Wavelet-expansion-based stochastic response of chain-like MDOF structures

This paper presents a wavelet-expansion-based approach for response determination of a chain-like multi-degree-of-freedom (MDOF) structure subject to full non-stationary stochastic excitations. Specifically, the generalized harmonic wavelet (GHW) is first utilized as the expansion basis to solve the dynamic equation of structures via the Galerkin treatment. In this way, a linear matrix relationship between the deterministic response and excitation can be derived. Further, considering the GHW-based representation of the stochastic processes, a time-varying power spectrum density (PSD) relationship on a certain wavelet scale or frequency band between the excitation and response is derived. Finally, pertinent numerical simulations, including deterministic dynamic analysis and Monte Carlo simulations of both the response PSD and the story-drift-based reliability, are utilized to validate the proposed approach.