2016•DOAJ (DOAJ: Directory of Open Access Journals)Open access

Periodic Solutions of the Duffing Harmonic Oscillator by He's Energy Balance Method

A.M. El-Naggar, Gamal M. Ismail

Abstract

Duffing harmonic oscillator is a common model for nonlinear phenomena in science and engineering. This paper presents He´s Energy Balance Method (EBM) for solving nonlinear differential equations. Two strong nonlinear cases have been studied analytically. Analytical results of the EBM are compared with the solutions obtained by using He´s Frequency Amplitude Formulation (FAF) and numerical solutions using Runge-Kutta method. The results show the presented method is potentially to solve high nonlinear oscillator equations.

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Key concepts: Harmonic balance, Duffing equation, Nonlinear system, Energy balance, Harmonic oscillator, Amplitude, Mathematical analysis, Balance (ability)