Abstract
The probability density function of the stationary response of a single-degree-of-freedom nonlinear stiffness system under non-Gaussian random excitation is analyzed. The random excitation is modeled by a zero-mean stationary stochastic process prescribed by both the non-Gaussian probability density and the power spectrum with bandwidth parameter. In this paper, two approximate analytical methods for the probability density of the stationary displacement of the system are presented based on the knowledge of the characteristics of the response distribution observed in the previous study. One of the two methods is used when the bandwidth of the excitation power spectrum is narrower than that of the frequency response function of the system, and the other is used in the case of the wider bandwidth than the system bandwidth. By using these methods, the response distribution can readily be obtained without complicated calculation.In numerical examples, the proposed methods are applied to a nonlinear system under three types of nonGaussian random excitation whose non-Gaussianity is quite different from each other. The results demonstrate that for all excitation probability densities considered in this paper, the response distribution obtained through the present methods is in good agreement with Monte Carlo Simulation result in both cases where the excitation bandwidth is narrower and wider than the system bandwidth.
