Numerical methods for determining the stability and response of periodic systems with applications to helicopter rotor dynamics and aeroelasticity

AbstractThis paper reviews and extends some recently developed numerical techniques for analyzing the stability, linear response and nonlinear response of periodic systems, which are governed by ordinary differential equations with periodic coefficients. The main emphasis is on applications aimed at rotor blade aeroelastic stability and response calculations in forward flight. First Floquer theory is br4iefly reviewed and numerically efficient methods for evaluating the transition matrix at the end of one period are described. Next the numerical treatment of the linear response problem is discussed. Finally the numerical solution of the nonlinear response problem is treated using quasilinearization and periodic shooting. Applications illustrating numerical properties of the methods are described