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This paper presents an application of equivalent non-Gaussian excitation method for the response analysis of systems subjected to non-Gaussian random excitation with an asymmetric probability distribution. The non-Gaussian excitation is prescribed by the probability density function and the power spectrum. The excitation is governed by the Itô stochastic differential equation. Moment equations for the response can be derived from the stochastic differential equation for the excitation and the equation of motion of the system. However, the moment equations are generally not closed due to the nonlinearity of the diffusion coefficient in the stochastic differential equation for the excitation even though the system is linear. In the previous paper, equivalent non-Gaussian excitation method was developed to obtain a closed set of the moment equations. It was demonstrated that for obtaining the variance and kurtosis of the response, the method is applicable to the case of the symmetric non-Gaussian excitation with a wide range of the kurtosis and bandwidth. In this study, equivalent non-Gaussian excitation method is utilized to analyze a linear system subjected to non-Gaussian random excitation with extended generalized Gaussian distribution. The probability distribution can express a variety of asymmetric non-Gaussian distributions with the quite different skewness and kurtosis. The results are compared with those obtained by Monte Carlo simulation. The application in the present paper shows that the method can accurately estimate not only the variance and kurtosis of the response but also the non-zero skewness caused by the asymmetry of the excitation.

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Application of equivalent non-Gaussian excitation method for systems subjected to non-Gaussian random excitation with asymmetric probability distribution