fuel tanks permanently mounted on the' wing tips. The t e s t airplane was a Learjet Model 25B (figure 1). Main exterior features,include a T- ta i l , two j e t engines instal- For t e s t purposes, the airplane was f i t ted w i t h two accelerometers on each t i p tank and a potentiometer on each ai leron, calibrated to measure aileron position. Aileron sjnusoidal excitation was provided by i n p u t of a voltage signal of variable frequency into the autopilot rol l servos. An airborne recording system was used t o record s t ructural response data. Accelerometer outputs were processed through a GLC 1250 signal conditioner, converted t o pulse duration modulation w i t h a Vector 527 encoder, and recorded on magnetic tape by a Honeywell 5600 tape recorder. The f l i g h t test procedure consisted of recording response data for three types of excitation. A t each t e s t speed, the plan called for obtaining two- minute recordings o f random response data due to atmospheric turbulence, sinu- soidal response data for a frequency range of 1.5 to 10 cycles per second and t ransient response data due t o aileron pulses by the p i lo t . The t e s t speeds ranged from 250 to 350 knots a t an a l t i t ude of 4.57 km (15,000 f t ) w i t h fu l l fuel i n the wing and t i p tanks. Computer Program T h i s section describes br ief ly the computer program developed i n order to analyze response data from a single channel transducer. (figure 2 ) i s a Varian 620L w i t h accessories such as ASR-33 Teletype, Tek- tronix 4010 Cathode Ray Tube ( C R T ) , Pertec 6x40 Tape Drive and Statos 31 Printer/Plotter. k inds of randomdec signatures and a system identification parameter routine us ing a leas t squares approach. scribed i n re fs . 2 and 3, respectively. The computer system The program includes subroutines capable of generating three T h e randomdec methods a re based on Cole's and Houbolt's techniques de- These methods are as follows: Option 1: Cole's approach of triggering each time the response crosses a preselected leve l , regardless of the s i g n of the slope (figure 3a). 396 Option 2: Cole' approach of triggering eac time the response cr Option 3: i t h a positive slope ( f i g u r Houbo t ' s approach of triggering each time the re i t h a positive slope, and triggering and in he response crosses w i t h a negative slope (figure 3c). The least squares approach follows the technique given i n ref. 4. The pro- gram is capable of deducing the aeroelastic properties of both a one- and two- degree-of-freedom system, buried i n a randomdec signature o r function. us ing an autocorrelation analyzer. The la t ter i s not a par t of the computer program, and is obtained Data Reduction Procedure The data reduction procedure was established based on both an extensive checkout of the program and the guidelines suggested by Chang (ref, 5) . data used for the checkout was obtained from a typical f l ight f lutter tes t hav ing two closely spaced modes. and then exercises an option t o use all or pa r t of the time history record. The next step i s t o choose one of the three randomdec options and t o init iate the analysis using the selected response da ta . averaging process i s progressing, the program i s conveniently displaying the signature generation on the CRT. Once convergence i s achieved, the user may discontinue the averaging process and then proceed t o curve f i t a preselected length of the randomdec signature. The proper signature l e n g t h t o be curve fi t ted is usually chosen based on a detailed analysis of the da ta obtained a t the initial tes t speed. mended procedure is t o curve f i t different segments of the converged randomdec signature, and t o plot damping and frequency values of the simulated modes ver- sus signature length. Based on the constant behavior of these parameters and on a computed normalized standard deviation of the curve f i t , the engineer can adequately select a signature length which assures h i m of reliable results. the unknown parameters to be determined. ing ratio, amplitude, phase angle, and zero offset. Through an iterative pro- cess, the program solves for the final parameters which best match the experi- mental da ta . The closer the assumed parameters are t o the actual values, the more 1 i kely convergence wi 11 occur. The Initially, the engineer monitors the response data displayed on the CRT, A t the same time the randomdec The recom- To use this program, the-engineer is required t o i n p u t i n i t i a l estimates of These parameters are frequency, damp- RESULTS AND DISCUSSIONS The procedure outlined in the previous section has been applied t o response The data obtained a t one wing location using sinusoidal and random excitation. sinusoidal and random results are f i r s t discussed separately and then compared w i t h those obtained by the pilot pulse for f i n a l evaluation. 397 In l ine w i t h the recommended data reduction procedure, the sinusoidal re- sponse data obtained a t 250 knots was analyzed f irst i n order to se l ec t the proper length of the randomdec signature.. The randorndec signature was deter- mined us ing Houbolt's technique (option 3) and was curve f i t t ed for signature lengths of .45, - 9 , 1.35, 1.8 and 2.2 seconds. The curve f i t analysis was per- formed to deduce the modal properties of the f i r s t and second wing antisym- metric modes. T h e resul ts a re shown i n f igure 4. A study of f igure 4 reveals that the two natural frequencies and the damp- ing coefficient of the second mode are f a i r l y constant w i t h signature length. The damping coeff ic ient of the f i r s t mode, on the other hand, shows inconsis- tent behavior a t f i r s t , b u t t h e n tends to s t ab i l i ze fo r signature lengths between 1.6 and 2.2 seconds. Results from a similar analysis a t 350 knots tend t o confirm these observations (f igure 5 ) . 1.8 was selected. Consequently, a signature length of The above analysis was repeated a t 250 knots using Cole's zero crossing method (figure 6 ) . roughly equivalent values. on the sinusoidal response data obtained a t each t e s t speed. Figure 7 shows the results of the analysis a t 250 knots us ing option 3. As shown, figure 7a i s the measured response due t o sinusoidal aileron osci l la t ion and figure 7b shows the converged randomdec signature. Figure 7c is a plot o f the selected length of this signature (symbolized by X ) and of the simulated signature shown as a solid l ine. The SD i n figure 7c indicates the percent of the normalized standard deviation. curve f i t s the experimental data. are the simulated decay responses of the two modes extracted by this analysis. The resul ts of a similar analysis a t 350 knots a re shown i n figure 8. This f igure indicates t ha t b o t h options 2 and 3 yield Having established the proper signature, a complete analysis was conducted This parameter is a measure of how well the theoretical The curves presented i n figures 7d and 7e Some d i f f i c u l t i e s , due to f l i g h t tes t ing problems, were experienced i n the analysis o f the random response data. Lack of atmospheric turbulence d u r i n g this f l i g h t test necessitated a long search fo r an area w i t h adequate turbu- lence, and as a result, this par t of the t e s t was conducted under very rough a i r conditions. d i f f i cu l t to obtain. almost inadequate fo r the purpose of this study. However, i n sp i te of these problems, an attempt was made t o analyze the longest response record. record consisted of 15 seconds of d a t a a t 350 knots. T h u s , the desired two minutes of random response records were The f l i g h t records obtained were so short tha t they were T h i s Figure 9 presents the resu l t s of this analysis. Convergence of the ran- domdec was never achieved. attempts to deduce the f i rs t mode fai led. T h i s was possibly due t o the pre- dominance of the second mode, as migh t be seen i n the random response data (figure sa) . The natural frequency predicted seems to be reasonable b u t the damping is on the low side. analysis, as indicated by the poor curve f i t and the high SD (figure Sc) , needs to be improved before any confidence is placed i n the results. Such improve- ment m i g h t be achieved by incorporating a band-pass f i l t e r i n the system, as described i n reference 6. As shown, only the second mode was predicted. All In any case, the poor quali ty of the signal 398 As a final check on the resul ts determined by the randomdec method, the 350 knot transient response data obtained using p i l o t pulse was analyzed, method of analysis was the peak amplitude method. the peaks and troughs of the f ree decay was sketched. The height between the envelope l ines was t h e n measured a t each peak or trough. height was plotted against the number of the wave (figure 10) and the best s t ra ight l ine was then drawn through the first par t of the curve. The slope of this l ine was used to determine the damping ra t io . The Basically, an envelope of The logarithm of the The results obtained a t 350 knots by the peak amplitude method and the ran- domdec technique, using the random and sinusoidal response data, are summarized i n Table 1. Also, the frequencies obtained by ground vibration testing a re i n - cluded i n this table . A review of this information reveals t ha t a l l methods compare well on frequencies. The randomdec method, using sinusoidal excitation, gives damping values fo r the second mode t h a t agree well w i t h those obtained from the peak amplitude analysis. W i t h regard t o the f i r s t mode, only the ran- domdec w i t h sinusoidal excitation yielded damping values. basis of the small SD parameters and the reasonable resul ts of the second mode, one cannot help b u t assume that the resul ts obtained by the randomdec method, using sinusoidal excitation, a re correct. However, on the T h i s same conclusion cannot be drawn from the resu using random excitation. T h i s i s due t o the f a c t that had never converged nor was a good curve f i t ever obta ts of the randomdec the randomdec signature ned. CONCLUSIONS The following conclusions can be stated on the basis of the discussions and resul ts presented i n this paper. 1. 2. 3. 4. The application of the randomdec method us ing sinusoidal excitation appears t o be a reasonable technique fo r use i n f l i g h t f l u t t e r tes t ing. Although a i r turbulence is present i n i solat ion, the problem of f i n d i n g i t dur ing a f l i g h t f l u t t e r t e s t makes i ts f eas ib i l i t y , as a source of excitation, questionable. The use of the randomdec method using random excitation m i g h t be improved by ut i l iz ing a band-pass f i l t e r . A least squares curve f i t routine seems to be an e f f i c i en t and accurate method fo r determining modal properties of a two mode system. 399 I, ~ i ~ e r m a n ~ N . H , : eissenburger, J,T. : Prediction of Flutter Onset Speed Based on Flight Testing a t Subcritical Speeds. Journal o f Aircraft , July - August 1964. 2. Cole, H,A. , J r . : On-line Failure Detection and Damping Measurements of Aerospace Structures by Random Decrement Signatures. March 1973. NASA CR-2205, 3. Houbolt, J.C. : Subcritical Flutter Testing and System Identification. NASA CR-132480, August 1974. 4. Wilcox, Philip R. and Crawford, William L. : A Least Squares Method for 5. Chang, C.S.: Study of Dynamic Characteristics of Aeroelastic Systems Reduction of Free Oscillation Data. NASA TN 0-4503, 1968. U.tilizing Randomdec Signatures. NASA CR-132563, 1975. 6. Brignac, W.J.; Ness, H . B . ; Smi th , L.M.: The Random Decrement Technique Applied to the YF-16 Flight Flut ter Tests. AIAA Paper No. 75-776, presented a t the AIAA/ASME/SAE 1 6 t h Structures, Structural Dynamics, and Materials Conference, Denver, Colorado, May 1975. 400 VELOCITY- KNOTS METHOD GROUND VIBRATION TEST PEAK AMPLITUDE RANDOMDEC RANDOMDE C RESPONSE DATA CO-QUAD FREE DECAY SINUSOIDAL RANDOM FREQUENCY --HZ MODE 1 5.7 5.3 - MODE 2 6.56 6.34 6.27 6.2 DAMP I NG RAT I O MODE 1 - .037 MODE 2 .047 .0488 ,034 Table 1 Comparison o f Resul ts a t 350 Knots 401 402 HONEY W ELL 5600 TAPE 3 - 0 6 7 3 Figure 2.- Varian 620L computer system. 403 0 0 0 0 o m ? 0 ~ 0 o m ? 0 0 W AlZ 0 W 4 lz O C n ? W lz 404 8 .08 6 e 06 Frequency Darnpi ng HZ Rat io 4 .04 2 .02 0 0 8 6 F r eq u e n cy Hz 4 2 0 .8 1.2 1.6 2.0 2.4 Signa tu re Length, Seconds pOK-F] 0 c 0 Frequency 0 Damping Rat io I I I I I I .4 .8 1.2 1.6 2.0 2.4 Signa tu re Leng th , Seconds .08 - 06 lampi ng Rat io .04 .02 0 Figure 4.- Modal c h a r a c t e r i s t i c s versus s i g n a t u r e l eng th u s i n g s inuso ida l e x c i t a t i o n a t 250 knots. 405 8 6 Frequency Hz 4 2 0 8 - 6 - F r eq u en cy Hz 4 - 2 - 0 Frequency ODamping Ra t io 6 Frequency - .08 ODamping Ra t io 0 n v n 0 - .06 Damp i ng Ra t io - .04 - .02 0)- 0 I I B I I J 08 .06 Damp i ng Rat io .04 .02 0 0 . 4 .8 1.2 1.6 2.0 2.4 S igna tu re Length, Seconds 406 pm--i1) a 0 Frequency .08 - RDamping Ratio 6 - .06 F r e q u e n cy Damping Hz Ratio 4 - .04 2 - .02 - Option 3 0 8 - 6 - F r eq u en cy Hz 4 - 2 - - - - - 4 Signature Length, Seconds -2) 0 Frequency 0 Damping Ratio e V n W 0 .08 .06 Damping Ratio .04 .02 --- Option 2 - Option 3 Si gna ture Length , Seconds Figure 6.- Randomdec analysis u s i n g options 2 and 3 a t 250 knots. 407 408 Figure 76 Figure 7. - Randomdec ana l i s i s using sinusoidal exc i ta t ion ax 250 knots. RNOOMDFf RNF,L$’SIS I - lq;NQ STk’jLT-IIPRL E X C X T f i T I 3 Y VELOCITY = 350 KtiOT8 0 0 LEFT T I P TRHG RFT f4 E R SUR ED RES P 13 N S E 1 4 1-- Figure 8e T-- -I--- - ---1 7- ,. ______ -.._ -- : J ~ - - ~ - ~ _ _ _ N ’ 0.00 4.00 3.QO 12.00 16.00 20.00 24.00 28.00 32.00 TIME-SECONDS ml0 Figure 8.- Randomdec ana lys i s using s inusoidal e x c i t a t i o n a t 350 knots. 409 Figure 9. - Randomdec analysi s us i ng random exci ta t ion a t 350 knots. 410 0 me 0 0 = .047 I I I I I I f 0 2 4 6 8 10 12 HALF WAVE NUMBER Figure 10.- Logarithmic amplitude a t 350 knots. 411 F-15 FLIGHT FLUTTER TEST PROG Henry Katz, Francis 6, Foppe, and Daniel T. Grossrnan McDonnell A i rc ra f t Company ABSTRACT The F-15 f l i g h t f l u t t e r test program is described. Spec ia l emphasis is given t o test philosophy, da ta reduction techniques, and test r e su l t s . The approach u t i l i z e d f o r t h i s program not only provided the da t a necessary t o e s t a b l i s h a measure of s t a b i l i t y f o r all” important f l u t t e r mechanisms a t each test poin t , bu t a l s o allowed ex t rapola t ion of t he data t o ac tua l ly def ine a l l c r i t i c a l f l u t t e r boundaries. Such quan t i t a t ive information w a s not only use- f u l t o d e f i n i t i v e l y e s t a b l i s h the f l u t t e r s t a t u s of the a i r c r a f t as i t w a s flown, but a l s o provided a s o l i d foundation f o r assess ing t h e impact of any f u t u r e design changes. INTRODUCTION With very few exceptions, f l i g h t f l u t t e r conducted on a r a t h e r q u a l i t a t i v e bas i s ; t h a t the damping a v a i l a b l e a t the test po in t being t e s t i n g has h i s t o r i c a l l y been is, t h e only d a t a obtained w e r e flown, with a poss ib le extrapo- There generally w a s no l a t i o n of damping trends of t h e lower damped-modes. quan t i t a t ive ind ica t ion as t o t h e amount of s t a b i l i t y remaining a t any given point. The goal set f o r t h e F-15 f l i g h t f l u t t e r test program w a s t o provide a system which would - accurately, quickly, and with a high degree of v i s i - b i l i t y - allow ext rapola t ion of t h e da ta t o a c t u a l l y def ine cr i t ical f l u t t e r boundaries, i n add i t ion t o providing a measure of s t a b i l i t y f o r - a l l t h e important mechanisms at each test point. This w a s accomplished by designing t h e a i r c r a f t e x c i t a t i o n and instrumentation systems t o provide high-quality response da ta which could be speedi ly and accura te ly converted t o complete (i.e.