Analytical approximate solutions for the Helmholtz-Duffing oscillator

Analytical approximate solutions for the Helmholtz-Duffing oscillator

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. Generall...

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Main Authors: Md. Alal, Hosen, Chowdhury, Md. Sazzad Hossien
Format: Article
Language:English
Published: Asian Research Publishing Network (ARPN) 2015
Subjects:
QA76 Computer software
Online Access:http://irep.iium.edu.my/47978/
http://irep.iium.edu.my/47978/
http://irep.iium.edu.my/47978/1/Analytical_approximate_solutions_for_the_Helmholtz-Duffing_oscillator_-.pdf
id iium-47978
recordtype eprints
spelling iium-479782016-07-18T03:42:19Z http://irep.iium.edu.my/47978/ Analytical approximate solutions for the Helmholtz-Duffing oscillator Md. Alal, Hosen Chowdhury, Md. Sazzad Hossien QA76 Computer software 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. Asian Research Publishing Network (ARPN) 2015-12 Article PeerReviewed application/pdf en http://irep.iium.edu.my/47978/1/Analytical_approximate_solutions_for_the_Helmholtz-Duffing_oscillator_-.pdf 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 http://www.arpnjournals.com/
repository_type Digital Repository
institution_category Local University
institution International Islamic University Malaysia
building IIUM Repository
collection Online Access
language English
topic QA76 Computer software
spellingShingle QA76 Computer software
Md. Alal, Hosen
Chowdhury, Md. Sazzad Hossien
Analytical approximate solutions for the Helmholtz-Duffing oscillator
description 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.
format Article
author Md. Alal, Hosen
Chowdhury, Md. Sazzad Hossien
author_facet Md. Alal, Hosen
Chowdhury, Md. Sazzad Hossien
author_sort Md. Alal, Hosen
title Analytical approximate solutions for the Helmholtz-Duffing oscillator
title_short Analytical approximate solutions for the Helmholtz-Duffing oscillator
title_full Analytical approximate solutions for the Helmholtz-Duffing oscillator
title_fullStr Analytical approximate solutions for the Helmholtz-Duffing oscillator
title_full_unstemmed Analytical approximate solutions for the Helmholtz-Duffing oscillator
title_sort analytical approximate solutions for the helmholtz-duffing oscillator
publisher Asian Research Publishing Network (ARPN)
publishDate 2015
url http://irep.iium.edu.my/47978/
http://irep.iium.edu.my/47978/
http://irep.iium.edu.my/47978/1/Analytical_approximate_solutions_for_the_Helmholtz-Duffing_oscillator_-.pdf
first_indexed 2023-09-18T21:08:10Z
last_indexed 2023-09-18T21:08:10Z
_version_ 1777411074042101760

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