Approximate Method for Nonlinear Random Vibration

Abstract

An approximate method for nonstationary solution of nonlinear systems under random excitation is presented. The nonlinearities in the restoring force are polynomial type. The excitation is either shot noise or filtered shot noise. The solution is based on a Markov-vector approach. The unsteady Fokker-Planck-Kolmogorov equation for the nonlinear system is solved approximately by a Galerkin method where a time-dependent Hermite-series expansion is used and the equation is reduced to a system of first-order ordinary differential equations. The method is illustrated by numerical examples on a damped Duffing oscillator and a Ramsberg-Osgood yielding system. Comparison of results obtained herein with exact stationary solution and Monte Carlo results indicates that the proposed method is powerful and efficient for study of nonlinear systems.