Response distribution of a SDOF linear system under non-Gaussian random excitation by using difference index of power spectra between excitation and response

Abstract

Response distribution of a SDOF linear system subjected to non-Gaussian random excitation is investigated. The excitation is modeled by a zero-mean stationary stochastic process prescribed by the non-Gaussian probability density and the power spectrum with bandwidth and dominant frequency parameters. In this paper, we use bimodal and Laplace distributions for the non-Gaussian distribution of the excitation. The excitation is generated numerically by using the Ito stochastic differential equation. Monte Carlo simulations are carried out to obtain the stationary probability densities^ of the system displacement and velocity. It is found that the shape of the response distribution changes depending on a difference in the shape of power spectral density between the excitation and the response. In order to evaluate the difference of the spectral densities quantitatively, a new index is defined. The correspondence of this index to the shape of the response distribution is shown. Next, we compare the present difference index of power spectra and another index which the authors used in the previous study to investigate the response distribution of a non-Gaussian randomly excited system. The comparison shows that when the present index is close to 0, the shape of the response distribution looks like the shape of the excitation distribution. For the index around 0.6, the response distribution becomes the middle shape between the excitation probability density and a Gaussian distribution. In the case of the index greater than 1.2, the response distribution is nearly Gaussian. The difference index of power spectra between the excitation and the response can be calculated readily from the frequency response function of a linear system and the excitation power spectrum, regardless of the excitation probability density function. This index enables us to roughly estimate the shapes of the probability distributions of the displacement and velocity responses without Monte Carlo simulation.