$ concerning a l l modes of i n t e r e s t ) damping and frequency information which - i n turn - could be u t i l i z e d f o r r e l i a b l e f l u t t e r margin pred ic t ions by t h e methods of Reference 1. The accuracy and r e l i a b i l i t y of these f l i g h t f l u t t e r test system da ta not only permitted the pu r su i t of a minimum f l u t t e r margin design concept (and with i t optimum weight - see Reference 2) through i n f l i g h t v e r i f i c a t i o n of a c t u a l f l u t t e r margins of s a fe ty , bu t a l so provided a quan t i t a t ive b a s i s on which t o quickly assess t h e impact of fu tu re design changes. This paper concerns i t s e l f primarily with test philosophy, da ta reduction techniques and systems, and test r e su l t s . t i ons are covered i n Reference 3. A i r c r a f t systems and test opera- 413 ABBREVIATIONS AND SYMBOLS CRT H PC I m KEAS M NBFM PCM Q Re T~~ T-plot vE vT lJ w w n cathode ray tube s t r u c t u r a l damping c o e f f i c i e n t pressure a l t i t u d e , ca l ib ra t ed imaginary p a r t of t r ans fe r func t ion a t frequency w knots e q d v a l e n t airspeed left-hand s i d e Mach number narrow band frequency modulation pulse code modulation dynamic pressure real p a r t of t r a n s f e r func t ion a t frequency w right-hand s i d e temperature a t a l t i t u d e t r a n s m i s s i b i l i t y p l o t equivalent a i r speed t r u e airspeed r a t i o of s t r u c t u r a l mass t o aerodynamic mass dens i ty a t a l t i t u d e frequency n a t u r a l frequency APPROACH The q u a n t i t a t i v e d e f i n i t i o n of F-15 f l u t t e r boundaries from f l i g h t test d a t a w a s accomplished by means of the F l u t t e r Margin technique of Reference 1. This technique permits r e l i a b l e pred ic t ion of f l u t t e r speeds on t h e b a s i s of s u b c r i t i c a l test data. Its appl ica t ion requi res knowledge - a t every test 414 point - of damping f l u t t e r mechanisms. tained from a unique d a t a reduction f a c i l i t y opera t ing on t h e a i r c r a f t d a t a provided by the exciter and instrumentation systems described i n d e t a i l i n Reference 3. frequency of every mode involved i n p o t e n t i a l l y c r i t i c a l This complete damping and frequency information w a s ob- The method of Reference 1 assumes t h a t d a t a i s obtained a t d i f f e r e n t vel- o c i t i e s while maintaining the same aerodynamic center and l i f t curve s lopes . S t r i c t l y speaking, i t is therefore v a l i d only when Mach number is kept con- s t a n t . The emphasis i n t h i s program w a s , therefore , t o obta in constant Mach number c ros s sec t ions which could be u t i l i z e d f o r ex t rapola t ion of the d a t a t o projected f l u t t e r boundaries. number c ross sec t ions t o obta in a high subsonic ex t rapola t ion poin t fo r r e f e r - ence and f o r co r re l a t ion with subsonic analyses and wind tunnel tests. primary c ross sec t ion w a s taken a t M = 1 . 2 , t h e F-15 sea-level design Mach number. Additional Mach numbers a t which cross sec t ions w e r e taken were selected on the b a s i s of analyses, wind tunnel tests, and the e a r l y por t ion of t he test program, which w a s dedicated t o determining cri t ical Mach numbers by obtaining test d a t a from 0.73 t o 1.5 Mach numbers while maintaining a constant dynamic pressure (442 KEAS). The da ta obtained a t t h i s constant dynamic pres- sure w e r e then reduced i n terms of the F l u t t e r Margin parameter t o a i d i n sel- ec t ing c r i t i ca l Mach numbers f o r t he various c r i t i ca l f l u t t e r mechanisms. M = 0.80 w a s s e l e c t e d as one of t h e primary Mach AnotBer Figure 1 shows F l u t t e r Margin as a function of Mach number f o r one of t h e Bas ica l ly , a subsonic and a supersonic l e v e l can be observed - with cri t ical f l u t t e r mechanisms: ro t a t ion . some secondary a l t i t u d e (or 11) e f f e c t s . The h ighes t Mach number a t which the lower subsonic level occurs i s j u s t s l i g h t l y above M = 0.9. data, and similar r e s u l t s f o r o t h e r modes, M = .93 and M = 1.1 were se l ec t ed as add i t iona l primary Mach numbers and 'a cross . sec t ion with th ree o r more f l i g h t test poin ts was taken a t these points.. Secondary Mach numbers of 0.98, 1.04, and 1.15 (with only two f l i g h t test poin ts ) w e r e s e l ec t ed t o provide intermediate checks a t a minimum c o s t i n t e r m s of f l i g h t s required. antisymmetric boom to r s ion versus s t a b i l a t o r Based on such A t y p i c a l f l u t t e r pred ic t ion a t a cr i t ical Mach number is shown i n Figure 2. It should be noted t h a t t he ex t rapola t ion is made on t h e b a s i s of a para- bola through the f l i g h t test po in t s and the zero airspeed poin t . Wind tunnel test d a t a have shown t h a t t he a c t u a l f l u t t e r speed w i l l be o f f s e t s l i g h t l y from the parabol ic ex t rapola t ion toward a point obtained by a s t r a i g h t - l i n e extra- pola t ion through , the i n f l i g h t test po in t s alone. convex (curving toward the abc issa) , t he r e s u l t s w i l l be s l i g h t l y conservative, and t h e parabola w i l l be used t o e s t a b l i s h t h e f l u t t e r boundary. I n t h e case of a concave parabola, t h e s t r a i g h t - l i n e ex t rapola t ion w i l l be more conserva- t i v e and should the re fo re receive more consideration. Thus, when the parabola is Although, i n i t s strictest sense, the p red ic t ion method is inva l id f o r constant a l t i t u d e da t a , secondary ex t rapola t ions w e r e made a t constant a l t i - tudes of 1525 and 10 400 m (5000 and 34 000 f t ) by taking advantage of t h e f a c t t h a t , once supersonic flow i s es tab l i shed , the aerodynamic center and l i f t curve s lope are aga in q u i t e w e l l behaved. ex t rapola t ion is shown i n Figure 3 . An example of a constant a l t i t u d e 415 Figure 4 shows the po in t s a t which f l i g h t f l u t t e r da ta were taken and a l s o ind ica t e s t h e d i r ec t ion of t h e ex t rapola t ions , EXCITER SYSTEM The a i r c r a f t e x c i t e r system, described ;In d e t a i l i n Reference 3, furn ishes the known fo rc ing function t o which a i r c r a f t response can be measured. It has the capab i l i t y t o o s c i l l a t e e i t h e r the s t a b i l a t o r s o r t h e a i l e rons . E i the r set of con t ro l sur faces can be exc i ted symmetrically (in-phase) or antisymmetrically (out-of-phase). Exci ta t ion can be provided either i n t h e form of sweeps (slowly varying frequency through a given range) o r dwells/decays ( exc i t a t ion a t a given frequency f o r a c e r t a i n s h o r t t i m e , followed by an abrupt e x c i t e r shut-off). INSTRUMENTATION SYSTEM A s described i n Reference 3, the a i r c r a f t instrumentation system c o n s i s t s primarily of s t r a i n gages, which provide n o t only t h e des i red response charac- t e r i s t i c s bu t a l s o permit r e l a t i v e l y independent measurement of t he modes of i n t e r e s t . This is important, s ince it i s des i red t o separa te t h e response i n the various modes, e spec ia l ly when these modes are c lose t o each o the r i n fre- quency. Figure 5 shows t h e sensor loca t ions on the a i r c r a f t and a l s o denotes t h e primary degree of freedom t o be measured by each. DATA SYSTEM The h e a r t of the F-15 f l i g h t f l u t t e r test system is the d a t a handling system, It reduces the information provided by a i r c r a f t instrumentation i n response t o the forcing func t ion furnished by the a i r c r a f t e x c i t e r system t o several forms use fu l t o t h e f l u t t e r engineer. The F-15 d a t a system can be divided i n t o two p a r t s : a. The on-line system, which a i d s i n the assessment of s t a b i l i t y a t the test po in t being flown a t the t i m e ; and b. The pos t - f l igh t system, which provides a complete eva lua t ion of a l l t he da t a ava i l ab le t o a id i n a r r i v i n g a t damping and F l u t t e r Margin t rends so as t o e s t a b l i s h the f l u t t e r s a f e t y of t he next po in t ( s ) t o be flown and a l s o t o ex t rapola te t o predicted f l u t t e r boundaries. On-Line Data System This po r t ion of t he d a t a system provides real-time information as t o t h e s t a b i l i t y of t h e a i r c r a f t a t the point(s) being flown. represented i n Figure 6. A s can be seen, i t involves a mixture of conventional It is schematically 416 disp lays ( s t r i p recorders and Lissa jous f igu res ) and less conventional informa- t i o n i n the form of d i g i t a l l y computed t r ansmiss ib i l i t y p l o t s , S t r i p cha r t recorders Thirty-two channels of narrow band frequency modulated (NBFM) da ta are displayed on four s t r i p char t recorders. s t r a i n gages t o desc r ibe a i r c r a f t response and forc ing functions. The channels are arranged so t h a t components of c r i t i c a l f l u t t e r mechanisms ( fo r example, boom lateral bending and f i n bending) are side-by-side t o enable close monitor- ing f o r t he development of any co r re lk t ion between these degrees of freedom. These channels present t he output of The da ta displayed on the recorders perform the following functions: a. Allow observation of any co r re l a t ion between any two degrees of free- dom during acce lera t ion i n t o an unexplored f l i g h t regime. l a t i o n could ind ica t e t h e approach t o an i n s t a b i l i t y . Such corre- b. Permit real-time determination of cr i t ical modal frequencies during turbulence exc i t a t ion . c . Obtain t h e damping of modes of i n t e r e s t whenever dwell/decay exc i ta - t i o n is u t i l i z e d . d , Ind ica te t h e frequencies of maximum response during a frequency sweep. e. Monitor t h e q u a l i t y of t h e forcing func t ion during sweeps. f . Allow observation of t h e level of turbulence, t o determine i f acqui- s i t i o n of exc i t a t ion response data is f eas ib l e . Lissajous d isp lays Four Lissajous f igu res each are displayed on four oscil loscopes. The p a i r s are chosen t o provide m a x i m u m information on the s t a b i l i t y of p o t e n t i a l f l u t t e r mechanisms. gages, e.g. from boom lateral bending and f i n bending, aga ins t each o ther . The s i g n a l from any of t h e thirty-two NBFM channels can be se l ec t ed f o r e i t h e r axis of any of the sixteen Lissajous f igu res . These f igu res are used t o observe t h e phase and frequency r e l a t ionsh ip between important modal p a i r s during accelera- t i o n i n t o an unexplored f l i g h t regime, and are a l s o used t o observe the f r e - quency dependence of amplitude and phase during sweeps. This is accomplished by "beating" the s i g n a l s from two Transmiss ib i l i ty p l o t s Transmiss ib i l i ty p l o t s are obtained by normalizing response parameters t o a parameter which is a measure of t he forcing function, e.g. s t a b i l a t o r hinge moment when the s t a b i l a t o r s are o s c i l l a t e d . d i g i t i z e d a i r c r a f t response d a t a and present amplitude and phase information as a function of frequency. These p l o t s are computed from Figure 7 shows a t y p i c a l t r ansmiss ib i l i t y p l o t . 417 One real-time t r ansmiss ib i l i t y p t (T-plot) f o r a se ata channel is displayed on a cathode r a y tube (C ) during a sweep. ob ta in response information f o r the cri t ical mode of interest. is more accura te than can be obtained from t h e s t r i p recorders i n a real-time environment. A s i d e b e n e f i t of t he real-time T-plot is t h e immediate acquisi- t i o n of cor rec ted f l i g h t parameters (equivalent airspeed, Mach number, a l t i t u d e , etc.) t is used t o The information which are a l s o displayed on the CRT. Hard-copy t r a n s m i s s i b i l i t y p l o t s f o r s ix se l ec t ed d a t a channels are pro- duced on a Gould p l o t t e r wi th in 90 seconds a f t e r a sweep. these p l o t s , i n conjunction w i t h t h a t already obtained from the real-time T-plot, a f fo rds the opportunity t o obta in a check on frequency and damping values f o r most of the modes of i n t e r e s t . frequencies almost immediately permits t h e s e l e c t i o n of accurate dwell f re - quencies during the f l i g h t , thus providing good-quality decay data. The information from The a b i l i t y t o determine resonant Post F l igh t Data System This system involves a complete eva lua t ion of a l l t he da t a a v a i l a b l e t o a r r i v e a t damping and F l u t t e r Margin t rends s o as t o e s t a b l i s h the f l u t t e r s a f e t y of t h e next test p o i n t ( s ) , and a l s o t o ex t rapola te t o pred ic ted f l u t t e r boundaries. formation by the methods of Reference 4 and t o provide the data s to rage and computational c a p a b i l i t i e s required f o r t h e F l u t t e r Margin ca l cu la t ions and predic t ions , A s can be seen, there i s considerable madmachine in t e rac t ion . A d i g i t a l computer is used t o extract frequency and damping in- Figure 8 shows t h e data flow i n t h i s system. Extraction of frequency and damping da ta After t he completion of each test f l i g h t , t r ansmiss ib i l i t y p l o t s are gen- e ra t ed from the onboard tape f o r a l l parameters of i n t e r e s t , nominally 1 2 per sweep, 6 f o r each s i d e of t h e a i r c r a f t . Frequency and damping are obtained manually from these t r ansmiss ib i l i t y p l o t s by observing resonant peaks and ca l cu la t ing damping on the b a s i s of bandwidth and/or t h e s lope of t h e phase s h i f t e This information is combined with frequency and damping d a t a ob rained from the dwell/decays and t h e output generated by t h e automatic modal extrac- t i o n technique. computer capac i ty there. ) (The la t ter is performed i n S t , Louis because of t h e l a r g e r I n the automatic technique, based on Reference 4 , t he resonant frequencies are considered t o occur when t h e der iva t ives of t he Argand arc-length reaches a maximum wi th respec t t o frequency. These max ima are ext rac ted using a least- squares straight-l ine-slope t e s t i n g technique. P l o t s of t h e de r iva t ive are provided t o t h e f l u t t e r engineer by the computer (see Figure 9 ) . t h a t a Hanning smoothing technique, applied t o both t h e t r a n s f e r func t ion and t o the d e r i v a t i v e data, s u b s t a n t i a l l y reduces the e r r o r induced by experimental scatter (turbulence, etc.). It was found To automatically obta in t h e damping values from the t r a n s f e r function, t h e The bandwidth of these segments depends on the frequency multi-degree of freedom funct ion i s i n i t i a l l y separated i n t o s i n g l e degree of freedom segments. 418 separa t ion of t he modes and is not t he same f o r a l l modes, Damping values ar ex t rac ted f o r each of t h e segments by f i r s t f i t t i n g a l e -squares circle t o the t r a n s f e r func t ion da ta i n t h e complex plane. culated f o r each d a t a poin t used t o def ine t h e circle, u t i l i z i n g the equation Damping values are then cal- 2 2 0 - - w w w I m n g = - - R e . The damping values obtained on t h e b a s i s of t h e po in t s n f a r t h e s t from the n a t u r a l frequency are considered t o be t h e most accurate, s ince they are least sensitive t o any e r r o r i n t h e frequency t e r m . emphasis i s placed on t h e four poirits which are f a r t h e s t from the resonant peak (two on each s ide ) . average, i n a t a b l e included wi th the de r iva t ive p l o t , Figure 9. Therefore, The four damping values are presented, along with t h e Generally, t h e automatically ex t rac ted modes w i l l f a l l i n t o three cate- gories: good modes, o ther phys i ca l modes, and f i c t i t i o u s modes. I n a "good" mode t h e four damping values w i l l be very c lose t o each o the r and the same resonant frequency w i l l be shown i n the t abu la t ion , the de r iva t ive p l o t and the o r i g i n a l t r a n s m i s s i b i l i t y p lo t . For example, on Figure 9 t h e 18.6 Hz boom lateral bending mode and the 33.8 Hz f i n t i p r o l l mode are the only good modes t o be ex t rac ted from t h i s p a r t i c u l a r gage. The second category of modes has the following c h a r a c t e r i s t i c s : a. S imi l a r i t y i n damping of t he two "lower" poin ts and the two "upper" poin ts , bu t a d i f f e rence between t h e ''upper" and "lower" poin ts . b. Good phase-shift a t t h e resonant frequency. c. Di f fe ren t resonant frequencies ind ica ted by the tabula t ion , t h e der i - va t ive p l o t , and the t r a n s m i s s i b i l i t y p l o t . Such modes are generally phys ica l , i.e. real, modes of t h e a i rp l ane , bu t t h i s p a r t i c u l a r gage is not t h e b e s t t o d i sce rn them; they are b e t t e r picked off from some o t h e r sensor. The 9.9, 13.4, 23.5 and 26.7 Hz modes tabulated i n Figure 9 f a l l i n t o t h i s category. The 35.4, 37.3 and 39.8 Hz modes are f i c t i t i o u s and can be recognized as such by : a. Unequal damping values wi th in the "low" and "high" po in t s , b. Low o r even negative damping ind ica t ions not subs t an t i a t ed by deriva- t ive and t r a n s m i s s i b i l i t y p lo t s . U t i l i z a t i o n of frequency and damping data Frequency and damping da ta obtained from t h e various sources are cross- p lo t t ed versus a l t i t u d e and Mach number f o r each mode of i n t e r e s t t o make s u r e t h a t they are properly tracked. damping versus Mach number a t a constant a l t i t u d e of 1525 m (5000 f t ) . Figure 10 shows a sample p l o t of frequency and Two 419 modes, f i n bending and boo 1 bending, are shown f o r one s i d e of t h c r a f t , t o demonstrate t h e r be A s is generally q u i t e cons is ten t , t he higher damped modes (see t h e fin-bending mode i n Figure lo), t h e r e may be some disagreement between t h e d i f f e r e n t b i t s of information. I n such cases, t h e input d a t a are reviewed regarding t h e i r relative m e r i t , e.g. t h e q u a l i t y of t h e decay d a t a , the consistency of the