An Analysis of Transient Response Moments of a Linear System Subjected to Non-Gaussian Random Excitation Using Higher-Order Autocorrelation Functions of Excitation

Abstract

We present the analytical solutions of the second-, third-, and fourth-order response moments of a single-degree-of-freedom linear system subjected to a class of non-Gaussian random excitation. The non-Gaussian excitation is a zero-mean stationary stochastic process prescribed by an arbitrary probability density and a power spectrum whose peak is located at zero frequency. The excitation is described by an Itô stochastic differential equation in which the drift and diffusion coefficients are determined from the probability density and spectral density of the excitation. In order to obtain the analytical solutions of the response moments, first, we derive the third- and fourth-order autocorrelation functions of the non-Gaussian excitation using its Markov and detailed balance properties. The third-order correlation function is given by the same expression regardless of the difference in the probability density function of the excitation. On the other hand, the fourth-order correlation function is derived under the assumption that the excitation probability density belongs to the Pearson distribution family, which is one of the widest classes of probability distributions. Then, combining the autocorrelation functions of the excitation and the convolution representation of the response, we obtain the exact solutions of the response moments, and it is shown what kind of components the response moments are composed of. Finally, we investigate the dominant time-varying components of the response moments for several different excitation bandwidths.