Higher-order analysis for random vibration of stochastic structures under Gaussian stationary excitation

Abstract

The stochastic structural parameters may lead to non-Gaussianity of response even under Gaussian stationary excitation. To deal with this hybrid random vibration problem, a new method by combining conditional expectation, pseudo excitation method and mixed-degree cubature formula is proposed. First, the hybrid random vibration problem is converted into a series of conventional random vibration ones of deterministic structures by deriving the conditional expectations of the moment spectra of response. Second, formulas of the power spectral density (PSD) and higher-order spectrum of response of the conditional deterministic structure are derived in terms of the PSD of the Gaussian excitation. Third, a more efficient and practical formula of the higher-order spectrum of response of the conditional deterministic structure is proposed based on pseudo excitation method. Fourth, the mixed-degree cubature formula is introduced to evaluate the integration of the conditional expectation and obtained the PSD and higher-order spectrum of the hybrid random vibration response. Finally, two examples are illustrated to verify the precision and efficiency of the proposed method.