Harmonic Wavelets based Response Power Spectrum Determination of MDOF Nonlinear Structural Systems

A response evolutionary power spectrum (EPS) determination technique based on harmonic wavelets is developed for nonlinear multi-degree-of-freedom (MDOF) structural systems. Specifically, first a linear relationship between the evolutionary power spectrum matrices of the excitation and of the system response is obtained by utilizing a recently proposed locally stationary wavelet based representation of nonstationary stochastic processes. The relationship can be construed as an extension to the wavelet domain of the celebrated spectral excitation-response relationship of the linear stationary random vibration theory. Further, a harmonic wavelet based statistical linearization technique is proposed for the MDOF nonlinear systems. The developed technique can be viewed as a generalization of a recently proposed technique by some of the authors to account for MDOF chain-like nonlinear systems. Numerical examples demonstrate the reliability of the proposed approach.