automatically ex t rac ted da ta , and the adequacy of t h e manually obtained da ta , Based on a j u qua l i t y of t h e d i f f e r e n t p ieces of information, a d e t e t i o n is made on t h e "final" frequency and damping values t o be used f o r t h i s mode and its "reason- ableness" is evaluated by reviewing cross-plots versus a l t i t u d e and Mach number. This "final" information f o r each s i d e of t h e a i r c r a f t is then en tered i n t o computer s to rage by means of a remote "Execuport" terminal loca ted a t the test site. These d a t a can be r e t r i eved e i t h e r i n tabular form o r as Gould p l o t s of frequency, damping, and F l u t t e r Margin versus a l t i t u d e and Mach number. be seeng the frequency and information o f r o ous However, i n some casesp espec ia l ly f o r some of A t t h i s po in t , t h e following da ta are therefore ava i l ab le t o the f l u t t e r engineer: a. P l o t s of frequency and damping versus a l t i t u d e f o r each mode of i n t e r e s t a t each cross-section Mach number - Figure 11 is an example of such a p lo t . b. P l o t s of frequency and damping versus Mach number f o r each mode of i n t e r e s t a t each constant a l t i t u d e cross s e c t i o n - see Figure 10 f o r sample da ta of t h i s kind. c. P l o t s of F l u t t e r Margin versus equivalent airspeed f o r each modal combination of interest a t each cross-section Mach number (this a l s o inc ludes a predic t ion of t he f l u t t e r speed based on a parabol ic ex- t r apo la t ion ) - see Figure 12. d. P l o t s of F l u t t e r Margin versus Mach number f o r each modal p a i r of i n t e r e s t at each cross-section a l t i t u d e - see Figure 13. Constant a l t i t u d e f l u t t e r ve loc i ty pred ic t ions are then obtained by manu- a l l y se l ec t ing t h e Mach number from t h e constant a l t i t u d e f l u t t e r margin p l o t s a t which supersonic flow c h a r a c t e r i s t i c s appear t o be es tab l i shed (e.g. M = 1.18 on t h e p l o t i n Figure 13), and u t i l i z i n g only test da t a above t h a t Mach number f o r t h e supersonic ex t rapola t iou at t h i s a l t i t u d e . A cross-plot of a l l the F l u t t e r Margin predic t ions is then made f o r each modal p a i r of i n t e r e s t (see Figure 14 f o r an example) and evaluated i n terms of minimum f l u t t e r margin. It should be noted t h a t , although modes as determined from left-hand and right-hand da ta were tracked independent-ly, on the F-15 they w e r e c lose enough t o each o the r t h a t one f l u t t e r boundary could be used t o represent them both, 420 RESULTS The modes to be observed during the F-4. selected on the bas i s of the res and ground vibration tests, The tracked on t h i s bas i s were: f i n f i r s t bend s t ab i l a to r bending, s t ab i l a to r p i tch , boom lateral bending, boom torsion, boom ve r t i ca l bending, wing f i r s t bending, wing second bending, wing f i r s t torsion, outer wing torsion, and aileron rotat ion. Data obtained fo r these various modes w e r e then evaluated i n terms of damp- ing versus airspeed a t 1525 m (5000 f t ) , damping versus a l t i t u d e a t the cross- section Mach numbers ( to extrapolate t o the damping value t o be expected a t sea l eve l ) , and f l u t t e r boundaries on the basis of F lu t te r Margin of various modal pa i r s representing poten t ia l f l u t t e r mechanisms. Tables I and I1 summarize the r e su l t s of these evaluations i n terms of minimum predicted f l u t t e r margin f o r the various mechanisms. that there are s i x f l u t t e r mechanisms (three symmetric and three antisymmetric) with predicted f l u t t e r margins between 15 and 20 percent, substantiating the success of the minimum weight design concept pursued on the F-15. It can be noted Based on our experience t o date , we f e e l t h a t predictions can re l iab ly be carried only t o a veloci ty which is no far ther from the last test point than about 1.5 t i m e s the difference between the f i r s t and last i n f l i g h t test points. On t h i s basis, s ince our tests w e r e between a l t i t udes of 6100 and 1525 m (20 000 and 5000 f t ) , f l u t t e r veloci ty predictions showing greater than 25% f l u t t e r margin of safe ty have no spec i f ic quant i ta t ive values attached t o them. Shapes of f l u t t e r boundaries Shapes of predicted f l u t t e r boundaries were generally e i the r i n the form of the boundary given i n Figure 14, with Mach numbers between 0.9 and 1.1 being c r i t i c a l , o r as shown i n Figure 15, with the maximum sea-level Mach number being c r i t i c a l . Application t o design changes The quant i ta t ive knowledge of actual f l u t t e r margins provides a firm basis on which t o assess the impact of prospective design changes. For example, we may want t o incorporate an a i r c r a f t modification which, according to analysis (which has been substant ia l ly ver i f ied by correlat ion with quant i ta t ive f l i g h t test data) and possibly a l so wind tunnel t e s t s , lowers the f l u t t e r speed of a cer ta in mechanism by 5%. I f we have f l i g h t test data i n hand tha t show tha t w e now have 25% margin i n t h i s mechanism, w e not only have considerable confidence tha t w e can go ahead, but we a l so have no need to go in to another involved f l i g h t f l u t t e r test program, W e have already had several such opportunities to apply the quant i ta t ive F-15 f l i g h t f l u t t e r test data t o the evaluation of design changes. 421 i g h t f l u t t e r test procedure used on the F-15 provides no t only a demonstration of adequate damping throughout the a i r c r a f t f l i g h t envelope, bu t a l s o permits quan t i t a t ive demonstration of margin of s a f e t y , information is not only use fu l t o d e f i n i t i v e l y e s t a b l i s h the f l u t t e r s t a t u s of t he aircraft as i t w a s flown, bu t a l s o provides a s o l i d foundation on which t o assess the impact of any f u t u r e design changes. Such q u a n t i t a t i v e REFERENCES 1. Zimmerman, N.H., and Weissenburger, J.T.: P red ic t ion of F l u t t e r Onset Speed Based on F l i g h t F l u t t e r Tes t ing at S u b c r i t i c a l Speeds. of A i r c r a f t , Vol. 1, No. 4, 1964. Journa l 2. Shelton, J .D. , and Tucker, P.B.: Minimum Weight Design of t h e F-15 Empennage f o r F l u t t e r . AIAA/ASME 16th S t ruc tures Meeting, May 1975. 3. Nash, D.E., Katz, H., and Moody, W.C.: F-15 F l i g h t F l u t t e r Testing: A i r c r a f t Systems and T e s t Operations. AIAA 1975 Ai rc ra f t Systems and Technology Meeting, August 1975. 4. Kennedy, C.C. and Pancu, C.D.P.: U s e of Vectors i n Vibration Measurement and Analysis. Journa l of Aeronautical Sciences, V o l . 14, 1947. 422 MECHANISM FIN BENDING vs BOOM LATERAL BENDING STABILATOR BENDING vs STABILATOR ROTATION WING FIRST BENDING vs OUTER WING TORSION BOOM VERTICAL BENDING vs STABILATOR ROTATION BOOM LATERAL BENDING vs BOOM TORSION STABILATOR BENDING vs BOOM TORSION STABILATOR ROTATION vs BOOM TORSION FIN BENDING vs FIN TORSION STABILATOR BENDING vs BOOM VERTICAL BENDING BOOM TORSION vs BOOM VERTICAL BENDING FIN TORSION vs FIN TIP ROLL WING FIRST BENDING vs WING FIRST TORSION WING SECOND BENDING vs WING FIRST TORSION WING SECOND BENDING vs OUTER WING TORSION MARGIN OF SAFETY 15% 19% 20% 25% > 25% > 25% > 25% > 25% > 25% > 25% > 25% > 25% > 25% > 25% GP15.07102 TABLE I1: MlNlMUM FLUTTER VELOCITY MARGINS FOR ANTI SYMMETRIC MECHANISMS MECHANISM FIN BENDING vs BOOM LATERAL BENDING STABILATOR ROTATION vs BOOM TORSION BOOM LATERAL BENDING vs BOOM TORSION WING FIRST BENDING vs OUTER WING TORSION STABILATOR BENDING vs BOOM TORSION BOOM VERTICAL BENDING vs STAB1 LATOR ROTATION WING SECOND BENDING vs OUTER WING TORSION STABILATOR BENDING vs STABILATOR ROTATION FIN BENDING vs FIN TORSION STABILATOR BENDING vs BOOM VERTICAL BENDING BOOM TORSION vs BOOM VERTICAL BENDING FIN TORSION vs FIN TIP ROLL WING FIRST BENDING vs WING FIRST TORSION WING SECOND BENDING vs WING FIRST TORSION MARGIN OF SAFETY 16% 17% 20% 25% > 25% > 25% > 25% > 25% > 25% > 25% > 25% > 25% > 25% > 25% 423 NORMALIZED FLUTTER MARGIN MACH NUMBER GP75 07104 Figure 1.- Flutter margin at constant dynamic pressure. Antisymmetric boom torsion versus stabilator rotation at 442 KEAS. PROJECTED FLUTTER VELOCITY (STRAIGHT INE EXTRAPOLATION; FLIGHT TEST POINTS ONLY) 6000 rn (20 000 FT) NORMALIZED FLUTTER MARGIN 3000 rn (IO 000 FT) TEST POlN 1500 rn (5000 FT) TEST POlN PROJECTED FLUTTER VELOCITY (PARABOLIC EXTRAPOLATION INCL. ZERO-AIRSPEED POINT) OWbOllOl l VELOCITY Figure 2.- Flutter prediction at constant Mach number. 424 0.2 NORMALIZED FLUTTER MARGIN 0 PROJECTED SUPERSONIC \ \\ FLUlTER CRITICAL TRANSONIC MACH NUMBER FOR THIS MECHANISM 0.6 0.4 \ PROJECTED SUBSONIC FLUTTER VELOCITY\ MACH NUMBER OP7*0110 7 Figure 3.- Flutter prediction at constant altitude. 3000 t I I I I I AIRSPEED KEAS MACH NUMBER Figure 4.- F-15 flight flutter test points. 425 TYPE - _ FIN TORSION RUDDER ROTATION OF GAGE 0 BENDING A TORSION STRAIN GAGES STABlLATOR 0 HINGEMOMEN 0 ACCELEROMETER (BOTH SIDES GAGED) OUTER WING BENDING BENDING (WITH STORES) NDAMENTAL WING FUNDAMENTAL WING BENDING (CLEAN) TORSION (CLEAN) OP,B071010 Figure 5.- Location of instrumentation. 32 CHANNELS NARROW BAND FM; 1 "REAL-TIME" TRANSFER FUNCTION TR DISPLAYED DURING FU SWEEP ON CATHODE 90 RAY TUBE AFTER SWEEP COMPLETION 32 NARROW BAND 16 LISSAJOUS FM PARAMETERS FIGURES DISPLAYED DISPLAYED CONTINUOUSLY ON CONTINUOUSLY ON 4 STRIP RECORDERS 4 OSCILLOSCOPES OP75071012 Figure 6.- On-line data reduction of telemetered signals. 426 PHASE ..................... 1 .oo DATE ....................... 01/24n4 RUN NUMBER .................... 02 Hpc 1512 m (4959 FT) M ............................. 1.105 CONDITION OF SWEEP EMPEN. SYMMETRIC VE 663.4 KTS VT ........................... 718.7 KTS (1 ................... 72.35 kPa (1511 PSF) TAF 4% (392'F) .................. 0.75 ............................ 0.50 ........................ 0.25 PA ....... 1.06 k g / J (0.002057 SLUGS/FT3) R/H Boom Lateral Bending Normalized to R/H Stabilator Rotation 180 90 0 -90 -180 Figure 7.- St. Louis transmissibility plot. DATA STORAGE AND MANAGEMENT MANUAL EXTRACTION AND DAMPING VALUES EXCITATION Figure 8.- Post-flight data system schematic. 427 FIRST DERIVATIVE R/H Boom Lateral Bending Normalized to R/H Stabilator Rotation F'-15 FLIGHT FLUTTER ANALYSIS SYSTEM AIRCRAFTNO. ................ 1280 FLIGHT RO. .................. .341 DATE ................... 01/24/74 RUN NUMBER .................. .02 Hpc ............... 1512m (4959 FT) M ........................ 1.105 CONDITION OF SWEEP EMPEN.SYMMETRIC VE .................... 663.4KT-S VT .................... 718.7KTS Q .............. 72.35kPa (1511 PSF) TAF ................. .4OC (392'F) PA . .... .1.06 kg/m3 (0.002057 SLUGS/FT3) NUM 1 2 3 4 5 6 7 9 10 11 12 a - HERTZ FREQUENCY AND DAMPING DATA AVG FREQ DAMP DAMP DAMP DAMP DAMP 9.90 0.123 0.114 0.169 0.164 0.142 13.40 0.038 0.031 0.024 0.024 0.029 18.60 0.019 0.018 0.020 0.021 0.019 23.50 0.118 0.100 0.272 0.240 0.183 26.69 0.005 0.001 0.034 8.033 0.018 33.80 0.025 0.026 0.023 0.028 0.026 35.48 -0.002 4.002 0.001 0.001 0.001 37.31 0.033 0.027 0.007 0.008 0.019 39.80 0.005 -0.008 -0.009 -0.014 0.005 Figure 9 . - S t . Louis Argand derivative plot and automatic frequency and damping extraction results. STRUCTURAL DAMPING g (XI FREQUENCY HZ y Manual Techniques y Automatic Techniques 0.7 0.8 0.9 1 .o 1 .l 1.2 MACH NUMBER GP7i07lC14 Figure 10.- Frequency and damping versus Mach number for symmetric f i n bending and boom lateral bending modes. L/H data at 1525 m (5000 f t ) altitude. 428 0 STRUCTURAL DAMPING g (%) -7 0 -20 20 FREQUENCY '9 HZ 18 17 0- AIRSPEED SEA LEVEL ALTITUDE - krn (iP75-0710 14 Figure 11.- Frequency and damping versus a l t i t u d e f o r symmetric boom lateral bending a t constant Mach number of 1.10. 1.50 1 .oo NORMALIZED FLUTTER MARGIN 0.50 I I 1 150 300 450 600 750 900 EQUIVALENT AIRSPEED - KTS G P X 0,105 Figure 12.- F l u t t e r margin versus equivalent airspeed. Symmetric boom lateral bending versus f i n bending f o r constant Mach number of 1.10. 429 MACH NUMBER OP76.071DIS Figure 13.- F l u t t e r margin versus Mach number. Synrmetric boom lateral bending versus f i n bending a t constant a l t i t u d e of 1525 m (5000 f t ) . AIRSPEED KEAS DP75-07,016 MACH NUMBER Figure 14.- F l u t t e r boundary f o r f i n bending versus boom lateral bending mechanism - symmetric. 430 MACH NUMBER G P I S 07,017 Figure 15.- F l u t t e r boundary f o r wing f i r s t bending versus o u t e r panel. t o r s i o n mechanism - symmetric. 431 YF-16 FLIGHT FLUTTER TEST Warren J. Brignac, Halvor B. Ness, Maynard K. Johnson, and Larz M e Smith For t Worth Division General Dynamics Corporation SUMMARY The procedures used f o r "Elight f l u t t e r t e s t i n g of t h e YF-16 l ightweight f i g h t e r prototype a re described. The Random Decrement technique was incorporated t o augment the i n i t i a l plan t o use only the p i l o t pulse approach. With Random Decrement, s u b c r i t i c a l damping of the s t r u c t u r a l modes i s extracted from the turbulence- induced random vibra t ions of the s t ruc tu re . Hence, the method by- passes the requirement f o r an exc i ta t ion system needed i n the conventional approaches. Damping is obtained from the Randomdec Signature of each mode. The Randomdec Signature i s analogous t o the t rans ien t response t o an i n i t i a l displacement. To obtain a Randomdec Signature, one c o l l e c t s and averages a number of seg- ments of the random response of the mode. Expeditious f l u t t e r clearance of the YF-16 w a s accomplished, marking the f i r s t known appl icat ion of the technique t o a f u l l - s c a l e t e s t a r t i c l e . Although the Random Decrement apparatus used w a s lacking i n completeness, i t produced damping on check problems which were consis tent w i t h values from conventional methods. For the YF-16, i t w a s possible t o ident i fy and t rack most of the modes of i n t e r e s t for each of the configurat ions tes ted. Good quant i ta t ive damping w a s obtained for the lower surface modes. Most of the higher modes were detectable and a t l e a s t a qua l i t a t ive evaluat ion of the damping w a s possible. Most of t h e t e s t ing w a s done a t the more c r i t i c a l low a l t i t u d e s where the random exc i t a t ion i s high. Due t o equipment l imi ta t ions , only one channel could be monitored on a r e a l t i m e bas i s . Therefore, most of the ana lys i s w a s accom- pl ished on a pos t f l i gh t bas i s . t i a t e the adequacy of the f u t t e r margin of sa fe ty . Damping values obtained substan- 433 ght tes t procedure included t h e ca re fu l monitoring 0 three a x i s pulses, r o l l s and pullups. s a r e t h a t , for the YF-16, the procedures used, including Random Decrement, were a sa t i s fac tory a l t e r n a t e t o more cos t ly conventional t es t procedures. INTRODUCTION A v i t a l s t ep i n an a i r c r a f t development program i s the sub- s t a n t i a t i o n of freedom from f l u t t e r by means of f l i g h t f l u t t e r t e s t s . Since f l u t t e r clearance i s a pacing item fo r expanding the speed envelope, the need for accurate , rapid and low cos t means t o forecas t f l u t t e r i s widely recognized. Because f l i g h t f l u t t e r t e s t s have been cos t ly and time consuming, there have been continuing e f f o r t s by industry (Reference 1) and government agencies (Reference 2) t o upgrade t h e i r procedures. A s indicated by a recent survey (Reference 3 ) , most current methods require onboard forced exc i ta t ion , usually s inusoidal , t o exc i te the s t r u c t u r a l modes. Damping i s then obtained by a var ie ty of methods including from decay records from the well-known "shake and stop" technique. computers i n t o the d a t a acquis i t ion and reduction opera-tions has resul ted i n some s ign i f i can t advances i n the state of the ar t . The methods, however, s t i l l tend t o be both expensive and time consuming. item, The incorporation of high speed d i g i t a l The exc i t a t ion system i t s e l f i s usual ly a cos t ly Alternat ives t o methods requir ing forced exc i ta t ion have been advanced. These methods u t i l i z e i n f l i g h t o r wind tunnel turbulence as the exc i ta t ion source. I n one approach, PSD analyses of the response s ignals a r e made and damping i s obtained from the frequency and bandwidth associated with each peak i n the PSD p lo t , The PSD approach i s more widely used i n Europe a t t h i s t i m e . The Random Decrement approach, the appl icat ion of which i s t o be discussed herein, i s a second a l t e r n a t e t o forced exci ta- t i o n methods. The method w a s invented by H. A . Cole, J r . , and i s 434 documented Reference 4 and 5). The Random Decreme d is basical y an ensemb induced random vi rations of gure 1, Cole advocates triggering each data sample at a constant level, Yt. Assuming li tion, the time history of each sample can be regarded as the combined solution from (1) an initial step displacement, (2) an