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

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DOI: 10.4236/jemaa.2013.510061    3,331 Downloads   5,094 Views   Citations

ABSTRACT

In this paper, we implement a new approach coupled with the iteration method. This procedure is obtained by combining Hes frequency-amplitude formulation and Hes 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.

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

T. Nofal, G. Ismail, A. Mady and S. Abdel-Khalek, "Analytical and Approximate Solutions to the Fee Vibration of Strongly Nonlinear Oscillators," Journal of Electromagnetic Analysis and Applications, Vol. 5 No. 10, 2013, pp. 388-392. doi: 10.4236/jemaa.2013.510061.

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