Joint response distributions of a linear system subjected to non-Gaussian random excitation with a wide range of bandwidth

Abstract

We examine the joint response probability distributions of a linear system subjected to non-Gaussian random excitation with a wide range of bandwidth. In the previous studies, the transient response characteristics of linear systems subjected to non-Gaussian random excitation were investigated from the view point of the displacement response distribution and velocity response distribution. It was revealed that the probability distribution of the response varies significantly depending upon the bandwidth of the excitation power spectrum. In this paper, firstly, we calculate the joint response distribution of the displacement and velocity by Monte Carlo simulation. The non-Gaussian excitation is prescribed by both a probability density function and a power spectrum with bandwidth parameter. In order to find the response characteristics that appear commonly for different non-Gaussian excitations, we consider two kinds of non-Gaussian distributions for the probability distribution of the excitation. Their shapes are much different from a Gaussian distribution and also distinct from each other. For such non-Gaussian random excitations, the joint response distribution is obtained, and the relationship between the response distribution and the bandwidth of the excitation power spectrum is examined in detail. In addition, we also focus on the property of the distribution to concentrate on a straight line, which is important in discussing the non-Gaussianity in the response. When the bandwidth of the excitation is zero, the excitation can be considered as a step input. In this case, we can derive the solution of the straight line analytically. We illustrate the way of deriving the line for the zero bandwidth. Furthermore, it is shown that the line derived for the zero bandwidth can be used as the line even for the non-zero bandwidth. We also demonstrate that the duration for which the joint distribution concentrates on the straight line becomes shorter as the bandwidth becomes wider.