The higher-order analysis of response for linear structure under non-Gaussian stochastic excitations with known statistical moments and power spectral density

Abstract

The frequency-domain analysis method is a fundamental component of the random vibration analysis, in which the corresponding moment spectrum of excitations are the prerequisite. Nevertheless, the determination of the higher-order moment spectra for non-Gaussian stochastic excitations continues to pose a significant challenge in the existing research works. This paper introduces an accurate and efficient computational approach for determining higher-order moment spectra of non-Gaussian stochastic excitations with known statistical moments and power spectral density (PSD). Firstly, following the idea of the simulation method of non-Gaussian stochastic processes, the transformation model between the stationary non-Gaussian stochastic process and underlying Gaussian stochastic process is determined based on the known statistical moments, the PSD of the underlying Gaussian stochastic process is determined using the transformation model. Secondly, the approximate higher-order moment spectra models of stationary non-Gaussian stochastic processes are presented by the PSD of the underlying Gaussian process. Subsequently, the higher-order moment spectra models of non-Gaussian excitations are utilized to compute the higher-order moment spectra of response for the linear structure via the auxiliary harmonic excitation generalized method. Finally, three numerical examples are examined to assess the efficiency and accuracy of the proposed approximate models for the higher-order moment spectra of non-Gaussian stochastic processes.