Flapping-Torsional Response of Helicopter Rotor Blades to Turbulence Excitation

166 p.Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 1983.Dynamics of a helicopter rotor system in atmospheric turbulence is investigated theoretically. Modeling turbulence components as stationary random processes, differential equations governing the coupled flapping-torsional motion of a rotor blade are derived. The blade is treated as being rigid and centrally hinged for the flapping motion, and as being elastic with a linear deformation mode for the torsional motion. Classical steady theory is used to formulate the aerodynamic forces due to blade flapping. For those due to blade pitching, a quasi-steady theory is used. The governing equations so obtained contain random turbulence terms in the coefficients and the inhomogeneous parts.By the use of the stochastic averaging method introduced by Strotonovich, the original physical equations are converted to the Ito equations governing a Markov vector process, which is an approximation for the original physical response state vector. These Ito equations are then used to derive the equations for the statistical moments of the response variables. The derivation of the second moment equations requires an application of Ito's differential rule. Since the coefficients of the statistical moment equations are periodic, Floquet's theory is applied to obtain the stability conditions. Another problem investigated is concerned with the time variation of the first and second statistical moments when the motion is stable. The problem is important for the evaluation of structural damage due to fatigue. The effects of changing the turbulence levels and the other system parameters are determined and presented graphically.In the second stage of investigation, the analytical procedure is extended to multibladed systems. An orthogonal multiblade transformation is used to convert the set of governing equations referred to rotating coordinates of individual blades to a set referred to non-rotating coordinates fixed on the helicopter body. The transformation replaces the lower harmonic terms to constants and higher frequency terms, thus extending the validity range in which a time-averaging procedure can be applied to simplify the equations after the stochastic averaging procedure. Examples are given to illustrate the application of the present analytical methods.U of I OnlyRestricted to the U of I community idenfinitely during batch ingest of legacy ETD