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

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)

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Abstract

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.

Item Type:	Article (Journal)
Additional Information:	5807/74562
Uncontrolled Keywords:	Nonlinear stiffnesses; Harmonic balance method; Iterative method; Homotopy perturbation method; Couple-mass-spring systems; Two-degree-of-freedom oscillation systems; Duffing equation
Subjects:	Q Science > QA Mathematics > QA297 Numerical Analysis
Kulliyyahs/Centres/Divisions/Institutes (Can select more than one option. Press CONTROL button):	Kulliyyah of Engineering > Department of Science
Depositing User:	Dr. Md Sazzad Hossien Chowdhury
Date Deposited:	24 Sep 2019 09:31
Last Modified:	19 Nov 2019 16:36
URI:	http://irep.iium.edu.my/id/eprint/74562

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• Accurate approximations of the nonlinear vibration of couple-mass-spring systems with linear and nonlinear stiffnesses. (deposited 26 Jul 2019 08:41)
  • Accurate approximations of the nonlinear vibration of couple-mass-spring systems with linear and nonlinear stiffnesses. (deposited 24 Sep 2019 09:31) [Currently Displayed]

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