initial velocity and (3) a random forcing function. sample represents the response to the same initial displacement as Figure l(b), a different initial velocity with the opposite sign, and a different random forcing function. It can be rea- soned intuitively that when a large number of samples are aver- aged, only the response to the constant initial displacement will remain because the average of responses due to the alternating initial velocities and the random forcing functions will tend to zero. Thus, it is seen that the ensemble average converges toward the transient response to an initial step. For a constant trigger level, the ensemble average (Randomdec Signature) will be constant even if the amplitude of the forcing function varies. If the ensemble average is made up of samples with initial posi- tive slopes only, then the resulting trace represents the tran- sient response to a combined step and initial velocity. Under these conditions the Randomdec Signature would vary with the intensity of the forcing function, thus minimizing the use of the signature trace as a failure detector. However, the damping as determined from the decay rate of the signature trace would be valid. A rigorous mathematical derivation of Random Decrement is given in Reference 6. Included are descriptions of other trig- gering procedures and automated methods of analyzing the Random- dec Signature to obtain damping. Note that the Figure l(c) The main objective of this paper is to present the results of the application of a simplified flutter test technique to a flight article. It is hoped that these results will be of use to others who may be considering new methods and/or improvements for similar techniques. BACKGROUND The YF-16 is a lightweight fighter prototype whose high performance credits include supersonic sea-level capability. A top and side view of the airplane is shown in Figure 2. The design features a thin (4%) aluminum wing with leading-edge maneuver flaps and trailing-edge flaperons. The all-movable 435 tyrizontal takl and the convent have graph te composite skins, considerations had a considerab schedule constraints on the pro prevention program which minimized flight flutter tests. the initial planning, flight flutter tests were to be conducted with pilot pulses. The austere flight flutter test p to be supported by comprehensive analyses scale flexible model to be tested in the NASA Langley 16-Foot Transonic Tunnel. utilized for design. In A twenty percent margin of safety was to be It was during early tests of the YF-16 1/4-scale model components that General Dynamics was first exposed to the Random. Decrement concept. NASA LRC tunnel personnel had assembled a Random Decrement analyzer and were using it to monitor the tunnel tests. Although the single-channel instrument limited the extent of on-line monitoring, the capability to extract quantitative damping was demonstrated. An example of the damping of one mode at successive speed increments is shown in Figure 3 . NASA LRC had also indicated (see Figure 4) satisfactory agreement between Random Decrement and PSD methods on predicting the flutter speed of an SST wing model. Following the exposure to Random Decrement at the tunnel test, General Dynamics assembled a Random Decrement analyzer analogous to the NASA equipment and undertook a further evaluation of its capability. An investigation was made on an electric analog computer model of a simple two-degree of freedom system illustrated in Figure 5. The electric model is analogous to a model in a wind tunnel or an airplane in flight and subcritical damping can be determined by the "shake and stop" procedure. Using the Random Decrement analyzer, damping was also obtained with the model being excited by sea-level simulated atmospheric turbulence. As shown in Figure 5, consistent damping and flutter speeds were obtained by the two methods. The damping obtained by the Random Decrement analyzer did not vary significantly with excitation levels higher by a factor of two. An additional limited evaluation was made using F-111 taped flight flutter test data. tion on the F-111 program; consequently, generally good wing damping records had been obtained. that good damping agreement was observed for modes with high ambient response levels and, conversely, poor agreement was shown when the ambient excitation level was low. It was observed that, 436 Wing tip vanes were used for excita- The general observation was in cases of low ambient eva ed by the from the forced excitation, g the somew it was decided to implement flight flutter test program. the method were recognized, damping could be obtained for the ambient environment. frequencies are close were expected but this problem plagues all methods, In addition, the capability to analyze rapidly any unexpected vibratory phenomenon was highly desirable. Some appare Separation problems when mode PROCEDURE The four airplane configurations which were tested are shown in Figure 6. The 1400 liter (370 gallon) external tank loading was tested full, empty and at two intermediate fuel levels, onboard flutter instrumentation is shown in Figure 7. Included are two accelerometers in each wing tip, one in each horizontal tail tip and one in the vertical tail tip. The output of each transducer was telemetered to the ground and also recorded on- board on magnetic tape. Each telemetered item was displayed on an analog recorder. Variable band-pass filters were used on the accelerometer signals to narrow the response to the frequency range of interest. Random Decrement analyzer for analysis individually. The Any six channels could also be patched to the The test procedure included a slow acceleration to the test point while the strip charts were carefully monitored. was stabilized for 30 to 60 seconds to accumulate data for Random Decrement analysis. Then the pilot would pulse the controls about all three axes, roll 360° in each direction and do a symmetric pullup. Speed The test procedure was augmented with Random Decrement as follows. The stabilized period at each test point was sufficient to obtain damping only of one selected mode. Random Decrement analyzer was available, analysis of additional modes could only be accomplished on a rotating basis at the expense of a longer stabilized period. In general, this was not done because the need was not apparent. Instead, all channels were carefully analyzed on a postflight basis. Since only one 437 output s igna l w a s f i r s t run t a mode before going through t system is t h e Hewlett-Packard performed the function of acq playing an updated average con Programming on t h i s computer i button cont ro ls which enable commands. This fea ture prove u t i l i t y s ince ana lys i s could be rapidly updated t o r e f l e c t a change i n f l i g h t condi t ion o r t o examine a d i f f e ren t measurement locat ion. The a b i l i t y t o switch i n and display the random wave- form on the scope w a s very valuable w i t h regard t o s e t t i n g the t r i gge r l e v e l for sampling. After t r igger ing , the system reads each data sample a t 1000 in t e rva l s . The analyzer may be somewhat l e s s than optimum i n t h a t i t i s t r iggered by pos i t ive slope crossings only. A s previously mentioned, the ana lys i s t i m e f o r each damping record usual ly var ied from 30 seconds t o a minute depending on the exc i t a t ion l eve l and the frequency of the mode. Generally, the damping t race w a s observed t o converge a f t e r about 25 t o 40 samples were acquired. An i t e m which grea t ly f a c i l i t a t e d the pos t f l i gh t data ana lys i s w a s the conveniently located magnetic tape u n i t with s tar t , s top and rewind controls operated by the Random Decrement analyzer operator , The reason i s t h a t s e t t i n g optimum t r igger l eve l s and locat ing resonant frequencies can require many passes through the magnetic tape. The procedure f o r s e t t i n g up the analyzer w a s t o f i r s t observe the random s igna l on the osci l loscope t o determine exis tence of per iodic motion. The time scale w a s var ied on t h e CRT display t o cover the desired range of frequencies. Obvious aides i n detect ing spec i f i c frequencies w e r e the calculated v ibra t ion frequencies, the ground v ibra t ion t e s t r e s u l t s , and a frequency spectral ana lys i s described a t the end of t h i s sect ion. The var iab le band-pass f i l t e r s were adjusted t o focus on a spec i f ic desired frequency. The t r igge r l e v e l w a s adjusted by observing the f i l t e r e d s igna l on the osci l loscope and t r igger ing a t the maximum leve l possible t h a t would s t i l l allow the accumula- t i on of a sa t i s f ac to ry number of data samples within the t e s t period. The frequency detect ion port ion of t h i s process could be s t a r t e d while the a i rp lane w a s i n t r a n s i t t o the t e s t a rea o r otherwise preparing f o r the t e s t run. The t r i gge r s e t t i n g w a s 438 was preferred because the setup was easier and a shorter time period was required to accumulate a sufficient number of data samples, In extremely smooth air, the low structural amplitude caused problems in obtaining sufficient data samples and led to some loss of confidence in the accuracy of the results. A spectral analysis of each data channel was performed to confirm that all structural modes which were responsive to the random excitation were in fact being identified and tracked by the Random Decrement Analyzer. The analysis was performed using the AFFTC Time/Data 1923/50 Time Series Analyzer. This analysis produced the conventional power vs frequency chart and provided graphic confirmation of the frequency content of the response. OVERALL RESULTS The flutter free envelopes which were demonstrated are shown in Figure 9. It is noted that the cleared envelopes were those required for prototype evaluations and the design envelopes are somewhat larger. Although full envelope capability is indicated by analysis, model tests and flight flutter test results, the prototype program's tight schedule did not call for full clearance. All subsonic points for each configuration were accomplished on one flight. Generally, two points per flight were accomplished in the low supersonic region. was accomplished at the high supersonic speeds to allow a complete postflight evaluation before proceeding to the next test point. The flight flutter test program was planned as part of an integrated program in which considerable data in other disciplines was acquired before the envelope expansion was completed. The flutter test program was completed on schedule with the maximum test dynamic pressure of 103 000 N/m2 (2150 psf) being reached approximately three months after the first flight. Only one test point per flight As expected based on analysis and model test results, the flight flutter test program was accomplished expeditiously and without any major problems. One specific flight test incident occurred which had not been anticipated. Early in the flight test program, a gain sensitive oscillation of the nominal 6.5 Hz antisymmetric wing mode became apparent due to a coupling with 439 the f l i g h t cont ro l s t a b i l i t y augmentation i s reviewed i n d e t a i l i n a separ the highl ights w i l l be discussed encountered a t approximately .85M a t 6096 m i n s u f f i c i e n t cont ro l s y s t e m in t e rac t ion analyses had been accom- plished. Most of the cont ro l system in t e rac t ion analyses had been accomplished a t 1 . 2 M where f l u t t e r m a ns were a minimum and no problem w a s indicated. The ac tua l blem occurred where the r o l l effect iveness of the f laperons w a s the highest . The problem w a s quickly i d e n t i f i e d and a f i x worked out consis t ing of a notch f i l t e r i n the r o l l feedback loop and realignment of gains i n t h e command and feedback loops. It i s worth mentioning t h a t the YF-16's fly-by-wire con t ro l system made quick implemen- t a t i o n of the f i x possible . Random Decrement w a s very usefu l i n fu r the r def ining the region of i n s t a b i l i t y which i s shown i n Figure 10. The region w a s ac tua l ly t raversed with reduced r o l l gains before the f i n a l f i x w a s incorporated. A s w i l l subsequently be shown, the Random Decrement r e s u l t s show a s ign i f i can t difference between the mode's c h a r a c t e r i s t i c s with reduced gains and w i t h t h e notch f i l t e r i n s t a l l e d . The difference i s due t o the phase s h i f t which the f i l t e r introduces. Overal l , Random Decrement demonstrated t h a t most of the modes of i n t e r e s t were exci ted by the random environment and s o l i d damping i s indicated throughout the f l i g h t envelope. A review of the damping records obtained i s presented i n t h e following sec t ion. DAMPING The qua l i ty of the damping obtained i s described i n Table I f o r the bas ic configurat ion with and without t i p missi les . The t ab le ind ica t e s the modes of each surface t h a t were most ea s i ly detected. I n general , these a r e the f i r s t two wing modes and the fundamental t a i l modes. The higher modes, including some i n addi t ion t o t h e ones i n Table I, were usual ly detectable but the qua l i ty of the decay record w a s poor o r erratic. mental horizontal t a i l mode w a s detectable but highly damped. The higher horizontal t a i l modes were apparently very highly damped a l s o . A complete s e t of decay records fo r a missiles-on t e s t point i s shown i n Figures 11 and 12. Mode iden t i f i ca t ion The funda- 440 corresponds to that given in s of damping versus Mach number for the missiles- ic , antisymmetric, and vertical tail modes are shown in Figure 13, Corresponding decay records are shown in Figures 14 and 15. that the frequencies of the two wing mo and some difficulty was experienced in arating the responses. The problem was overcome by adding the signals from corresponding transducers on opposite sides to emphasize the symmetric re and subtracting to emphasize the antisymmetric response. T process is illustrated in Figure 16. A simple network of isola- tion resistors was used to combine the output of two discrimina- tors. The outputs were summed to get the symmetric response. The phase of one discriminator was reversed to obtain the anti- symmetric response. No attempt was made to correct for the slight difference in sensitivity of the accelerometers involved. Note are relatively close The basic wing modes for the configurations with pylon- mounted external stores were detected at approximately the same frequencies listed above and exhibited similar damping charac- teristics. The carriage of the external stores well inboard (at 27 percent of the exposed semispan) accounts for the small effect on the basic wing frequencies. For the external store configurations, the fundamental store pitch and yaw frequencies were also detected and their decay records extracted. Typical examples of external store decay records are shown in Figure 17 for the airplane with empty 1400 liter (370 gallon) tanks. Some further examples of the results obtained with Random Decrement are in connection with the oscillation of the anti- symmetric mode. Shown in Figure 18 is a comparison of the damping at .9M and 1520 m (5000 feet), before and after the notch filter was added. Before the notch filter was added, the motion of the mode was sustained although of extremely low magnitude for the applicable gain setting. Shown in Figure 18(a) are the individual decay records from opposite wing tips and the decay records obtained after adding and subtracting the wing tip response. It is noted that even though the antisymmetric mode appears to dominate the individual responses, a good damping record was obtained for the symmetric mode. corresponding records after the filter was added. Note that even though the numerical value of the feedback loop gain was close to the "before filter" value, positive damping is shown for the antisymmetric mode. A s previously mentioned, the difference is apparently due to the favorable phase shift from the filter. Shown in Figure 18(b) are the 441 obtained. Early in the test program, vertical tail data was obtained at hi the ambient response levels were ower than at low altitude, no difficulty was encountered in obtaining consistent damping at 6096 m (20 000 feet) and 9144 m (30 000 feet). Damping records for the fundamental tail modes at 1520 m (5000 feet), 6096 m (20 000 feet), and 9144 m (30 000 feet) are shown in Figure 19. The damping at the higher altitude is noticeably lower. The question arises as to whether the damping is lower due to lower density or to inaccuracies associated with the lower excitation levels. In the case of the fundamental tail modes, it is believed that sufficient excitation was provided from wing down- wash, etc., so that the high altitude damping is realistic. The high altitude damping for the higher modes is believed to be more questionable. CONCLUSIONS Application of Random Decrement to the flight flutter tests of the YF-16 has led to the following evaluation of the technique: 1. 2. 3 . 4 . 