Response distribution of a single-degree-of-freedom linear system subjected to non-Gaussian random excitation by using cross-correlation function

Abstract

Response probability density function of a single-degree-of-freedom linear system subjected to non-Gaussian random excitation is investigated. The excitation is assumed to be a zero-mean stationary stochastic process prescribed by both the non-Gaussian probability density and the power spectral density with bandwidth and dominant frequency parameters. In this study, bimodal and Laplace distributions are used as the non-Gaussian distribution of the excitation. Monte Carlo simulations are performed to obtain the stationary probability distributions of the displacement and velocity of the system. Then, we calculate the maximum absolute value of the real part of cross-correlation function between the excitation and the response, which is considered as an evaluation index of waveform similarity between the excitation and the response. It is shown that the response probability distributions vary with the maximum value. With the aid of this maximum value, the shapes of the probability distributions of the system response can be predicted roughly without Monte Carlo simulations.