Accurate approximations of the nonlinear vibration of couple-mass-spring systems with linear and nonlinear stiffnesses

An analytical technique has been developed based on the harmonic balance method to obtain approximate angular frequencies. This technique also offers the periodic solutions to the nonlinear free vibration of a conservative, couple-mass-spring system having linear and nonlinear stiffnesses with cubic...

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Main Authors:	Hosen, Md. Alal, Chowdhury, Md. Sazzad Hossien
Format:	Article
Language:	English English English
Published:	SAGE Publications 2019
Subjects:	QA297 Numerical Analysis
Online Access:	http://irep.iium.edu.my/74562/ http://irep.iium.edu.my/74562/ http://irep.iium.edu.my/74562/13/LFN854625_rev3.pdf http://irep.iium.edu.my/74562/20/Acceptance%20Letter%20LFN%20Manuscript%20ID%20LFN-19-0072.pdf http://irep.iium.edu.my/74562/26/74562_Accurate%20approximations%20of%20the%20nonlinear%20vibration%20of%20couple-mass-spring%20systems%20with%20linear%20and%20nonlinear%20stiffnesses_Scopus.pdf

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spelling	iium-745622019-11-19T08:36:27Z http://irep.iium.edu.my/74562/ Accurate approximations of the nonlinear vibration of couple-mass-spring systems with linear and nonlinear stiffnesses Hosen, Md. Alal Chowdhury, Md. Sazzad Hossien QA297 Numerical Analysis An analytical technique has been developed based on the harmonic balance method to obtain approximate angular frequencies. This technique also offers the periodic solutions to the nonlinear free vibration of a conservative, couple-mass-spring system having linear and nonlinear stiffnesses with cubic nonlinearity. Two real-world cases of these systems are analysed and introduced. After applying the harmonic balance method, a set of complicated higher-order nonlinear algebraic equations are obtained. Analytical investigation of the complicated higher-order nonlinear algebraic equations is cumbersome, especially in the case when the vibration amplitude of the oscillation is large. The proposed technique overcomes this limitation to utilize the iterative method based on the homotopy perturbation method. This produces desired results for small as well as large values of vibration amplitude of the oscillation. In addition, a new suitable truncation principle has been used in which the solution achieves better results than existing solutions. Comparing with published results and the exact ones, the approximated angular frequencies and corresponding periodic solutions show excellent agreement. This proposed technique provides results of high accuracy and a simple solution procedure. It could be widely applicable to other nonlinear oscillatory problems arising in science and engineering. SAGE Publications 2019 Article PeerReviewed application/pdf en http://irep.iium.edu.my/74562/13/LFN854625_rev3.pdf application/pdf en http://irep.iium.edu.my/74562/20/Acceptance%20Letter%20LFN%20Manuscript%20ID%20LFN-19-0072.pdf application/pdf en http://irep.iium.edu.my/74562/26/74562_Accurate%20approximations%20of%20the%20nonlinear%20vibration%20of%20couple-mass-spring%20systems%20with%20linear%20and%20nonlinear%20stiffnesses_Scopus.pdf Hosen, Md. Alal and Chowdhury, Md. Sazzad Hossien (2019) Accurate approximations of the nonlinear vibration of couple-mass-spring systems with linear and nonlinear stiffnesses. Journal of Low Frequency Noise, Vibration & Active Control. ISSN 1461-3484 E-ISSN 2048-4046 (In Press) 10.1177/1461348419854625
repository_type	Digital Repository
institution_category	Local University
institution	International Islamic University Malaysia
building	IIUM Repository
collection	Online Access
language	English English English
topic	QA297 Numerical Analysis
spellingShingle	QA297 Numerical Analysis Hosen, Md. Alal Chowdhury, Md. Sazzad Hossien Accurate approximations of the nonlinear vibration of couple-mass-spring systems with linear and nonlinear stiffnesses
description	An analytical technique has been developed based on the harmonic balance method to obtain approximate angular frequencies. This technique also offers the periodic solutions to the nonlinear free vibration of a conservative, couple-mass-spring system having linear and nonlinear stiffnesses with cubic nonlinearity. Two real-world cases of these systems are analysed and introduced. After applying the harmonic balance method, a set of complicated higher-order nonlinear algebraic equations are obtained. Analytical investigation of the complicated higher-order nonlinear algebraic equations is cumbersome, especially in the case when the vibration amplitude of the oscillation is large. The proposed technique overcomes this limitation to utilize the iterative method based on the homotopy perturbation method. This produces desired results for small as well as large values of vibration amplitude of the oscillation. In addition, a new suitable truncation principle has been used in which the solution achieves better results than existing solutions. Comparing with published results and the exact ones, the approximated angular frequencies and corresponding periodic solutions show excellent agreement. This proposed technique provides results of high accuracy and a simple solution procedure. It could be widely applicable to other nonlinear oscillatory problems arising in science and engineering.
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	Accurate approximations of the nonlinear vibration of couple-mass-spring systems with linear and nonlinear stiffnesses
title_short	Accurate approximations of the nonlinear vibration of couple-mass-spring systems with linear and nonlinear stiffnesses
title_full	Accurate approximations of the nonlinear vibration of couple-mass-spring systems with linear and nonlinear stiffnesses
title_fullStr	Accurate approximations of the nonlinear vibration of couple-mass-spring systems with linear and nonlinear stiffnesses
title_full_unstemmed	Accurate approximations of the nonlinear vibration of couple-mass-spring systems with linear and nonlinear stiffnesses
title_sort	accurate approximations of the nonlinear vibration of couple-mass-spring systems with linear and nonlinear stiffnesses
publisher	SAGE Publications
publishDate	2019
url	http://irep.iium.edu.my/74562/ http://irep.iium.edu.my/74562/ http://irep.iium.edu.my/74562/13/LFN854625_rev3.pdf http://irep.iium.edu.my/74562/20/Acceptance%20Letter%20LFN%20Manuscript%20ID%20LFN-19-0072.pdf http://irep.iium.edu.my/74562/26/74562_Accurate%20approximations%20of%20the%20nonlinear%20vibration%20of%20couple-mass-spring%20systems%20with%20linear%20and%20nonlinear%20stiffnesses_Scopus.pdf
first_indexed	2023-09-18T21:45:33Z
last_indexed	2023-09-18T21:45:33Z
_version_	1777413425444421632

Accurate approximations of the nonlinear vibration of couple-mass-spring systems with linear and nonlinear stiffnesses

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