5. The frequency and damping of most of the predominant structural modes can be obtained. The quality of the damping depends on the excitation level, the damping level, and the accumulation of a sufficient number of samples, usually 25-40. The lower structural modes are more easily detected and good quality damping can be expected for these modes. The higher structural modes can usually be detected but damping values tend to be more qualitative than quantitative. Separation of symmetric and antisymmetric modes of nearly the same frequency was possible. 442 7. 8. The method has the obvious limitation of not being able to detect a particular mode if it is not excited. closely spaced modes cause analysis problems. A Some of the limitations mentioned here can be overcome with improved facilities and analysis techniques. For the YF-16, the results from the Random Decrement analysis substantiate the predicted flutter margins of safety. Hence, Random Decrement was a meaningful addition to the flight flutter test procedure and served as a satisfactory alternate to more costly conventional techniques. The principal result was that quantitative damping was obtained which would not have been possible for this airplane with the pilot pulse technique. FUTURE PLANS Full scale development of the production F-16 is now in progress. The flutter prevention plan is the same as followed for the prototype YF-16-including a twenty percent margin of safety for design. Planned flight flutter tests will use procedures similar to those described in this paper. test equipment is being expanded to provide two-channel capa- bility through acquisition of a second Hewlett-Packard Model 5480B Signal Analyzer. The flutter All flutter test data on the YF-16 was both recorded on . The F-16 full scale onboard tape and transmitted via telemetry to the ground receiving station using FM/FM techniques. development test aircraft will be equipped with the AFFTC Automatic Test Instrumentation System (ATIS). 512K bits/sec) PCM system. The existing Random Decrement analysis system uses analog input; therefore, digital-to-analog conversion will be required. Experimental confirmation of the sampling rates necessary in order to produce an acceptable damping record has been accomplished. mum of four samples per cycle of response is required. This is a high rate (up to It has been determined that an absolute mini- 443 SYMBOLS f f F f0 A f Xn XO Yt points at, which response crosses specified reference amplitude, Yt frequency, Hz flutter frequency, Hz frequency of selected response mode, Hz band width of response mode at half-power point, Hz damping coefficient translational spring constant, dynes/cm rotational spring constant, dyne cm/rad Mach number dynamic pressure , N/m2 time, sec airspeed, knots flutter speed, knots equivalent initial velocity at points A and B half-amplitude of nth cycle of exponential decay curve half-amplitude of initial cycle of exponential decay curve reference amplitude of response viscous damping ratio Y 444 1. Baird, E, F,, and Clark, W, Be: Recent Developments in Flight Flutter Testing in the United States. Presented at 34th Meeting of the AGARD Structures and Materials Panel, April 1972, AGARD Report 596 2 . Houbolt, J. C.: Subcritical Flutter Testing and System Identification. NASA CR-132480, August 1974 3. Rosenbaum, Robert: Survey of Aircraft Subcritical Flight Flutter Testing Methods. NASA CR-132479, August 1974 4. Cole, Henry A., Jr.: Method and Apparatus for Measuring Damping Characteristics of a Structure. United States Patent No. 3,620,069, 16 November 1971 5. Cole, H. A., Jr.: On-Line Failure Detection and Damping Measurements of Aerospace Structures by Random Decrement Signatures. NASA CR-2205 , March 1973 6. Chang, C.S.: Study of Dynamic Characteristics of Aeroelastic Systems Utilizing Randomdec Signatures. NASA CR-132563 7. Peloubet, R. P., Jr.: YF-16 Active-Control-System/ Structural Dynamics Interaction Instability. Presented at 16th AIAA/ASME/SAE Structures, Structures Dynamics and Materials Conference, May 1975 445 n W u u w W W P n a w n & n 0QE- I 0 0 0 O P I Z u u u u W W W W nnnn 4 4 4 0 F r h F r P I m d . o a O b N O r- lr lmd. . . . . m ww * * * * 44-44 u u u u w w w w nnnn w w w w n n n n n & n & 0 0 0 0 0 0 0 0 c3PIoPI nn u 0 0 H w crl m 3 * . P 2 P 2 z 0 PI Fr z 0 H m P E3 3 I !-4 H - 4 4 P Fr Fr 0 m W A H " : zo " w crl H m " H c 446 T l A L CONDITIONS: t Figure 1 Random AVERAGE OF MANY DATA SAMPLES - t Decrement Concept Figure 2 YF-16 Airplane 447 Figure 3 Model Pylon Damping 0 RANDOMDEC METHOD 0 PSD METHOD .08 PSD METHOD RESPONSE DAMP I NG RATIO .04 Y PS D 0 DYNAMIC PRESSURE, PSF (lPSF= 47.88 N/m2) FREQUENCY, f, Hz RANDOMDEC METHOD X, TIME - Figure 4 SST Model Damping 448 08 e 04 n " 0 100 200 300 400 500 600 9 700 800 900 V (KNOTS) P ONLY SS LES I Figure 5 Analog Model Damping TIP MISSILES+ TANKS I CLEAN LAUNCHERS - ONLY TIP MISSILES+ MK-84 BOMBS Figure 6 YF-16 Test Configurations 449 NOT SHOWN - SW049-LIH VERT. ACCEL. AS001 U T . ACCEL. AS003 FbAPERON H.M. T035-RUDDER H. M. Figure 7 YF-16 Test Instrumentation Figure 8 Random Decrement Analyzer 450 M 2 30 20 * 10 z x u, I w - 2 0 X I I I I I I I 1400 LITER TANKS .9 1.1 . 1.3 1.5 1.7 .6 . 7 .8 .9 1.0 1.1 30 20 t 0 0 s cc 5 a 10 0 .9 1.1 1.3 1.5 1,7 MACH NUMBER MACH NUMBER 1000 ft =304.8m MACH NUMBER Figure 9 YF-16 Test Points lOOOft 304.8m STABLE .6 . 7 .8 .9 1.0 1.1 1.2 MACH NO. Figure 10 Control System Instability 451 -g = ,124 Figure 11 YF-16 Wing Decay R e c ords - 1.34M, 3048m (10 000 HOR I ZONTAL TA I L 1ST BEND I NG VERTICAL TAIL 1ST BENDING AT001 25 HZ AT002 25 HZ HORIZONTAL TAIL PITCH VERTICAL TAIL 2ND BENDING 1.34M 42 HZ AT003 1.34M 93.0 HZ Figure 1 2 YF-16 T a i l Decay Records - 1.34M, 3048m (10 000 Ft) 452 FIRST WING BENDING-SYMMETRIC MISSILES ON 4.9 HZ . 3 151 1 g .2 - CI, 5 .1 0 . 8 .9 1.0 1.1 1.2 1.3 1.4 d MI S S I LE P ITCH -ANT I SYMMETR I C MISSILES ON 6.4 H7 - .8 .9 1.0 1.1 1.2 1.3 1.4 MACH NUMBER MACH NUMBER FIRST F I N BENDING MISSILES ON 15.2 HZ . 3 c3 .2 f 5 .1 s 0 ul 2 n .a .9 Figure 13 YF-16 1.0 1.1 1.2 1.3 1.4 MACH NUMBER Damping vs Mach Number M=.85 M = .95 M = 1.20 M = 1.34 M = 1.40 ANTI. MISSILE PITCH Figure 14 YF-16 Wing Decay Records 453 VERTICAL TAIL 1S1 .85M g = .111 16.6 HZ .90M g = .133 16.1 Hz .95M g = ,105 16.7 Hz 1.05M g = .136 16.7 Hz . BEND I NG 1.12M 16.9 Hz g = .183 1.20m 17.6 Hz g * .197 1.27M 16.7 Hz g .144 1.34M g = .119 19.1 H, 1.40M g = .173 18.6 HZ Figure 15 YF-16 Vertical Tail Decay Records . 85M 1520111 (5000ft) AW003 AW004 AWN3 + AW004 g = .070 f = 4.7 HZ A W N 3 - AW004 g = . lo5 f = 6.0 Hz F 454 'igure 16 Symmetric and Antisymmetric Response STORE PITCH MODE STORE YAW MODE Figure 1 7 (BEFORE NOTCH FILTER ADDED r TO ROLL CHANNEL) 1 Figure 18 External S tore Damping AW003 AW004 AW003 AW004 t AW003 AW004 - + Effec t of Notch F i l t e r 455 (a1 HORIZONTAL TAIL (b) VERTICAL TAIL Figure 19 T a i l Damping vs A l t i t u d e 456 IKFLIGHT ROTOR STABILITY MONITOR W i l l i a m A. Kuczynski Sikorsky Aircraft Division United Technologies Corporation ABSTRPLCT An inf l igh t rotor s t a b i l i t y monitor which has been developed a t Sikorsky Aircraft t o support s t a b i l i t y t e s t ing o f new rotorcraf t i s described. monitor has as i t s core a damping estimation algorithm which embodies spectral analysis techniques. The interact ive system i s activated and controlled from a Cathode Ray Tube (CRT) and operates on-line i n a f l i gh t t e s t telemetry envi- ronment. Accurate estimates of the leve l of damping of c r i t i c a l system modes are generated within one minute of the completion of a prescribed t e s t maneuver. The s t a b i l i t y monitor has been used successf'ully during the past two years t o support various Sikorsky research and development f l igh t programs including the UTTAS, CH-53E, s-67 Fan-in-Fin, and ABC. The INTRODUCTION One of the more d i f f i cu l t tasks the engineer i s faced with i s the identi- f icat ion and estimation of the l eve l of damping of c r i t i c a l system modes from experimental data. ment where the pressure to make decisions quickly i s high and the consequences of poor judgement may be severe. I n the past , it was not uncommon for an engineer t o be asked t o bless the continued expansion of a test envelope with only time history oscillograph records from previous t e s t conditions upon which t o base h i s judgement. For well-behaved, l i g h t l y damped modes, which a re suffi- c ient ly separated i n frequency from other modes and forced response frequencies, r ea l t i m e f i l t e r i n g improved h i s capabili ty of estimating damping levels . Bowever, the effect ive use of f i l t e r i n g techniques required sinusoidal frequency sweep excitations or suff ic ient pr ior knowledge of the systems' character is t ics t o allow the use of bandpass f i l ters. Sinusoidal sweep excitations are not always pract ical , par t icular ly i n f l i gh t . compatible with system time trends and sweeps rates i n order t o avoid over- estimating damping because of spectrum averaging a t c r i t i c a l frequencies, course, the overriding disadvantage of these techniques is that the engineer w a s s t i l l working with analog records which was very time consuming. most of h i s judgements were necessarily qual i ta t ive. H i s task i s par t icular ly formidable i n the t e s t environ- Also, f i l t e r r i s e times must be O f Thus, With the acquisit ion of the Real-Time Acquisition and Processing of Inf l ight - Data (RAPID) system a t 'Sikorsby7Aircraf-t Tsee Reference 17 i n the early-l970's, the avenue was paved for the development of improved inf l igh t s t a b i l i t y monitoring techniques. and has been used extensively for the past two years. An inf l igh t s t a b i l i t y monitor was developed at Sikorsky i n 1973 It has as i ts core a 457 modal damping estimation algorithm which i s based on well-known spectral analysis techniques. i s transferred t o the frequency domain where modal responses are separated *om each other and from steady state responses. of l igh t ly damped system modes. The advantage of spectral analysis i s tha t a time signal This permits easy ident i f icat ion There i s no one task i n the s t a b i l i t y monitor procedure which w a s partic- u l a r i l y d i f f i c u l t t o develop. forward and eas i ly achieved by standard methods. technique i s now thought t o be ubiquitous i n the industry (see Reference 2) though a description of it is not known t o be published i n the l i t e r a t u r e . The r ea l challenge i n the development of the system was t o make it work i n the f l i gh t t e s t telemetry environment. and accuracy while minimizing t o t a l time required t o estimate system s t a b i l i t y . On the contrary, each s tep i s quite s t ra ight- Even the damping estimation This involved providing adequate f l e x i b i l i t y DESCRIPTION OF INFLIGHT STABILITY MONITOR SYSW The Inf l igh t Rotor S tab i l i t y Monitor is an interact ive system designed t o provide an on-line s t a b i l i t y estimation capabili ty during the envelope expansion of nev rotorcraf t . s ta t ion , RAPID,which consists of a SYSTEMS 86 computer with a f u l l complement of standard and special peripheral devices (see Reference 1). involves two a c t i v i t i e s , the real-time acquisition, conditioning and calibra- t i on of measurements telemetered from an a i r c ra f t and the estimation of l i gh t ly damped modes of the t e s t a r t i c l e from these data. The f irst of these steps is a standard function of the RAPID system. The damping estimates are made with a special purpose program designed t o operate i n telemetry environment during the short in te rva l of t i m e between t e s t conditions. The s t a b i l i t y monitor i s shown schematically i n Figure 1. During a f l i gh t , data are continuously trans- mitted t o RAPID v ia telemetry. example the rotorcraf t i s excited by a control pulse, the engineer-captures a "burst" of data by activating the Telemetry program from the CRT. The en t i re t rack of data (10 measurements) are digi t ized and calibrated (changed from vol ts t o engineering uni t s ) i n rea l t i m e and stored on a disc. The Stab i l i ty Estimation Program is then activated from the CRT. described i n d e t a i l l a t e r , i s highly interact ive and consists of 3 steps: (1) review of the time data, (2 ) ident i f icat ion of c r i t i c a l system modes, and (3) calculation of the damping of these modes. very f a s t with the speed largely dependent upon the user's reaetion time. Plots and printouts of pertinent data a re program options. Upon the completion of the data processing, the user returns control of the system t o the telemetry program for acquisit ion of another data burst . The core of the system is the Sikorsky Aircraft ground The monitor When a s t a b i l i t y t e s t is conducted, say for The program, which w i l l be The program i s very f lex ib le and The a t t r i bu te s which w e r e considered important during the development of the Inf l ight S t ab i l i t y Monitor were speed, f l ex ib i l i t y , and accuracy. The t i m e required t o estimate the damping of the c r i t i c a l system modes was the most i q o r t a n t consideration. Since the program i s an interburst processor, i f the elapsed t i m e r equ i r ed to complete the analysis i s appreciably greater than the 458 t i m e required by the p i l o t t o set up for the next test is increased result ing i n increased r i s k and cos t . On the maximum allowable t i m e f o r the computation c r i t i c a l mode. and depends l a rge ly upon the t i m e share demands o f the computer from t h e other sources when the On-line S t a b i l i t y Monitor is i n use. One minute elapsed t i m e is generally achievable regardless of the demands on the computer. n t , t o t a l test t i m e nute was targeted as a dmping estimate of a s i Minimum elapsed time ac tua l ly achieved i s approximately 30 seconds Since the times associated w i t h computer calculations and data transfer are measured i n micro- and milli-seconds and human response t i m e s are measured i n seconds and minutes, e f f o r t was focused on speeding up the t i m e required t o make decisions by the mers. which allowed the achievement of a one minute elapsed t i m e for a damping esti- mate i s the l ightpen on the CRT. The most important feature of t h e RAPID System .~ ~- Nearly a l l t h e decisions which have t o be made in te rac t ive ly are done so Options are preprogrammed and the user simply s e l e c t s t he with the l ightpen. options which fulfi l ls h i s requirements with t h e l ightpen. i n the options i s preprogrammed t o handle most s i tua t ions . i s much f a s t e r than decidiqg wha t a value should be. computer w i t h the lightpen i s faster than ac t iva t ion through a keyboard input. Suff ic ient l a t i t u d e Selecting an option Also ac t iva t ing t h e F lex ib i l i t y was a l so considered important during t h e development o f t he program. The a b i l i t y t o se l ec t from a number of d i f fe ren t measurements and t o choose a a rb i t r a ry sect ion o f t h e t i m e data from the t o t a l record were require- ments. It was reasoned t h a t one would not always know, ap r io r i , the measure- ment which responds the most i n a mode so the a b i l i t y t o choose in te rac t ive ly w a s desirable. factors which were considered. Also de f in i t i on of mode shape and sensor r e l i a b i l i t y w e r e The accuracy of t h e frequency and damping estimates were of course, of great importance. ac tua l algorithm developed t o ca lcu la te modal damping. Desired accuracy was achieved by specif ic features i n the DESCRIPTION OF STABILITY ESTIMATION PROGRAM The s t a b i l i t y estimation program involves three basic tasks : Selection of time data for analysis Ident i f ica t ion of l i g h t l y damped modes Calculation of damping Each task has a CRT display associated with it and options which are exer- cised in te rac t ive ly t o accomplish t h e task. by discussing each CRT display. application. This control impulse generates a t rans ien t response of t h e ro to r and airframe. The program can be best described The displays are from a typ ica l ro to rc ra f t The ro to r i s exci ted i n f l i g h t with a longi tudinal s t i c k pulse. 