PERTURBATION-GALERKIN APPROACH FOR RANDOM VIBRATION RESPONSES OF STRUCTURES WITH RANDOM PARAMETERS OF DIFFERENT PROBABILITY DISTRIBUTIONS

Combining the stochastic perturbation-Galerkin method with the frequency domain analysis method in stochastic vibration, a novel method is proposed to derive the analytical solutions for random vibration responses of the structure with random parameters of different probability distributions under stationary random excitation. Assuming that the structural stiffness matrix contains multiple random variables with different probability distributions, the power series expansion of the frequency response function (FRF) matrix involving multiple random variables is derived based on the high-order perturbation and stochastic Galerkin projection. By using the frequency-domain transfer relationship between structural responses and external random excitations, the analytical expression of the response power spectral density (PSD) function with respect to the random variables is obtained. Numerical results demonstrate that this method outperforms the generalized polynomial chaos expansion method (GPC) in both the computational accuracy and efficiency for the random vibration analysis of structures with multiple random variables of different probability distributions.