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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/44796/1/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
http://irep.iium.edu.my/44796/
http://www.sciencedirect.com/science/article/pii/S111001681500023X
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spelling my.iium.irep.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 REM 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
institution Universiti Islam Antarabangsa Malaysia
building IIUM Library
collection Institutional Repository
continent Asia
country Malaysia
content_provider International Islamic University Malaysia
content_source IIUM Repository (IREP)
url_provider http://irep.iium.edu.my/
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/44796/1/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
http://irep.iium.edu.my/44796/
http://www.sciencedirect.com/science/article/pii/S111001681500023X
_version_ 1643612645197086720
score 13.211869

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