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Applicable Analysis
An International Journal
Volume 91, 2012 - Issue 5
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Original Articles

Analytical approximate solutions for the generalized nonlinear oscillator

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Pages 965-977 | Received 23 Sep 2010, Accepted 27 Jan 2011, Published online: 23 Mar 2011
 

Abstract

He's energy balance method (HEBM) is employed in this article to obtain the analytical approximate solution of the generalized nonlinear oscillator. Existence of periodic solutions is analytically verified and consequently the relationship between the natural frequency and the initial amplitude is obtained in an analytical form. A number of numerical simulations are carried out and accuracy of the HEBM is then examined within an error analysis. The exact values of the natural frequency numerically obtained via the elliptic integrals are taken into account as the references bases and the relative error is then evaluated for a range of oscillation amplitudes. Excellent correlation of the approximate frequencies with the exact ones demonstrates that the approximate solutions are quite consistent even for large amplitudes of oscillation.

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