Analytical and Approximate Solutions to the Fee Vibration of Strongly Nonlinear Oscillators

Taher A. Nofal, Gamal M. Ismail, Amal Ali M. Mady, Sayed Abdel-Khalek

Department of Mathematics, Faculty of Science, Sohag University, Sohag, Egypt.
Department of Mathematics, Faculty of Science, Taif University, Taif, KSA.

DOI: 10.4236/jemaa.2013.510061                

Abstract

In this paper, we implement a new approach coupled with the iteration method. This procedure is obtained by combining He’s frequency-amplitude formulation and He’s energy balance method into a new iteration procedure such that excellent approximate analytical solutions, valid for small as well as large values of amplitude, can be determined for nonlinear oscillators. This study has clarified the motion equation of nonlinear oscillators by the iteration method to obtain the relationship between amplitude and angular frequency. We compare the approximate periods obtained by our procedure with the numerical solution and with other methods like energy balance method and variational iteration method. The results show that the approximations are of extreme accuracy.

Keywords

Periodic Solution; Nonlinear Oscillators; Energy Balance Method; Variational Iteration Method

Conflicts of Interest

The authors declare no conflicts of interest.

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