Stochastic response of MDOF system to non-stationary random excitation

Abstract

Abstract An approximate scheme is developed for efficiently determining non-stationary response PDF of multi-degree-of-freedom (MDOF) dynamical system to time-modulated random excitation. It further generalizes state-space-split exponential polynomial closure (SSS-EPC) technique and enhances its application for determining non-stationary response probability density function (PDF). To this aim, time variable is introduced into the approximate solution by setting polynomial coefficients as time dependent ones. With the proposed procedure, non-stationary solution to high-dimensional FPK equation can be obtained. Meanwhile, Monte Carlo simulation (MCS) method is conducted to assess the reliability of the proposed method. Three typical examples of linear and nonlinear MDOF dynamical systems to different modulated Gaussian white noise excitations are considered. Comparisons with the simulated results and computational time of the MCS method demonstrate the relatively high efficiency and accuracy of the proposed procedure.