Global Residue Harmonic Balance Method for a System of Strongly Nonlinear Oscillator

Abstract

In this paper, the global residue harmonic balance method is applied to obtain the approximate periodic solution and frequency for a well-known system of strongly nonlinear oscillator in engineering. This method can improve accuracy by considering all the residual errors in deriving each order approximation. With this procedure, the expressions of the higher-order approximate solution and corresponding frequency for the considered system can be determined easily. The comparison of the obtained results with previously existing and corresponding exact solutions shows the high accuracy and efficiency of the method.

A simple modified harmonic balance method for strongly nonlinear oscillator with cubic non-linearity and harmonic restoring force

“…Many types of modification like the global residue harmonic balance method, [27][28][29][30][31] the modified energy balance method, 32,33 the modified harmonic balance method, [34][35][36] the modified homotopy perturbation method, [37][38][39][40] the modified Lindested-Poincare method, 41,42 the modified Laplace based variational iteration method 43 etc. were also used by many researchers to solve strong nonlinear problems.…”