Random Vibration of Nonlinear System under Nonwhite Excitations

Abstract

The method of quasiconservative averaging, developed originally to treat the random vibration of a system with a strongly nonlinear stiffness and under white-noise excitations, is modified to apply to the case of nonwhite wide-band excitations. The excitations can be either additive, multiplicative, or both. The total energy of the system is approximated as a Markov diffusion process under the condition that the damping and excitations are weak. A general procedure is given for calculating the drift and diffusion coefficients of the energy process by using Fourier series expansions. The nonwhite characteristics of the excitations are taken into account in the modified version of quasiconservative averaging. For illustration, the procedure is applied to a Duffing oscillator under both additive and multiplicative excitations with nonwhite spectral densities. Monte Carlo simulations are performed to substantiate the accuracy of the proposed procedure.