等価非ガウス励振化法とエルミートモーメントモデルを用いた非ガウス性不規則励振を受ける線形系の信頼性解析

抄録

The analytical method using the equivalent non-Gaussian excitation method and the Hermite moment model is proposed to obtain the stationary response distribution and the mean upcrossing rate of linear systems subjected to non-Gaussian random excitation. The excitation is prescribed by the non-Gaussian probability density function and the power spectrum. In this paper, the stationary response distribution of the system is obtained by using the Hermite moment model. The parameters in the model are determined based on the higher-order statistical moments of the response, which are calculated from the moment equations for the response and the excitation by utilizing the equivalent non-Gaussian excitation method. From the resulting response distribution, we obtain the mean upcrossing rate of the stationary response of the system. In numerical examples, the proposed method is applied to a linear system subjected to non-Gaussian excitation with Rayleigh and generalized Gaussian distributions. The analytical results are compared with Monte Carlo simulation results. It is shown that this method is valid for the non-Gaussian excitation with the asymmetric or heavy-tailed distribution and a wide range of the bandwidth.