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

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...

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Main Authors:	Hosen, Md. Alal, Chowdhury, Md. Sazzad Hossien
Format:	Article
Language:	English English
Published:	Published by Elsevier 2015
Subjects:	QA Mathematics
Online Access:	http://irep.iium.edu.my/44796/ http://irep.iium.edu.my/44796/ http://irep.iium.edu.my/44796/ http://irep.iium.edu.my/44796/1/A_new_analytical_technique_based_on_harmonic_balance_method_to_determine_approximate_periods_for_Duffing-harmonic_oscillator.pdf http://irep.iium.edu.my/44796/4/44796__WOS_and_SCOPUS.pdf

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recordtype	eprints
spelling	iium-447962017-11-10T03:09:16Z http://irep.iium.edu.my/44796/ A new analytical technique based on harmonic balance method to determine approximate periods for Duffing-harmonic oscillator Hosen, Md. Alal Chowdhury, Md. Sazzad Hossien QA Mathematics 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. Published by Elsevier 2015-06 Article PeerReviewed application/pdf en http://irep.iium.edu.my/44796/1/A_new_analytical_technique_based_on_harmonic_balance_method_to_determine_approximate_periods_for_Duffing-harmonic_oscillator.pdf application/pdf en http://irep.iium.edu.my/44796/4/44796__WOS_and_SCOPUS.pdf 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 http://www.sciencedirect.com/science/article/pii/S111001681500023X 10.1016/j.aej.2015.03.009
repository_type	Digital Repository
institution_category	Local University
institution	International Islamic University Malaysia
building	IIUM Repository
collection	Online Access
language	English English
topic	QA Mathematics
spellingShingle	QA Mathematics Hosen, Md. Alal Chowdhury, Md. Sazzad Hossien A new analytical technique based on harmonic balance method to determine approximate periods for Duffing-harmonic oscillator
description	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.
format	Article
author	Hosen, Md. Alal Chowdhury, Md. Sazzad Hossien
author_facet	Hosen, Md. Alal Chowdhury, Md. Sazzad Hossien
author_sort	Hosen, Md. Alal
title	A new analytical technique based on harmonic balance method to determine approximate periods for Duffing-harmonic oscillator
title_short	A new analytical technique based on harmonic balance method to determine approximate periods for Duffing-harmonic oscillator
title_full	A new analytical technique based on harmonic balance method to determine approximate periods for Duffing-harmonic oscillator
title_fullStr	A new analytical technique based on harmonic balance method to determine approximate periods for Duffing-harmonic oscillator
title_full_unstemmed	A new analytical technique based on harmonic balance method to determine approximate periods for Duffing-harmonic oscillator
title_sort	new analytical technique based on harmonic balance method to determine approximate periods for duffing-harmonic oscillator
publisher	Published by Elsevier
publishDate	2015
url	http://irep.iium.edu.my/44796/ http://irep.iium.edu.my/44796/ http://irep.iium.edu.my/44796/ http://irep.iium.edu.my/44796/1/A_new_analytical_technique_based_on_harmonic_balance_method_to_determine_approximate_periods_for_Duffing-harmonic_oscillator.pdf http://irep.iium.edu.my/44796/4/44796__WOS_and_SCOPUS.pdf
first_indexed	2023-09-18T21:03:41Z
last_indexed	2023-09-18T21:03:41Z
_version_	1777410791249543168

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

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