459 The first CRT display, Figure 2, is used t o scan the t i m e data and select an appropriate section of a measurement f o r further processing, i s comprised of plot ted t i m e h is tor ies , a column of options t o f a c i l i t a t e selection o f specif ic data for further processing and pr in t and plot options. Time h is tor ies of four parameters are displayed at a time. The program is s ized t o accomodate up t o twenty signals with the NEW CURVES c - option, the vehicle by which different s e t s of curves a re brought t o the screen. section of t he burst of data which i s displayed can be changed with the PAGE option, + t o move forward i n t i m e and - t o move backward. The length of the section of data displayed is arbi t rary (within l i m i t s ) and prescri input data. The frequencies i n the data and the sample r a t e are considerations i n s iz ing these i n i t i a l t i m e h is tory displays. Generally, these t i m e history curves are only used t o f ind the t ransient response which is necessary for the damping calculation, so good signature is not required. user prescribes the time at which he wants t o start the analysis by keying i n a value TO. The s t a r t time i s usually when the system transient response t o the excitation i s a maximum. The length of the data sample which i s processed i s prescribed %y the number of points (2N, N i s an integer) ani the SAMPLE RATE FOR ANALYSIS options. t o t a l length of the data sample is : The display The The For the example shown TO = 2.65 sec i s selected. The T = (SAMPLE RATE)(2’)(At) where A t i s the digi t iz ing rate. The length of data determines the fundamental frequency w = 1/T Hz and t h e achievable resolution i n the spectral analysis f which i s performed Lext. 2’ data points are used because the FFT algorithm used for the spectral analysis i s cornputationally most e f f ic ien t with t h i s constraint . The highest frequency i n the spectral analysis i s and must be selected t o prevent a l ias ing of the data. must be kept conveniently higher than the preprocessing f i l t e r bandwidth. I n tha t respect, wmax The measurement which i s t o be analyzed is selected with the CHOOSE CURVE option. by prescribing a posit ive center frequency i n the FILTER option. roll off and bandwidth are prescribed i n the input data. i s not needed for accurate damping estimates except for those s i tuat ions where the t ransient response signal t o noise r a t i o i s very poor. A zero phase shaft d i g i t a l band-pass f i l t e r can be applied t o the data The f i l t e r I n general, the f i l t e r It i s worthwhile t o note tha t default values for a l l options are specified i n the program imput. i s t i c s , his only actions are t o select a start time (TO) and lightpen the CONTINUE Thus, if the user i s familiar with h i s system’s character- option t o proceed t o the next s tep i n the analysis. The ident i f icat ion of l i g h t l y damped modes is performed i n the frequency domain. Transform of the time data sample selected. normalized t o yield Fourier coefficients and plotted versus frequency i n the second CRT display (Figure 3 ) . 460 A Fast Fourier Transform i s used t o calculate the discrete Fourier The magnitude of the transform is A simple search routine is bu i l t i n to the program t o select peaks i n the spectrum within a predetermined frequency range (input) e the r ight of the plot . These frequencies a re ordered by t h e i r magnitude and displayed a t For rotary wing applications, the system norma rotat ional frequency (forced response of the rotor frequencies i f properly excited.* Prior knowledge of the system being t e s t ed makes ident i f icat ion of forced responses t r i v i a l and thus permits the easy recognition of s ignif icant t ransient modal responses. pen) the frequency of the mode for which he wants a PICK F5BQWCY option. He then can proceed t o the exercising the CONTINUE option. Fourier Transform plot that a significant t ransient modal response i s not present i n the s ignal , he may return to display 1 b y act ivat ing the FUITURN t o A option. Records of the spectral data may be obtained with the PLOT & PRINT opt ions. The user selects ( l ight- ing estimate with the g estimation task by Should it be obvious t o the user from the It i s worthwhile t o note at t h i s juncture the value of the Fourier Trans- form i t s e l f i n dynamic testing. engineers task i s t o monitor for a t ransient modal response caused by random excitations during t e s t envelope expansion. excellent tool for detecting such responses, resonance peaks i n the Fourier Transform can also be used d i rec t ly t o estimate modal damping if the system modes a r e suff ic ient ly separated i n frequency so tha t a single degree of freedom i s approximated. There a re many s i tuat ions when the tes t The Fourier Transform i s an Of course, the shape of t he I n the example shown i n Figure 3, there a re two modal responses, one a t The former is primarily a SAS/flapping mode 7.0 Hz and the other at 6.0 Hz. and the l a t t e r a blade edgewise mode. forced responses a t one and two per rotor rev. The peaks at 4.9 HZ and 9.8 Hz are Before continuing t o the description of t he t h i r d CRT display it is timely Knowledge of the technique t o discuss the actual damping estimation procedure. i s a prerequisite t o a meaning= discussion of the data on the th i rd display. Damping Estimation Procedure Assume that there exis ts a time history of a signal which contains the t ransient response of one or more natural modes of a system. tha t the system is approximately l inear . The damping of a mode (as defined by i t s frequency wo ) , can be estimated as follows. data sample which comprises an integer number of cycles of the frequency of in te res t i s first selected. The discrete +Fourier coefficient F(wo) of t h i s data sample i s then calculated. of data which a re successively displaced i n time generates the function F(wo) Assume fur ther A percentage of t he t o t a l .- Repeating this computation for similar blocks * An exception i s when the system s t ab i l i t y i s governed by periodic coefficients i n which case the modal frequencies can be a t integer multiples of 1/2 t he rotor frequency . 461 versus t i m e , curve kn F(w0) vs time divided by the frequency woe An estimate of the damping ( 5 ) of the mode is the slape of the I f one accepts less than rigorous mathematics, the appropriateness of t h i s procedure can be i l l u s t r a t ed . Consider the d,aaped sinusoidal function - 5wot f ( t ) = A e wet+$) The Fourier s ine and cosine coefficients f o r N cycles of data s t a r t i ng at an arbi t rary t i m e t are defined as 0 0 Expanding these integrals and manipulating intensively, w e arrive at two relat ively simple expressions f o r a, and b, : Ae -( 1-e 2nN These can be combined -gw t 0 0 to compute the magnitude of the Fourier coefficient 1 ain( 2woto+24 I 15 r(r2+4) + Rearranging, we see tha t c i.e., has the same form as the or iginal function f(t); 1 -gw t c1 = Ke 0 0 sinC2woto+6) 462 e K i s a constant and @ a phase angle which i s of no concern, Thus, t h e envelope o f decay of the Fourier coeff ic ient C1 is exactly the same as t h a t of f ( t ) e and the l inears lopediv ided by t h e modal frequency t o obtain an estimation of f. I n the s t a b i l i t y estimation program, t h e curve I n C1 vs t i s developed 0 Inaccuracies i n the Dmnping E s t i m a t e The major problem which is encountered i n the damping estimation procedure arises because a t y p i c a l t i m e h i s to ry response is composed of responses at several frequencies. Since f i n i t e length data samples a re processed, frequency in te rac t ion occurs when the Fourier coeff ic ients are calculated. The in te rac t ion is commonly cal led leakage and can be i l l u s t r a t e d qui te eas i ly . I f you calcu- la te the Fourier transform of a simple s ine function f ( t ) = s i n w t f o r a data sample of f i n i t e length , it w i l l have the following form: 0 463 The maximum value of w i l l be zero when If a signal contains the transform w i l l occur when w = wo and the sidelobes nn w - w = - ( n = 1, 2, 3, ... > o T two or more f’requencies, the Fourier Transform i s the summation of the transforms at each frequency. two sine waves having frequencies wo and w For example, the transforms of are sketched below, 1 - F(wo) F(w1) /n ,it.? \ / I \ ‘ I ‘ / I \ / I \ w 0 w It can be seen that when summed, the sidelobs from one transform w i l l a f fect the transform at the other frequency. occurs when the damping of a mode i s computed when other frequencies present i n the .time history. For many cases, the leakage has minimal effect ; the frequencies are well separated, the magnitude of the response at the frequency of in te res t i s la rge compared t o other responses or the data sample i s of suff ic ient length t o minimize the magnitudes of the sidelobes. D i f f i - cu l t ies a r i s e when two or more f’requencies a re very close t o each other or the magnitude of t h e modal response i s s m a l l compared t o other system responses. For the case of two frequencies which a re close, the length of the data system can be adjusted so that the sidelobe from one frequency i s zero a t the other frequency, v i z , This i s exactly the phenomenon that are 464 For t h i s example, the Fourier analysis a t wo i s unaffected by the response at w For three or more frequencies which a re close, the length of the data sample required t o achieve similar decoupling m a y be impractical. For these cases, p ref i l te r ing of the data with low, high or bandpass d i g i t a l f i l ters may be required. estimates may ha,ve t o be corrected accordingly. the data through a t i m e window such as a Hanning window as a par t of the damping estimation procedure. The e f fec t of the window i s t o increase the r a t e of roll- off of the sidelobes at the expense of broadkng the main lobe. and vice versa. 1 Since f i l t e r s have associated rise times, the damping Another technique i s t o pass Though alJ of these treatments of the data a re possible, our experience has shown the sat isfactory resu l t s a re almost always achieved u t i l i z ing only the simple adjustment of smple length t o decouple the frequency of i n t e re s t from i ts major competing frequency, With a general knowledge of the procedure used t o estimate the damping of a mode, we are i n a position t o discuss the steps leading t o the actual calculation. After a frequency has been selected fromthe second CRT display, an i n i t i a l percentage [program input data) of the time s ignal i s selected t o form the data sample for the damping calculation. The frequency of the mode i s then corrected. This is necessary because the FFT produces only 2 spectral l ines and the actual frequency of the mode can be expected t o be between two l ines . mizing the magnitude of the Fourier coefficient as a function of frequency i n the v ic in i ty of the transform frequency. by adjusting the length of the data sample by one point at a time. curve of amplitude versus frequency is developed; i . e . , N-1 The adjustment of the frequency is accomplished by m a x i - V e r y f i ne frequency changes are made Thus, a Amp1 of Fourier Coeff. Hz Freq. from FFT correct mo dal frequency w 465 and the corrected modal frequency determined, applied t o the frequency of the largest response in the signal within the designated frequency range and the sample length further adjusted t o minimize the interaction of the two This same procedure i s then After these preparations a re complete, the damping of the mode i s calcu- lated. The f i n a l CRT display (Figures $ & 5 ) presents the estimated modal damping and data with which t o Judge i ts accuracy. Two figures are shown, one for each of the modes ident i f ied f’rom the Fourier Transform. The display consists of a time history plot of the t i m e data and a p lo t of the natural log of the Fourier coefficient versus time. t ha t the LOG, (FC) of a fixed percentage of the t o t a l data sample which moves with t h e . examples shown approximately 7% of the record length formed the data sample which moved from t = 2.65 t o t = 3.19, or 0.54 seconds. Backtracking momentarily, it i s recalled curve is developed by performing repetative Fourier analyses For the AS discussed ea r l i e r , the l inear slope of the LOG, (F.C.) vs time curve A s a general ru le , the divided by t h e modal frequency i s the modal damping. more l inear t h i s c m e , the be t t e r the damping estimate. columi of the displ8y a re printed the corrected modal frequency, the modal damping irm decimal form and the standard deviation of the l ea s t squares Pinear curve f i t through the Fourier analysis curve. The deviation is used as a measure of the accuracy of t he damping estimate. There a re occasions when it is obvious from the Fourier coefficient plot that the en t i r e cume should not have been used fo r the damping estimate. Typical examples are s t a r t i ng the analysis before the t ransient response has b u i l t up t o i t s maximum value or continuing the analysis beyond a time when the signal t o noise r a t i o i s accept- able. beginning (TO) and end (T1) of the Fourier coefficient curve for t he damping estimate. deviation a re automatically updated. I n the right-hand For such conditions, the EDIT feature can be-used t o prescribe the When e i ther TO and/or T 1 are changed, the damping and standard Several options are available t o the user a f t e r he has completed h is review of the damping estimate. provide hard copy of pertinent .data. The user may return t o the Fourier Trans- form display (CHOOSE NEW W ) t o select another frequency for a damping estimate, o r he may re turn t o display 1 (CHOOSE NEW CURVES) t o process another measure- ment or he aay return t o the telemetry program (RETURN TO T/M) t o record another burst of data. There are the standard plot and pr int options which _~ - CONCLUDING REMARKS During the past two years, the applications of the Inf l ight S t ab i l i t y The first on-line application w a s the Monitor at Sikorsky have been many. expansion of the CH-53E t a i l rotor s t a b i l i t y envelope on a whirl stand. The estimated saving i n t e s t t i m e on that program was 80% over the then accepted s t a b i l i t y tes t techniques. Since tha t beginning, the system has been used t o support the s-67 Blackhawk Fan-inLFin, the UTTAS, the CH-53E, and ABC f l i gh t test programs. Confidence i n the technique has grown and the system i s fast becoming a standard tool fo r s t a b i l i t y t e s t ing during a i r c ra f t development. 466 The s t a b i l i t y estimation program has a lso received extensive use as an off-line diagnostic and data processing too l . RAPID i n exactly the same way as it is on-line, with t source of t i m e dat an analog tape ra ther than telemetry. Off-line applic ons are typical ly modal cdamping calculations, mode shape def ini t ion and harmonic and spec t ra l analyses. his tory data from analyt ical ro tor simulation programs. at Sikorsky, a UNIVAC U O computer version of the program i s available which is coupled with the simulation program. The t o t a l system i s also a natural application f o r wind tunnel tests, especially i f the f a c i l i t y has a dedicated d ig i t a3 computer. It i s operated off-l ine i n The program also receives extensive use as a post.processor of time For these a@plications RFFERENCES 1. RAPID--A Data Acquisition and Processing System fo r Fl ight Test Cost and Schedule Improvement, Victor G . Berecz, Presented at the 30th Annual National Forum of the American Helicopter Society, Washington, D . C . , May, 1974. 2. Integrated Rotor/Body Loads Prediction, R . M. Carlson, A. W. Kerr, Presented at the AGARD Specialists.Meeting on Helicopter Rotor Loads and Prediction Methods, Milan , I t a l y , March 30-31 , 1973. 467 FILTER f I 1 \ I I ----- - I_ -- -- PROGRAM (CRT) " DATA BU R ST " FI DIGITIZE CALIBRATE DATA * DIGITAL DATA FILE " DISC" , - - - S T A B I L I T Y ESTIMATION PROGRAM- - - - TIME ~ HISTORIES REVIEWTIME DATA (CRT) I I $. Figure 1 I n f l i g h t Rotor S t a b i l i t y Monitor Flow Chart. 468 RUN 20 55w I 1 w a 4 SBBB QI EB1 - dm0 8.8 1 .E 2.8 3.8 4.8 5.8 TIME "QRFIMETER SELECTION CHODSE CUR& 1 2 3 4 I CHDoSE N FOR 2ailN POtNTS 6 7 8 9 % CHOOSE' TO 0.0H SM4PLE RATE f O R PfWLhY$lS 4 ~a USE FILTER CENTER FREQ -1.50 OPT IONS R O T PRINT ON NEW CURVES + - CONTINUE PAGE + - Figure 2 CRT D i s p l a y 1, Time H i s t o r y D a t a . 469 RUN 20 sua- 4.58- 4.88. 3.w- MRUEB 1 T 1 = 2.65 p I L K ;RtO -CPS U t 7 .0 U h 6.8 U 8 * 4.9 u c 8.8 u 5 8.1 FREOXWY 1.m TO ?E.m OPTIONS PL- 7 PRINT OFF CONTINUE ETURN 1 0 FI F-igme 3 CRT Display 2 , Magnitude of Fourier Transform. (1 cps = 1 Hz.) 470 R U N 2 0 MRUEBl T 1 = 2.65 “7B LOG 7. 58 - 8 . W B.?? 8.38 8.W 8.58 8.68 8.78 0.W 8.W 1.m T I N 7.48 L-. . 4999.99’ F < T ) B.6533. -4999.99 L-----.-P----,- . * 3.m 3.58 4 . a 4.98 5.88 5.58 6.88 6.58 7.83 7.98 TI* Figure 4 CRT Display 3. Modal Damping E s t i m a t e , w = E D I T m P.B T I 8.56 FREC! -CPS 7. Be DAMPING 8.812 DEUIQTION 8. 8849 OPT IONS PL9T PRINT OFF CHOOSE NEW W CHOOSE NEW CURVES RETURN TO T I M ‘ .02 Hz. 471 RUN 20 MRUEBl 1 1 = 2.65 4999.99 F < T > 8.88. 