Equivalent non-Gaussian excitation method for moment calculation of non-Gaussian randomly excited systems

Abstract

Equivalent non-Gaussian excitation method is developed to obtain the statistical moments up to 4th order of the response of non-Gaussian randomly excited systems. The non-Gaussian excitation is prescribed by the probability density function and the power spectrum. The excitation is governed by the Itôstochastic differential equation. Generally, moment equations for the response, which are derived from the stochastic differential equation for the excitation and the equation of motion of the system, are not closed form due to the complex nonlinearity of the diffusion coefficient in the governing equation for the excitation even though the system is linear. In equivalent non-Gaussian excitation method, the diffusion coefficient is replaced with the equivalent diffusion coefficient approximately to obtain a closed set of the moment equations. The square of the equivalent diffusion coefficient is expressed by a second-order polynomial. The coefficients of the polynomial are determined according to the criterion of minimization of the mean square error between the original diffusion coefficient and the equivalent diffusion coefficient. In order to assess the validity of the present method, a linear system subjected to a non-Gaussian random excitation with the generalized Gaussian distribution and the power spectral density with the bandwidth parameter is analyzed. From the comparison with the Monte Carlo simulations, It is shown that for obtaining the variance and the kurtosis of the response, the proposed method is applicable to the case of the non-Gaussian excitation with a wide range of the kurtosis and the bandwidth. In order to discuss the accuracy of the method, the statistical moments of the equivalent non-Gaussian excitation are also investigated.