Perturbation-Galerkin approach for random vibration responses of structures with random parameters of different probability distributions

Innovation and Contributions

Under the supervision of Professor Bin Huang, master’s student Miancheng She applied the group’s stochastic perturbation–Galerkin method to random vibration response calculations for the first time. The study addresses the computation of random vibration responses of multi-degree-of-freedom structures whose random parameters follow different probability distributions. In particular, it uses an elementary algebraic approach to invert random matrices, providing a new approach to solving problems in mechanics involving random parameters.

Abstract

This paper combines the stochastic perturbation–Galerkin method with frequency-domain random vibration analysis to derive analytical solutions for the random vibration responses of structures with random parameters following different probability distributions under stationary random excitation. Assuming that the structural stiffness matrix contains multiple random variables with different probability distributions, a power series expansion of the frequency response function (FRF) matrix is derived using high-order perturbation and stochastic Galerkin projection. The frequency-domain transfer relationship between structural responses and external random excitation then yields an analytical expression for the response power spectral density (PSD) as a function of the random variables. The numerical examples show that the method achieves higher computational accuracy and efficiency than generalized polynomial chaos expansion (GPC) for the structures examined.

Keywords: structures with random parameters; random vibration; frequency response function; stochastic perturbation-Galerkin method; power spectral density function

Selected Figures

Citation

DOI: 10.6052/0459-1879-25-164