Random structural dynamic response analysis under random excitation

Abstract

A numerical procedure to compute the mean and covariance matrix of the random response of A numerical procedure to compute the mean and covariance matrix of the random response of stochastic structures modeled by FE models is presented. With Gegenbauer polynomial approximation, the calculation of dynamic response of random parameter system is transformed into an equivalent certainty expansion order system’s response calculation. Non- stationary, non-white, non-zero mean, Gaussian distributed excitation is represented by the well known Karhunen-Loeve (K-L) expansion. The Precise Integration Method is employed to obtain the K-L decomposition of the non- stationary filtered white noise random excitation. A accurate result is obtained by small amount of K-L vectors with the vector characteristic of energy concentration, especially for the small band-width excitation. Correctness of the method is verified by the simulations. The effects to the response mean square value by different probability density functions of random parameters with the same variable coefficient are studied, and a conclusion is drawn that it is inappropriate to approximate other types of probability distribution by normal distribution.