Coupling of energy and harmonic balance method for solving a conservative oscillator with strong odd-nonlinearity

Document Type : Article

Author

Department of Mathematics, Rajshahi University of Engineering and Technology (RUET),Kazla, Rajshahi - 6204, Bangladesh

Abstract

In this paper, a new analytical technique, combining the energy balance method (EBM) with harmonic balance method (HBM), is presented to obtain higher-order approximations of a conservative oscillator with strong odd-nonlinearity. To show the accuracy of the present method, one nonlinear oscillator named as cubic-quintic Duffing oscillator is investigated. The results obtained in this paper are compared with those results determined by other methods and exact solutions. The results give high accuracy and also provide better result than other existing results for both small and large amplitudes of oscillation. The main advantage of the present paper is its simplicity, which contains a few harmonic terms with lower order terms and these terms make the solution quickly converges. The present technique can be used to other nonlinear oscillators.

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