Excitation–response relationships for linear structural systems with singular parameter matrices: A periodized harmonic wavelet perspective

Abstract

Novel wavelet-based input–output (excitation–response) relationships are developed referring to stochastically excited linear structural systems with singular parameter matrices. This is done by relying on the family of periodized generalized harmonic wavelets for expanding the excitation and response processes, and by resorting to the concept of Moore–Penrose matrix inverse for solving the resulting overdetermined linear system of algebraic equations to calculate the response wavelet coefficients. In this regard, system response statistics in the joint time–frequency domain, such as the response evolutionary power spectrum matrix, can be determined in a straightforward manner based on the herein derived input–output relationships. The developed technique can be construed as a generalization of earlier efforts in the literature to account for singular parameter matrices in the governing equations of motion. The reliability of the technique is demonstrated by comparing the analytical results with pertinent Monte Carlo simulation data. This is done in conjunction with various diverse numerical examples pertaining to energy harvesters with coupled electromechanical equations, oscillators subject to non-white excitations modeled via auxiliary filter equations and structural systems modeled by a set of dependent coordinates.