Application of the Global Residue Harmonic Balance Method for Obtaining Higher-Order Approximate Solutions of a Conservative System

Abstract

In the current paper, an iterative approximate analytical approach, namely global residue harmonic balance method (GRHBM), is introduced for investigation a nonlinear conservative oscillatory system. The equation of motion for the considered system has been derived as a nonlinear ordinary differential equation. The GRHBM is based on the ideas of homotopy perturbation and the residue harmonic balance method. The results of the presented method are compared with those of other analytical approaches as well as those predicted by the fourth-order Runge–Kutta numerical technique. The correctness of the obtained results reveals that the presented method is very effective, simple and exact and is valid for small and large amplitudes. Furthermore, the impact of system parameters on the ratio of nonlinear to linear frequency is investigated. Consequently, the presented method provides an effective tool to study the effects of material and geometrical parameters in designing of devices composed of nonlinear conservative oscillators.