Response EPSD of chain-like MDOF nonlinear structural systems via wavelet-Galerkin method

•PGHW method is used to analyze the response of chain-like MDOF nonlinear structural systems in the time and frequency domain.•This is the first time that quasi-Newton method is used to get wavelet coefficients of the response.•Quasi-Newton method is more efficient than Newton method whether it is used for SDOF or MDOF systems.•The displacement and EPSD of the response are obtained and shown in the examples. The periodic generalized harmonic wavelet (PGHW) method is used to analyze the response of the chain-like multi-degree-of-freedom (MDOF) nonlinear structural system with seismic excitation in the time and frequency domain. First, the theoretical background of PGHW is briefly introduced, and the relationship between the power spectral density (PSD) of the stochastic process and the corresponding wavelet coefficient is given. Next, the wavelet-Galerkin method is used to study the MDOF system, and a set of nonlinear algebraic equations can be obtained to get the wavelet coefficient of the response. The quasi-Newton method is selected to solve these equations. It is more efficient than Newton method because the Davidon-Fletcher-Powell (DFP) algorithm is used to approximate the Jacobian matrix in the iterative process. Then, the displacement and estimated power spectral density (EPSD) of the response can be obtained by using the solved wavelet coefficient. Finally, numerical examples of the single-degree-of-freedom (SDOF) and MDOF systems are shown to prove the feasibility and efficiency.