Analytical approximate solutions for the Helmholtz-Duffing oscillator

Md. Alal, Hosen and Chowdhury, Md. Sazzad Hossien (2015) Analytical approximate solutions for the Helmholtz-Duffing oscillator. ARPN Journal of Engineering and Applied Sciences, 10 (23). pp. 17363-17369. ISSN 1819-6608

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Abstract

In the present paper, analytical approximate periodic solutions for the Helmholtz-Duffing oscillator are obtained. Modified Harmonic Balance Method (MHBM) is adopted as the solution method. A classical harmonic balance method does not apply directly for solving Helmholtz-Duffing oscillator. Generally, a set of difficult nonlinear algebraic equations is found when MHBM is applied. Investigating analytically for such kinds of nonlinear algebraic equations is a tremendously difficult task and cumbersome especially for large amplitude. In this work, the offered technique eradicate this aforementioned limitation and to avoid numerical complexity. Using iterative homotopy perturbation method, only two or three iteration produces desired results even for large oscillation. It is remarkably important that a second-order approximate solution gives excellent agreement compared to exact ones.

Item Type:	Article (Journal)
Additional Information:	5807/47978
Uncontrolled Keywords:	helmholtz-duffing oscillator, harmonic balance method, iterative homotopy perturbation method
Subjects:	Q Science > QA Mathematics > QA76 Computer software
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:	18 Jan 2016 09:50
Last Modified:	18 Jul 2016 11:42
URI:	http://irep.iium.edu.my/id/eprint/47978

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