A new analytical technique based on harmonic balance method to determine approximate periods for Duffing-harmonic oscillator

Hosen, Md. Alal and Chowdhury, Md. Sazzad Hossien (2015) A new analytical technique based on harmonic balance method to determine approximate periods for Duffing-harmonic oscillator. Alexandria Engineering Journal, 54 (2). pp. 233-239. ISSN 1110-0168

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Abstract

The Duffing-harmonic oscillator is a common model for nonlinear phenomena in science and engineering. In this paper, a new analytical technique has been presented to determine approximate periods of a strongly nonlinear Duffing-harmonic oscillator. Generally, a set of difficult nonlinear algebraic equations appear when harmonic balance method is imposed. The power series solutions of these equations are invalid. The proposed idea avoids this limitation and the necessity of numerically solving such nonlinear algebraic equations with very complex nonlinearities. In this technique, different parameters for the same nonlinear problems are found, for which the power series solution yields desired results. Besides a suitable truncation formula is found in which the solution measures better results than existing solutions. It is remarkable that this procedure is simple and takes less computational effort for determining second and higher order periods of oscillation for such nonlinear problems and shows a good agreement compared with the exact ones.

Item Type:	Article (Journal)
Additional Information:	5807/44796
Uncontrolled Keywords:	Duffing-hamonic oscillator; harmonic balance method; nonlinear algebraic equations; power series solutions; analytical technique; truncation principle
Subjects:	Q Science > QA Mathematics
Kulliyyahs/Centres/Divisions/Institutes (Can select more than one option. Press CONTROL button):	Kulliyyah of Engineering > Department of Science
Depositing User:	Dr. Md Sazzad Hossien Chowdhury
Date Deposited:	22 Sep 2015 15:33
Last Modified:	10 Nov 2017 11:09
URI:	http://irep.iium.edu.my/id/eprint/44796

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