145Y9.98- I 9999.98 -4999.99 I - . ..I 3.88 3.58 4.m 4.W 5.6% 5.58 6.88 6.58 7-88 7.58 TItE E D I T TO 8.BB T l 8.56 -REO -CPS 6.53 DFIMP I NG 8.834 DEUIHTION 8.9214 OPT IONS R 9 T PRINT OFF CHUOSF NEW W CHOOSE NEW CURUES RETURN ra T/M Figme 5 Modal Damping Estimate, w = 6.09 Hz. 472 OF AEROEUSTIC STABILITY PHENO~NA OF A HELICOPTER BY IN-FLIGHT SHAKE TEST Wen-Liu Hiao, We Thomas Edwards, and David E. Brandt Boeing Vertol Company ABSTRACT The aeroelastically stable Boeing yuH~6l.A helicopter was developed through The analytical capability of the a systematic program of configuration analysis and model testing which has resulted in a successful flight test program, helicopter stability program, C-56, is discussed. The parameters which are found to be critical to the air resonance characteristics of the soft in-plane hingeless rotor systems are detailed. A summary of two model test programs, a 1/13.8 Froude-scaled BO-105 model and a 1.67 meter (5.5 foot) diameter Froude-scaled YUH-6lA model, are presented. Emphasis is placed on the selection of the final parameters which were incorpo- rated in the full scale YUH-61A helicopter, and model test data for this configuration are shown, The actual test results of the YUHc61A air resonance in-flight shake test stability are then presented. This includes a concise description of the test setup, which employs the Grumman Automated Telemetry System (ATS), the test technique for recording in-flight stability, and the test procedure used to demonstrate favorable stability characteristics with no in-plane damping augmen- tation (lag damper removed), resonance with forward speed and the stability trend of ground resonance for percent airborne are presented, The data illustrating the stability trend of air INTRODUCTION The successful development of a helicopter with a soft in-plane hingeless rotor system requires that certain potential aeroelastic stability problems be examined, in particular the air and ground resonance phenomena, ground resonance are coupled rotorlairframe instabilities which may occur when the natural aircraft body pitch or roll frequency, involving hub motion, is equal to or close to the difference between rotor speed and the in-plane natural frequency, However, with the proper choice of certain critical rotor parameters, such as, blade precone, pitch-flap coupling, pitch-lag coupling, control system stiffness, and blade in-plane natural frequency, the stability of the coupled rotor/airframe can be controlled. strated with the Boeing Messerschmitt-Boelkow-Blohm BO-105 helicopter, Both air and This has already been demon- 473 For the development of the Boeing ertol YW-6fA approach was made to the aeroelastic d the optimization of the critical parameters, ign of the alrcra The approach entails Computer analysis of stability characteristics Preliminary model testing, to correlate analysis and determine the most influential stability parameters Detailed model testing of the proposed configuration Flight envelope expansion of the full scale helicopter by deter- mining degree of stability through in-flight shake test The YUH-6I.A stability testing was performed at the Grumman Aerospace Corporation facility at Calverton, Long Island, To expedite this work and to promote minimum risk, the Grumman Automated Telemetry System (ATS) was used to provide on-line real-time analysis of the data, Many of the model test data were presented in previous papers, For the sake of completeness, portions of those works are summarized herein, The authors express their appreciation to W, F, White and C, E, Hammond of the U, S, Army Air Mobility Research and Development Laboratory at Langley for their help with processing and verifying the WH-61A flight test data with the moving block/Randomdec computer program, ANALYSIS A method for determining the ground resonance characteristics of a heli- copter with an articulated rotor (Reference 1) has existed for over thirty years. generated by blade cyclic in-plane motions with a single effective hub mass restrained to move in two translational directions without aerodynamic effects, This translating, effective hub mass attempted to represent a modal combination of hub and airframe translations and pitching and rolling motions, pitching and rolling motions are of little consequence in the analysis of a rotor with small flap hinge offsets. However, if there is a sizeable effective flap hinge offset, as in the case of a hingeless rotor system, these motions produce large aerodynamic flapping moments which can damp the ground resonance or related air resonance modes (Reference 2) . Therefore, the pitching and rolling motion as well as the aerodynamic consideration become indispensable for the hingeless rotor system, more exact representation, Analyses of this type considered only the resonance of the forces These The C-56 program was developed to provide this 474 Analytical Capability (C-56 Program) The C-56 analysis retains the degrees of freedom of the helicopter rotor and airframe which influence the air and ground resonance characteristics, This relatively simple but adequate analytical representation includes these pertinent freedoms: Three rigid-body fuselage translations Two rigid-body fuselage rotations (pitch and roll) Four mast or pylon motions (lateral and longitudinal translations, pitch, and roll) defined at the softest pylon-to-fuselage junction Two tail boom flexibilities Nine rotor freedoms (one collective and two cyclic modes for blade pitching, flapping, and in-plane motions) (excludes reactionless modes) A drawing of the 20 degrees of freedom is shown in Figure 1. The equations of motion for this entire multidimensional system are derived from Lagrange's equations. presented in Reference 3, A brief discussion of this derivation was This representation permits the investigation of a wide range of param- eters affecting rotorlairframe stability, In addition to making it possible to study the effects of basic characteristics, such as rotor speed, rotor thrust, aircraft gross weight, forward speed (in an extended version of the program), and Lock number, the representation makes it possible to examine the following parameters: precone, control system stiffness, lag frequency, and pitch-lag and pitch-flap coupling terms, be investigated, these in particular have a strong influence on stability. Although other parameters may also Parameter Sensitivity The mechanism of the air and ground resonance of the hingeless rotor helicopter and its attendant source of damping were discussed elsewhere, e,g,, Reference 2. It suffices to say that since the prime source of damping in the air and ground resonance mode is the blade flap response, any parameter which affects the coupled blade feather, flap, and lag motions has the potential for stabilizing or destabilizing the mode, A sensitivity study revealed that the favorable couplings were nose-up pitch and upward flap, both of which caused blade lag, and upward flap, which caused nose-down pitch, and blade design which result in these three types of coupling in a soft in- plane rotor system will beneficially affect the air resonance stability, us now examine some of the most common design parameters, Any hub geometry Let 475 Precone, Precone he re means t h e precone of t h e b lade fea ther ing ax is . Figure 2 shows t h e precone e f f e c t on t h e YUH-61A air r As t h e blade f e a a x i s precones up towards t h e equilibrium modal damping de a e mo As discussed i n Reference 2 , with t h e blade f ea the r ing bearing inboard of t h e blade f l exure , precone of t h e b lade fea ther ing axis d i r e c t l y con t ro l s t h e magnitude of t h e f lap-p i tch coupling caused by Cor io l i s fo rce , The per turba t ion Cor io l i s f o r c e due t o f lapping up ve loc i ty acts toward t h e leading edge of t h e blade. With t h e blade equilibrium pos i t i on above t h e fea ther ing axis producing a moment a r m , t he re r e s u l t s a nose-down per turba t ion p i tch ing moment, which is favorable. Figure 3 shows schematic y t h e reduction of t h e moment arm wi th increas ing precone; hence t h e reduction of t h e favorable f l ap - p i t c h coupling. Control system f l e x i b i l i t y , Figure 4 shows t h e e f f e c t of t h e con t ro l system f l e x i b i l i t y on t h e a i r resonance mode s t a b i l i t y of t h e YUH-GlA, ing t h e s t i f f con t ro l system t o the nominal con t ro l system, w e see t h a t t h e former degrades t h e s t a b i l i t y f o r c o l l e c t i v e p i t c h from 25 t o 240 percent of hover l g c o l l e c t i v e (8NOR) and enhances t h e s t a b i l i t y from then on up, Compar- Since t h e s t a b i l i t y is influenced by t h e blade flap-pitch and pitch-lag coupling, i t s dependence on t h e con t ro l system f l e x i b i l i t y i s expected, A s discussed i n Reference 2 , t h e r e e x i s t s favorable f lap-p i tch coupling f o r t h e low c o l l e c t i v e p i t c h region, i n t h i s case from 25 t o 200 percent 8NORI and unfavorable coupling a t high c o l l e c t i v e p i t c h , i n t h i s case from 200 percent on up. The s t i f f con t ro l system minimizes t h e coupling e f f e c t and therefore produces t h e trend shown i n Figure 4. The choice of t h e con t ro l system s t i f f - ness the re fo re depends on t h e p r a c t i c a l opera t iona l c o l l e c t i v e p i t c h range f o r which t h e r o t o r i s designed, Lag frequency, There are several f a c t o r s which have a primary influence on t h e a i r and ground resonance c h a r a c t e r i s t i c s of t h e he l i cop te r , t hese is t h e placement of t h e l a g frequency with r e spec t t o t h e coupled air- frame pitch-dominant and roll-dominant modes. a i r c r a f t wi th a gross weight of about 2045 kg (4500 pounds) i n Reference 4 . One of This has been discussed f o r an As s t a t e d i n t h a t re ference , t h e r e are two p o t e n t i a l resonance po in t s which are, i n general, de t r imenta l t o a i r c r a f t a i r resonance c h a r a c t e r i s t i c s . These poin ts , shown i n F igure 5 , should b e avoided f o r a l l f l i g h t conditions of t h e p a r t i c u l a r ’ a i r c r a f t , However, t h e r e are two poss ib l e s t a b l e regions of r o t o r opera t ion which are ava i l ab le f o r a given he l i cop te r design, Both of these reg ions now have been shown t o provide s a t i s f a c t o r y s t a b i l i t y margins, wi th t h e Boeing YUH-61A designed f o r reg ion 1 and t h e MBB BO-105 designed f o r region 2 , . The choice of t h e optimum operating region f o r t hese he l i cop te r s indi- r e c t l y r e s u l t s from t h e a i r c r a f t mission, system, a i r c r a f t gross weight, and p i t c h and r o l l i n e r t i a s , The r o l l pre- dominant and pitch-predominant modes are s t rongly coupled with t h e r o t o r The mission p r o f i l e sizes t h e r o t o r 476 cyclic flapping, which provides the stiffness for those directions in flight. Therefore, with the aircraft pitch- above considerations, the in-plane b quency and Q-wy, is then sen to meet r the rotor speed in the center of one of the operating regions. WH-61A Analytical Results For the final YUH-6lA configuration, the various beneficial parameters are combined to produce a stable configuration, A summary of the key rotor and fuselage parameters is shown in Table 1, Table 1 Summary of YUH-61A.Parameters Parameter In-plane Frequency (us) Pitch-Flap Coupling (63) Precone Droop Blade Torsion Frequency (we) Rigid Airframe Roll Frequency Rigid Airframe Pitch Frequency In-plane Damping Augmentation Landing Gear Damping Augmentation Value I 0.70 per NR (Normal Rotor Speed) -22.5' (Flap Up-Pitch Nose Down) 0' / 3.25' Up I 3.76 per NR 0,366 per NR 0,095 pyr NR 0% (Idplane Structural Damping 0%, / 1.0%) / These parameters were modeled for the C-56 program, and air resonance and ground resonance characteristics were determined, A plot of the predicted air resonance stability as a function of thrust and rotor speed is shown in Figure 6. Q-wy with the pitch-dominant mode, and the high RPM boundary corresponds to the resonance of the 62-wy mode and the roll-predominant mode, in stability at high thrust (or collective pitch) levels is due to detrimental flap-pitch coupling in this region, as explained in Reference 2. The low RPM boundary in this plot corresponds to the resonance of The reduction 477 The r e s u l t s of t he ground resonance ana lys i s as a function of percent airborne is shown i n Figure 7. Y S ing f o r t h r e e d i f f e r e n t r o t o r speeds ranging from t va lue (Nmin) t o t h e maximum design l i m i t speed ( N D L ) ~ t h e range explored later on t h e f i r s t test vehicle. MODEL TESTS The model tests performed i n conjunction with t h e development of an a e r o e l a s t i c a l l y s t a b l e WH-61A configuration were conducted i n two p a r t s . 1/13,8 Froude-scaled BO-105 model 1.67 m e t e r (5.5 foo t ) diadieter Froude-scaled YUH-61A model Froude-Scaled BO-105 Model This 1/13.8 Froude-scaled BO-105 model (Reference 2) w a s developed t o provide a d i r e c t means of va l ida t ing t h e a n a l y t i c a l methods de t a i l ed above and t o demonstrate t he power of t he several r o t o r parameters t o influence a i r c r a f t air resonance c h a r a c t e r i s t i c s . The model has t h e same blade f i r s t f l a p , l ag , and to r s ion frequencies as f u l l scale, wi th provisions t o vary hub precone, b lade sweep, and blade l a g damping t o observe t h e i r effects on r o t o r s t a b i l i t y , The model parameters are summarized i n t h e following t ab le . Table 2 1/13.8 Scale BO-105 Model Parameters Parameter Rotor Diameter Chord Gross Weight Precone og/Q W z u I & 3 ' Q 111 -1 2 a n 0 1 0 x 1 LATERAL Coupled Rotor-Fuselage Analytical Model (2-56. Figure 2 . Effect of Precone on A i r Resonance S tab i l i ty . 486 LARGE MOMENT ARM WITH ZERO PRECONE FOR LARGE FAVORAS LE COUPLING SMALLER MOMENT ARM WITH P O S I T I V E PRECONE REDUCES FAVORABLE COUPLING Figure 3 . Effect of Precone i n Reducing Favorable Flap-Pitch Coupling. I PERCENT COLLECTIVE P I T C H HOVER 1G COLLECTIVE Figure 4 . Effect of Control System Flexibi l i ty , 487 PGSS I BLE GPERGTI iJG LEG I Git! I / F.OTGP SPEED Figure 5. Potential A i r Resonance Points and Operating Regions, 488 500 400 300 200 LOO 0 -1oc IN-PLAME DAMPING = 1% FLAP-PITCH COUPLING = 22,5" DES I G!l GROSS WE1 GtIT 1 l a I . 1 I I I I 110 120 130 J - i o ' 80 90 LOO Figure 6. YUH-63.A Air Resonance Characteristics, 489 20 DESIGN GROSS WEIGHT NORMAL LANDING GEAR NO LAG DAMPER -1 0 I- LT 0 Be a c. N R CI I NMI N c3 10 z a E Y NDL a n a n -1 0 E 1 1 20 40 6 0 80 100 % AIRBORNE Figure 7. YUH-61A Ground Resonance Characteristics, 490 3 -5 A I R C R A F T ROLL MiQnEh A I R C R A F T PITCH MOT)E 60 80 100 120 Figure 8 , 1/13,8 Scaled BO-105 Model-Modal Frequencies and Damping, 491 INPLANE DAMPING = 0 . 8 5 % CRIT ICAL PRECONE = 2 . 5 O 20or 160- 120- 80- 40- 3 -I 4 0 I- @z - 2 O 1 u o CI I z I a L1 6 0 z 5 -1 LOW COLLECT1 VE J UNSTABLE REG1 ON a - 2 - 3 0 50 100 150 200 COI I ECTIVF PITCH HOVER 1G COLLECTIVE PITCH - PERCENT c- Figure 9 . Thrust Effect on Stability, +? I PRECONE = 2 . 5 DEGREES IN-PLANE DAMPING = 0 . 8 5 PERCENT CRIT ICAL I I '\.ho,,. TEST ANALY S IS I 1 I I 1 60 80 100 120 ROTOR SPEED - % NR Figure 10. Stability Map of 1113.8 Scaled BO-105 Model, 492 - PERCENT NORMAL ROTOR SPEED Figure 11. 1.67 Meter Diameter YUH--61A Model-Modal Frequencies, 0 STABLE d MARGINAL 0 UNSTABLE I u k CI a W > I- u W -1 -I 0 u CI I- z W 0 E W CL f W > I- u W -I -I 0 u a E w > 0 I Y %-l 2oc l o ( ( - 101 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 I I I I I I I I 6 0 80 100 120 140 ROTOR SPEED NORMAL ROTOR SPEED PERCENT Figure 12. M ~ D of Stability Test Points. 493 2 . a 0 2. 