The higher-order analysis method of statistics analysis for response of linear structure under stationary non-Gaussian excitation

Abstract

The classical random vibration theory has been well developed with broad applications, and the efficiency of analysis for random vibration has been improved by the pseudo-excitation method. However, random analysis for structural vibration under non-Gaussian excitation remains a substantial challenge. In this work, higher-order statistics for the response of the multiple-degree-of-freedom linear structure under stationary non-Gaussian excitation is analyzed, and a novel high-order analysis method is presented. Firstly, an analytical solution for the higher-order statistics of response is derived based on the mode superposition method, which is named the complete high-order combination method. Secondly, the expression for calculating higher-order moment spectrum of response is theoretically deduced. In contrast, the conventional pseudo-excitation method is just a particular case of the proposed method. Meanwhile, a novel and practical response analysis method is presented on the basis of the time-domain explicit formulation method. The higher-order moment spectrum of response can readily be achieved by the known response. Finally, two examples are investigated to demonstrate the effectiveness of the proposed method.