A novel analytical approximation technique for highly nonlinear oscillators based on the energy balance method

In the present paper, a novel analytical approximation technique has been proposed based on the energy balance method (EBM) to obtain approximate periodic solutions for the focus generalized highly nonlinear oscillators. The expressions of the natural frequency amplitude relationship are obtained us...

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Main Authors:	Hosen, Md. Alal, Chowdhury, Md. Sazzad Hossien, Ali, Mohammad Yeakub, Ismail, Ahmad Faris
Format:	Article
Language:	English English English
Published:	Elsevier 2016
Subjects:	QA Mathematics
Online Access:	http://irep.iium.edu.my/51653/ http://irep.iium.edu.my/51653/ http://irep.iium.edu.my/51653/ http://irep.iium.edu.my/51653/1/51653_A%20novel%20analytical%20approximation%20technique.pdf http://irep.iium.edu.my/51653/2/51653_A%20novel%20analytical%20approximation%20technique_SCOPUS.pdf http://irep.iium.edu.my/51653/3/51653_A%20novel%20analytical%20approximation%20technique_WOS.pdf

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recordtype	eprints
spelling	iium-516532017-05-30T03:53:57Z http://irep.iium.edu.my/51653/ A novel analytical approximation technique for highly nonlinear oscillators based on the energy balance method Hosen, Md. Alal Chowdhury, Md. Sazzad Hossien Ali, Mohammad Yeakub Ismail, Ahmad Faris QA Mathematics In the present paper, a novel analytical approximation technique has been proposed based on the energy balance method (EBM) to obtain approximate periodic solutions for the focus generalized highly nonlinear oscillators. The expressions of the natural frequency amplitude relationship are obtained using a novel analytical way. The accuracy of the proposed method is investigated on three benchmark oscillatory problems, namely, the simple relativistic oscillator, the stretched elastic wire oscillator (with a mass attached to its midpoint) and the Duffing-relativistic oscillator. For an initial oscillation amplitude Ao = 100 , the maximal relative errors of natural frequency found in three oscillators are 2.1637%, 0.0001% and 1.201%, respectively, which are much lower than the errors found using the existing methods. It is highly remarkable that an excellent accuracy of the approximate natural frequency has been found which is valid for the whole range of large values of oscillation amplitude as compared with the exact ones. Very simple solution procedure and high accuracy that is found in three benchmark problems reveal the novelty, reliability and wider applicability of the proposed analytical approximation technique. Elsevier 2016 Article PeerReviewed application/pdf en http://irep.iium.edu.my/51653/1/51653_A%20novel%20analytical%20approximation%20technique.pdf application/pdf en http://irep.iium.edu.my/51653/2/51653_A%20novel%20analytical%20approximation%20technique_SCOPUS.pdf application/pdf en http://irep.iium.edu.my/51653/3/51653_A%20novel%20analytical%20approximation%20technique_WOS.pdf Hosen, Md. Alal and Chowdhury, Md. Sazzad Hossien and Ali, Mohammad Yeakub and Ismail, Ahmad Faris (2016) A novel analytical approximation technique for highly nonlinear oscillators based on the energy balance method. Results in Physics, 6. pp. 496-504. ISSN 2211-3797 http://dx.doi.org/10.1016/j.rinp.2016.08.011 10.1016/j.rinp.2016.08.011
repository_type	Digital Repository
institution_category	Local University
institution	International Islamic University Malaysia
building	IIUM Repository
collection	Online Access
language	English English English
topic	QA Mathematics
spellingShingle	QA Mathematics Hosen, Md. Alal Chowdhury, Md. Sazzad Hossien Ali, Mohammad Yeakub Ismail, Ahmad Faris A novel analytical approximation technique for highly nonlinear oscillators based on the energy balance method
description	In the present paper, a novel analytical approximation technique has been proposed based on the energy balance method (EBM) to obtain approximate periodic solutions for the focus generalized highly nonlinear oscillators. The expressions of the natural frequency amplitude relationship are obtained using a novel analytical way. The accuracy of the proposed method is investigated on three benchmark oscillatory problems, namely, the simple relativistic oscillator, the stretched elastic wire oscillator (with a mass attached to its midpoint) and the Duffing-relativistic oscillator. For an initial oscillation amplitude Ao = 100 , the maximal relative errors of natural frequency found in three oscillators are 2.1637%, 0.0001% and 1.201%, respectively, which are much lower than the errors found using the existing methods. It is highly remarkable that an excellent accuracy of the approximate natural frequency has been found which is valid for the whole range of large values of oscillation amplitude as compared with the exact ones. Very simple solution procedure and high accuracy that is found in three benchmark problems reveal the novelty, reliability and wider applicability of the proposed analytical approximation technique.
format	Article
author	Hosen, Md. Alal Chowdhury, Md. Sazzad Hossien Ali, Mohammad Yeakub Ismail, Ahmad Faris
author_facet	Hosen, Md. Alal Chowdhury, Md. Sazzad Hossien Ali, Mohammad Yeakub Ismail, Ahmad Faris
author_sort	Hosen, Md. Alal
title	A novel analytical approximation technique for highly nonlinear oscillators based on the energy balance method
title_short	A novel analytical approximation technique for highly nonlinear oscillators based on the energy balance method
title_full	A novel analytical approximation technique for highly nonlinear oscillators based on the energy balance method
title_fullStr	A novel analytical approximation technique for highly nonlinear oscillators based on the energy balance method
title_full_unstemmed	A novel analytical approximation technique for highly nonlinear oscillators based on the energy balance method
title_sort	novel analytical approximation technique for highly nonlinear oscillators based on the energy balance method
publisher	Elsevier
publishDate	2016
url	http://irep.iium.edu.my/51653/ http://irep.iium.edu.my/51653/ http://irep.iium.edu.my/51653/ http://irep.iium.edu.my/51653/1/51653_A%20novel%20analytical%20approximation%20technique.pdf http://irep.iium.edu.my/51653/2/51653_A%20novel%20analytical%20approximation%20technique_SCOPUS.pdf http://irep.iium.edu.my/51653/3/51653_A%20novel%20analytical%20approximation%20technique_WOS.pdf
first_indexed	2023-09-18T21:13:09Z
last_indexed	2023-09-18T21:13:09Z
_version_	1777411387345076224

A novel analytical approximation technique for highly nonlinear oscillators based on the energy balance method

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