Auxiliary harmonic excitation generalized method for higher-order analysis of linear structure under multiple non-stationary non-Gaussian excitations

Abstract

In the classical random vibration analysis, the frequency-domain analysis method, especially the time-frequency domain analysis method based on the frequency domain analysis method, is the most commonly analysis method. However, the time-frequency domain analysis method is challenging when dealing with multiple non-stationary non-Gaussian excitations. In this paper, an accurate and efficient auxiliary harmonic excitation generalized method for higher-order analysis of linear structures under multiple non-stationary non-Gaussian excitations is proposed. Firstly, the expression for the higher-order moment spectrum of response is theoretically deduced by the mode superposition method, in which the time-varying generalized impulse response function and the time-varying generalized frequency response function are introduced. Secondly, according to the relationship between the response of harmonic excitation and the time-varying generalized frequency response function, the expression for the high-order moment spectrum of response is reconstructed in terms of the response of harmonic excitation and the higher-order moment spectrum matrix of the excitations, in which the response of the time-varying auxiliary harmonic excitation can be evaluated efficiently based on the time-domain explicit formulation method. Finally, two examples are investigated to verify the accuracy and efficiency of the proposed method.