Frequency-domain analysis and dynamic reliability assessment of random vibration for non-classically damped linear structure under non-Gaussian random excitations

Frequency domain analysis is the important component in the random vibration analysis. However, frequency domain analysis for the non-classically damped linear structure under non-Gaussian random excitations remains a challenge. Thus, this paper establishes a unified computational framework of higher-order moment spectra of response, and performs reliability assessment based on moment spectra of response. Firstly, the theoretical expressions of the higher-order moment spectra of response are deduced by the complex mode superposition method and the generalized impulse response function. Secondly, the expressions of the higher-order moment spectra of response are reconstructed with the help of responses for the harmonic excitation. Subsequently, the dynamic reliability is estimated based on the approximation joint probability density function which is constructed through the unified Hermite polynomial model and Gaussian Copula function. Finally, two numerical examples are investigated to verify the accuracy and efficiency of the calculation method of response the higher-order moment spectra and the dynamic reliability.