High-order approximate solutions of strongly nonlinear cubic-quintic Duffing oscillator based on the harmonic balance method

In this paper, a new reliable analytical technique has been introduced based on the Harmonic Balance Method (HBM) to determine higher-order approximate solutions of the strongly nonlinear cubicquintic Duffing oscillator. The application of the HBM leads to very complicated sets of nonlinear algebr...

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Main Authors:	Chowdhury, Md. Sazzad Hossien, Hosen, Md. Alal, Ahmad, Kartini, Ali, Mohammad Yeakub, Ismail, Ahmad Faris
Format:	Article
Language:	English English
Published:	Elsevier 2017
Subjects:	T Technology (General) TJ Mechanical engineering and machinery TS Manufactures
Online Access:	http://irep.iium.edu.my/60636/ http://irep.iium.edu.my/60636/ http://irep.iium.edu.my/60636/ http://irep.iium.edu.my/60636/1/025-2017%20Results%20in%20Physics.pdf http://irep.iium.edu.my/60636/7/60636_High-order%20approximate%20solutions_scopus.pdf

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recordtype	eprints
spelling	iium-606362018-07-10T09:37:59Z http://irep.iium.edu.my/60636/ High-order approximate solutions of strongly nonlinear cubic-quintic Duffing oscillator based on the harmonic balance method Chowdhury, Md. Sazzad Hossien Hosen, Md. Alal Ahmad, Kartini Ali, Mohammad Yeakub Ismail, Ahmad Faris T Technology (General) TJ Mechanical engineering and machinery TS Manufactures In this paper, a new reliable analytical technique has been introduced based on the Harmonic Balance Method (HBM) to determine higher-order approximate solutions of the strongly nonlinear cubicquintic Duffing oscillator. The application of the HBM leads to very complicated sets of nonlinear algebraic equations. In this technique, the high-order nonlinear algebraic equations are approximated in the form of a power series solution, and this solution produces desired results even for small as well as large amplitudes of oscillation. Moreover, a suitable truncation formula is found in which the solution measures better results than existing results and it saves a lot of calculation. It is highly noteworthy that using the proposed technique, the third-order approximate solutions gives an excellent agreement as compared with the numerical solutions (considered to be exact). The proposed technique is applied to the strongly nonlinear cubic-quintic Duffing oscillator to reveals its novelty, reliability and wider applicability. Elsevier 2017-10-08 Article PeerReviewed application/pdf en http://irep.iium.edu.my/60636/1/025-2017%20Results%20in%20Physics.pdf application/pdf en http://irep.iium.edu.my/60636/7/60636_High-order%20approximate%20solutions_scopus.pdf Chowdhury, Md. Sazzad Hossien and Hosen, Md. Alal and Ahmad, Kartini and Ali, Mohammad Yeakub and Ismail, Ahmad Faris (2017) High-order approximate solutions of strongly nonlinear cubic-quintic Duffing oscillator based on the harmonic balance method. Results in Physics, 7. pp. 3962-3967. E-ISSN 2211-3797 https://reader.elsevier.com/reader/sd/9E8D7837D218F55EEDF1C617D12D6E92E4BF3F5A852991314EA5E78FA2CBBCFB89A62D630BFBD70D723A46FB9C0BCC55 10.1016/j.rinp.2017.10.008
repository_type	Digital Repository
institution_category	Local University
institution	International Islamic University Malaysia
building	IIUM Repository
collection	Online Access
language	English English
topic	T Technology (General) TJ Mechanical engineering and machinery TS Manufactures
spellingShingle	T Technology (General) TJ Mechanical engineering and machinery TS Manufactures Chowdhury, Md. Sazzad Hossien Hosen, Md. Alal Ahmad, Kartini Ali, Mohammad Yeakub Ismail, Ahmad Faris High-order approximate solutions of strongly nonlinear cubic-quintic Duffing oscillator based on the harmonic balance method
description	In this paper, a new reliable analytical technique has been introduced based on the Harmonic Balance Method (HBM) to determine higher-order approximate solutions of the strongly nonlinear cubicquintic Duffing oscillator. The application of the HBM leads to very complicated sets of nonlinear algebraic equations. In this technique, the high-order nonlinear algebraic equations are approximated in the form of a power series solution, and this solution produces desired results even for small as well as large amplitudes of oscillation. Moreover, a suitable truncation formula is found in which the solution measures better results than existing results and it saves a lot of calculation. It is highly noteworthy that using the proposed technique, the third-order approximate solutions gives an excellent agreement as compared with the numerical solutions (considered to be exact). The proposed technique is applied to the strongly nonlinear cubic-quintic Duffing oscillator to reveals its novelty, reliability and wider applicability.
format	Article
author	Chowdhury, Md. Sazzad Hossien Hosen, Md. Alal Ahmad, Kartini Ali, Mohammad Yeakub Ismail, Ahmad Faris
author_facet	Chowdhury, Md. Sazzad Hossien Hosen, Md. Alal Ahmad, Kartini Ali, Mohammad Yeakub Ismail, Ahmad Faris
author_sort	Chowdhury, Md. Sazzad Hossien
title	High-order approximate solutions of strongly nonlinear cubic-quintic Duffing oscillator based on the harmonic balance method
title_short	High-order approximate solutions of strongly nonlinear cubic-quintic Duffing oscillator based on the harmonic balance method
title_full	High-order approximate solutions of strongly nonlinear cubic-quintic Duffing oscillator based on the harmonic balance method
title_fullStr	High-order approximate solutions of strongly nonlinear cubic-quintic Duffing oscillator based on the harmonic balance method
title_full_unstemmed	High-order approximate solutions of strongly nonlinear cubic-quintic Duffing oscillator based on the harmonic balance method
title_sort	high-order approximate solutions of strongly nonlinear cubic-quintic duffing oscillator based on the harmonic balance method
publisher	Elsevier
publishDate	2017
url	http://irep.iium.edu.my/60636/ http://irep.iium.edu.my/60636/ http://irep.iium.edu.my/60636/ http://irep.iium.edu.my/60636/1/025-2017%20Results%20in%20Physics.pdf http://irep.iium.edu.my/60636/7/60636_High-order%20approximate%20solutions_scopus.pdf
first_indexed	2023-09-18T21:25:58Z
last_indexed	2023-09-18T21:25:58Z
_version_	1777412192978599936

High-order approximate solutions of strongly nonlinear cubic-quintic Duffing oscillator based on the harmonic balance method

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