4 U I- : 2. s 1. z 1. a a * a n ' 0 a E U -I 0 E S C A L E D UP TO Q - W c FREQUENCY FROM S E N D 1 N G 4 0 20 41) 6 0 80 1 0 0 12r) I N D I C A T E D AIRSPEED - % VH Figure 13, S t a b i l i t y i n Forward F l i g h t , 494 I w 0 495 496 I COMPUTER OPERATIONS DEMODULATION D/A CONVE RS I ON (P CM) ENGINEERING-UNIT CONVERSION L IMIT CHECKS AN ALY S IS /PLOTS ‘TABS DIGITIZE (FM) STANDARD HEADING FREE FORMAT OUT OF LIMITS PLOTS AND TABS FROM: REAL TIME PLOT F ILE RECALL FILE C RT DIGITAL i\ RECALL STRIP CHARTS FILE J 1 Figure 16. Schematic of Real-Time Data System, 497 Ffgure 3.7, Typical Time History o f YU%-61A* 498 9 7 % NR DES I GN 25 20 15 10 5 - 6 0 - 4 0 - 20 10 0 Figure 18. PERCENT AIRBORNE YUH-61A Ground Resonance Test Data, 9'7% NR DESIGN GROSS WEIGHT LEVEL FLIGHT 0,A TEST DATA LANGLEY DATA ANALYSIS 0 20 40 60 80 100 120 INDICATED AIR SPEED % % VH Figure 19. YUH-61A A i r Resonance Test Data. 499 FLIGHT FLUTTER TESTING OF ROTARY WING AIRCRAFT USING A CONTROL SYSTEM OSCILLATION TECHNIQUE Jing G. Yen, Sathy Viswanathan, and Carl G. Matthys Bell Helicopter Company SUMMARY This paper describes a flight flutter testing technique in which the rotor controls are oscillated by series actuators to excite the rotor and air- frame modes of interest, which are then allowed to decay. The moving block technique (see ref. 1) is then used to determine the damped frequency and damping variation with rotor speed. The method has proved useful for tracking the stability of relatively well damped modes. pleted flight tests of an experimental soft-in-plane rotor are used to illus- trate the technique. This technique will also be used for flight flutter tests of the NASA/Army XV-15 Tilt Rotor Research Aircraft, to investigate its propeller whirl flutter stability characteristics, and this application is also discussed briefly . The results of recently com- INTRODUCTION A soft-in-plane rotor has recently been built and flight tested by Bell Helicopter Company. This type of rotor system has the potential for ground and air resonance instability. The potential mode of instability, the lead-lag motion of the blades coupled with the fuselage rigid body roll mode, has a fre- quency of 0.75 per rev (3.55 Hz) in the rotating system. to be well damped, since sufficient elastomeric lead-lag damping was employed. However, since it was the first rotor of this type developed by Bell Helicopter Company, an extensive ground/air resonance test program was conducted to inves- tigate the ground/air resonance phenomena. The mode was predicted The measurement of the stability characteristics of rotary wing aircraft is complicated by the need to excite modes in a rotating system and by the fact that both the rotor and the airframe are subject to steady state harmonic load- ing. damped mode. helicopters or tilt-rotor aircraft hence becomes a formidable task, both to cause the proper excitation and to reduce the data. A flight flutter testing technique has been developed, as described in this paper, to oscillate the rotor controls by means of the series actuators in a sense and a magnitude prescribed by the user. This loading tends to mask the transient response of any relatively well The'development of an on-line flight flutter testing technique for The authors acknowledge the assistance of Ken Builta of Electronics Development in the design of the rotor excitation system, and Al 'Eubanks of Scientific and Technical Computing in development of the analysis. SYMBOLS F(w) F o u r i e r t ransform of f ( t ) SCAS s t a b i l i t y and c o n t r o l augmentation system x(w) f ( t ) e x c i t a t i o n s i g n a l Four i e r t ransform of a response t t i m e n r o t a t i o n a l speed of r o t o r w frequency of a mode i n a dynamics system WI frequency of t h e mode of i n t e r e s t i n a dynamics system b lade lead-lag n a t u r a l f requency 5 w ROTOR EXCITATION SYSTEM For a so f t - in -p l ane r o t o r t es t program, i t i s d e s i r a b l e t o excite t h e r o t o r a t a r e l a t i v e l y low ampli tude and a t a p resc r ibed frequency. The system developed t o perform the e x c i t a t i o n f o r f l i g h t f l u t t e r t e s t i n g of t h e Bell Model 609 so f t - in -p l ane r o t o r u s e s t h e SCAS a c t u a t o r s , d r i v i n g them from an HP203A dua l s i g n a l gene ra to r . T h i s r o t o r exciter can supply e i t h e r a cont inuous s i g n a l of a s i n g l e f requency, o r a p u l s e s p e c t r u m which can be s e l e c t e d t o excite only one n a t u r a l frequency of several which may be present. A f u n c t i o n a l diagram of t h e system i s shown i n f i g u r e 1. The upper p o r t i o n shows the system which d r i v e : t h e r o t o r , and the lower p a r t shows t h e n u l l i n g system. Th i s n u l l i n g system i s an op t ion which al lows t h e u s e r t o cancel t h e s teady s t a t e one-per-rev and two- per - rev s i g n a l s b e f o r e t h e i n p u t spectrum i s app l i ed , t hus i s o l a t i n g t h e response t o the i n p u t s i g n a l only, F igure 2 shows a diagram of the r o t o r exciter. P o i n t A has a p u l s e output t o the computer t o i n d i c a t e when t h e inpu t has been com- p l e t e d . P o i n t B i s the demodulated one-per-rev t o t h e n u l l i n g system. The under ly ing p r i n c i p l e behind t h e single-mode e x c i t a t i o n technique can be explained i n terms of a l i n e a r system w i t h many degrees of freedom. The F o u r i e r t ransform of t h e response v e c t o r is obta ined by pos t -mul t ip ly ing the matrix of t h e frequency response f u n c t i o n by the column of t h e F o u r i e r t ransform of the fo rc ing func t ion . (See, f o r example, r e f . 2) The frequency response f u n c t i o n s e x h i b i t peaks corresponding t o n a t u r a l f r equenc ie s of t h e system. The shape of t he F o u r i e r t ransform of the f o r c i n g f u n c t i o n i s governed by the shape of t h e fo rc ing func t ion i n the time domain. For example, the Four ie r t r ans fo rm of the f o r c i n g f u n c t i o n depic ted i n f i g u r e 3a is shown i n f i g u r e 3b. F(y) has a l a r g e magnitude corresponding t o frequency w1, and a r a t h e r low magnitude elsewhere. S ince the Four i e r t ransform of t h e response, X(w), i s ob ta ined as a matrix product of frequency response f u n c t i o n and F(w), the response motions w i l l b e motions predominately a t t h e frequency w1. (This , however, does n o t mean that t h e mode of in terest a l o n e i s exc i t ed and the o t h e r 502 modes are properly suppressed.) chosen to produce a desired spectrum F(W), Various types of forcing function f(t) can be ON-LINE STABILITY ANALYSIS The Bell experimental Model 609 flex-hinge rotor, a four-bladed, soft-in- plane design, is mounted on a Bell 1501 fuselage. The elastomeric lead-lag hinge offset is 1 3 . 2 percent of the rotor radius which is 752 cm (296 in.). The blade first flapping frequency is 5.08 Hz ( 1 . 0 7 per rev). There are two potentially unstable modes for this experimental soft-in-plane rotor system. One, a coupled roll-yaw mode of the fuselage on the landing gear, has a frequency of 2 . 3 Hz. of 3 . 5 5 Hz at low strain conditions. The other, the blade first lead-lag mode, has a frequency Ground Resonance Test The roll mode stability was monitored by an accelerometer at the top of the mast. The test oscillated the SCAS actuators in a sense equivalent to moving the cyclic stick in a counter-clockwise direction at a frequency near 2 . 3 Hz. The aerodynamic hub moments and hub shears then excited the fuselage roll mode at its natural frequency. The high damping, the presence of high one-per-rev response, and some unknown noise made the data reduction difficult. Figure 4a shows the roll mode response at 260 rpm when a 7-Hz filter was used. block analysis of this response indicated the modal damping to be at 1 9 . 7 per- cent critical. Figure 4b shows the result of filtering the same raw data through a 3-Hz analog filter. In this case, the moving block technique showed ’ the modal damping to be at 20.8 percent critical. Since the 3-Hz filter brings out the highly damped roll mode more clearly, and since the calculated damping is approximately the same as in the other case, the decay plots of the roll mode in other ground run conditions were all filtered through 3-Hz filters before undergoing the moving block analysis. The moving The blade lead-lag motion was sensed by a strain gage on the grip damper arm. For the blade lead-lag stability test, the SCAS actuators were cycled as if the cyclic stick were being moved in a counter-clockwise direction at a fre- quency of one-per-rev minus the blade lead-lag frequency ( f 2 - 0 ~ ) . This is equiv- alent to exciting the lead-lag mode aerodynamically at its natural frequency in the blade rotating system. Figure 5a shows the response of the lead-lag mode to a SCAS input at high collective (immediately before lift-off) and a rotor speed of 280 rpm. The modal damping obtained from the moving block technique was 4 . 3 percent critical in the rotating system. The data were then passed through a 4-Hz filter with the results shown in figure 5b. The modal damping determined by the moving block analysis was 4 . 2 percent critical in the rotating system. The filtering process again highlighted the modal decay and did not affect the moving block result. A summary of damping variations measured at various rotor speeds for the lead-lag mode and fuselage roll mode in the fixed reference system is shown in figure 6 . uted to the destabilizing Coriolis force and the characteristic of an elasto- meric damper, a phenomenon predicted by the ground resonance analysis. The decrease in damping with increase in blade collective is attrib- , 503 Air Resonance Analysis The blade lead-lag mode in hover was also excited with the SCAS actuators. Figure 7 shows the lead-lag decay at the design rotor speed of 285 rpm filtered through a 4-Hz filter, The moving block technique determined the modal damping to be 5.4 percent critical. XV-15 VTOL FLIGHT FLUTTER TEST PLANS - in September 1976. Bell Helicopter Company, the prime contractor, is building two of these aircraft which will have a design gross weight of 57.8 kN(13000 lb: and a maximum speed of 364 knots. Of primaiy interest from the standpoint of flutter are the stability of the coupled rotor/airframe system and flutter of the empennage. The NASAlArmy XV-15 Tilt Rotor Research Aircraft will enter flight testing Coupled Rotor/Airframe Stability The XV-15 has a nacelle on each wingtip. Each nacelle houses a T-53 engine and a transmission, and each transmission drives a 25-foot, gimbaled, stiff-in- plane three-bladed rotor. The nacelles are oriented with their shafts vertical for takeoff, landing, and flight in the helicopter mode, and are mechanically tilted 90 degrees for flight in the airplane mode. stability of the coupled rotor/airframe system, the wing is designed to be very stiff in torsion and in bending (it is 23% thick with spars at 5% and 50% chord, fully monocoque) and the nacelle is attached to the wing at the front and rear spar to make the attachment stiff in pitch and yaw. To prevent aeroelastic in- The calculated coupled rotor/airframe stability characteristics in the air- plane mode of flight indicate that instability occurs first in the wing chord- wise bending mode and, at higher speeds, in wing beamwise bending and in torsion These are shown in figure 8. The instability is similar in nature to propeller nacelle whirl flutter; but involves elastic bending of the blade’ and elastic deflections of the blade pitch control system in addition to the precession of the rotor disc. There is considerable confidence in the predicted stability characteristics, since the coupled rotor/airframe stability analysis has shown excellent agreement with flutter model tests and with tests of a full-scale semi span wing in the NASA Ames 40 x 80 foot wind tunnel (ref. 3). Empennage Flutter The XV-15 has an H-tail, a configuration that gives it good high-speed directional stability characteristics. Although flutter was of concern during the design, the empennage was designed to avoid resonance of the empennage modes with rotor excitation frequencies. For good frequency placement, the horizontal stabilizer is very stiff in bending and torsion. The elevator and rudder are powered by irreversible hydraulic actuators (dual for the elevator) with lock and load mechanisms to make them irreversible in the event of a hydraulic system failure. As a result, the empennage has a large flutter margin that has been confirmed by flutter model tests in the 16-foot transonic tunnel at NASA Langley (ref. 4 ) . 504 F1 ight Flutter Testing For tests to determine the frequency and damping of the coupled rotor/ The copilot or airframe modes, the research XV-15 will have series actuators in the wing flaperon and rotor blade collective pitch control linkages. flight test engineer will control the amplitude and frequency of the actuators, which have limited authority so that a hardover cannot cause excessive stresses or aircraft responses that the pilot cannot easily control. quency response is flat to well above the frequency of the highest coupled mode of interest. The actuator fre- Frequency and damping of each mode of interest will be determined from the decay of that mode. The test procedure will be to select either the flaperon or collective actuator and tune its excitation frequency to the modal frequency, then turn off (the actuators automatically center) and record the decay. This procedure was used in the full-scale test in the 40 x 80 foot wind tunnel, and gave good results. flight safety during flight enveiopi expansion. The decays will be monitored and analyzed on the ground for The excitation system will also be used to generate transfer functions by slow-sweeping excitation frequency. These transfer functions will be used for an additional check on the validity of the coupled rotor/airframe stability analysis. Tests to evaluate the empennage flutter characteristics will excite the empennage modes with doublet inputs to the elevator and rudders. generated through the series SCAS actuators. These will be CONCLUDING REMARKS 1. For an elastomeric damper such as the one used on the Model 609 blade lead-lag hinge, the characteristics of the material depend on its strain. Since the lead-lag displacement (hence strain) varies with flight conditions, the lead- lag frequency varies throughout the flight test. It was learned from this study that, in the moving block analysis, a good estimate of the assumed frequency of computation could help the convergence. 2. The dynamic and aerodynamic environment of a rotor change as the flight condition changes; hence the steady state one-per-rev and two-per-rev harmonic loads also vary. Therefore it is suggested that the nulling system be retuned whenever the flight condition changes. the Model 609 test because-the rotor synchro was not operational. However this option was not used during 3. Because of the limitations on SCAS authority for the Model 609 testing, the signal-to-noise ratio for the modes of interest was relatively low. fore, a number of different analog filters were used to clean up the data. Low- pass filters from 3 Hz to 12 Hz, however, made no appreciable difference in damping calculations. There- 505 4. The single-mode excitation technique, using the SCAS actuators, produces excellent stability data since the input signal is well under the user's control. Depending on the input magnitude phasing and limitations of the SCAS authority, any mode in a rotary wing aircraft can be excited by the oscillation of the rotor controls in a prescribed manner. But whether the initial condition (mode shape) of the aeroelastic mode of interest is excited properly remains to be seen. The moving block analysis in most cases can be used in conjunction with the single- mode excitation technique to assess the stability information from ground run or flight test with real time computation. This testing and data reduction package is useful for on-line flight flutter testing of rotary wing aircraft. REFERENCES 1. Anderson, William D.: Investigation of Reactionless Mode Stability Charac- teristics of a Stiff Inplane Hingeless Rotor System. the 29th Annual National Forum of the American Helicopter Society, May 1973. Preprint No. 734, 2 . Lin, Y. K.: Probabilistic Theory - of Structural Dynamics. McGraw-Hill Book Company, 1967. 3. Edenborough, Kipling H., Gaffey, Troy M., and Weiberg, James A.: Analysis and Tests Confirm Design of Proprotor Aircraft. August 1972. AIAA Paper No. 72-803, 4 . Marr, Roger L., and Neal, Gordon T.: Assessment of Model Testing of a Tilt- Proprotor VTOL Aircraft. The American Helicopter Society Symposium on Status of Testing and Modeling Techniques for V/STOL Aircraft, October 1972. 506 F/A PILOT INPUT - - -9 I I -- TRANSDUCER LATERAL PILOT INPUT- * T h i s demodulator i s physical ly located i n the rotor exciter. BUFFER , 1/mv 4 AMPLIiE'ATION PHASE AMPLIFIER * ADJUSTMENTS MAIN ROTOR SYNCHRO 4 DEMODU- - ( l /REV SINUSOID) LATOR FREQUENCY DOUBLER To ADJUSTMENTS RECORDER Figure 1. Functional block diagram of rotor excitation system. I I I L W T AND SYNCHRO EXCITATION I I I c 218 VDC Figure 2. Diagram of rotor exciter. 507 (a) Plot of f(t). W / W l 0 (b) Four i e r transform of f(t). F i g u r e 3 . Forc ing f u n c t i o n f ( t ) . 508 7-Hz FILTER AMPLITUDE TIME (SEC) (a) With 7-Hz f i l t e r . I 0 .5 1.0 I. 5 2.0 2.5 3 . 0 3.5 TIME (SEC) (b) With 3-Hz f i l t e r . F igu re 4 . Fuselage r o l l mode decay i n ground run. 52 = 260 rpm; l o w c o l l e c t i v e . 509 AMPLITUDE AMPLITUDE NO FILTER .5 1.0 1.5 2.0 2.5 TIME (SEC) (a) With no f i l t e r . .5 1.0 1.5 2.0 2.5 TIME (SEC) ( b ) With 4 - H x f i l t e r . F i g u r e 5. Blade l ead - l ag decay i n ground run. high c o l l e c t i v e . fi = 280 rpm; 510 LOW COLLECTIVE HIGH COLLECTIVE 0 50 40 DAMPING 30 (% CRITICAL) 0 20 10 0 2 40 260 280 30 0 320 ROTOR SPEED ( R P M ) ! (a) Blade lead-lag damping. 50 40 DAMPING (% CRITICAL) 30 20 m 0 10 0 a LOW COLLECTIVE HIGH COLLECTIVE 240 260 2 80 300 3 20 ROTOR SPEED (WM) (b) Fuselage roll mode damping. Figure 6 , Damping in fixed system. 511 0 .5 1.0 1.5 2.0 2.5 10 + TIME (SEC) - WING BEAM - -- - WING TORSION -.-.- W I N G CHORD - - PYLON YAW F i g u r e 7 . F i l t e r e d blade lead- lag decay i n hover, 52 = 285 rpm. (% CRITICAL) 0 STABLE ---':.,.--. - Y - - - - . '. ~- c --- -. \ -.- '. - -- I I I \ I i \ '"I 5 FREQUENCY (Hd O J I 1 I I I 0 100 200 300 400 500 600 700 TRUE AIRSPEED (KNOTS) Figure 8. Calcula ted s t a b i l i t y for XV-15 a t d e n s i t y a l t i t u d e 6096 m. (20000 f t ) . 512 NASA-Langley, 1976 L-105 67 bYATlOt%#,L RERONWUTICS A N D SPACE ~ ~ ~ D M I N I S T R I ~ T I O N WASI4lI*IGTON. D.C. 2C546 PO§+AGE A M D CEES P A I D --- N A T I O N A L AERONAUTICS A N D OFF IC I AL E3U S I IN ESS S P A C E ADMINISTRA+IOM 4pil PEMALTY FOR P R I V A T E USE 1300 : If Undeliverable (Section 111 Postai hfaniinl) Do Not Reti T h e aeronautical and space ckctivzties of the United States shdl be conducted so ds t o contribute , . . t o the expansion of human Rnowl- edge of phenomena in the atmosphere m d space. 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Flight Flutter Testing Symposium

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