DYNAMIC ANALYSIS OF NONCLASSICALLY DAMPED SYSTEMS (MODAL ANALYSIS, DFT METHOD)

The objectives of the studies reported in this dissertation are: (1) to develop improved techniques for evaluating the dynamic response of viscously damped linear systems, and (2) to contribute concepts and information which will lead to an improved insight into the dynamic response of such systems. The dissertation consists of two major parts. The first part, reported in Chapters II through IV, deals with the analysis of the response of nonclassically damped discrete systems. A critical evaluation is first made of the generalized modal superposition method of analysis for such systems, with special emphasis on identifying the physical significance of the various terms in the solution and simplifying its implementation. Next, the response spectrum variant of the procedure is examined for base-excited systems. The interrelationship of the spectral values of deformation and relative velocity of single-degree-of-freedom systems is identified, and simple practical rules are presented for defining the design spectra for relative velocity for such systems. These rules are similar to those available for defining the corresponding spectra for maximum deformation. Finally, a recently proposed procedure for interrelating the steady-state and transient responses of classically damped systems is extended to nonclassically damped systems. The second part of this dissertation, comprised of Chapters V and VI, deals with the application of the Discrete Fourier Transform (DFT) method of dynamic analysis. The limitations and principal sources of potential inaccuracies of this approach are identified, and an evaluation is made of the nature and magnitudes of the errors that may result from its indiscriminate use. Two versions of a modification are then presented which dramatically improve the efficiency of the procedure, and the relative merits of the two techniques are examined. The concepts involved are developed by reference to single-degree-of-freedom systems and are then extended to the analysis of multi-degree-of-freedom systems