Wavelet-Galerkin approach for power spectrum determination of nonlinear oscillators

• Periodization of generalized harmonic wavelet and its connection coefficients.
• Wavelet-Galerkin formulation of nonlinear differential equation.
• Newton׳s iterative solution for nonlinear algebra equations.
• Power spectrum density determination of nonlinear stochastic dynamic systems.

A wavelet-Galerkin method based solution for nonlinear differential equation of motion is presented. Specifically, first, theory background of Periodic Generalized Harmonic Wavelet (PGHW) and its connection coefficients are briefly introduced. Next, wavelet coefficients of response are solved from a set of nonlinear algebra equations obtained via the wavelet-Galerkin approach. In this regard, Newton׳s method is employed to solve the nonlinear algebra equation. Further, stochastic response is determined by evoking a relationship between the wavelet coefficients and the corresponding response power spectrum density. Finally, pertinent numerical simulations demonstrate the reliability of the proposed approach.