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...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Asian Research Publishing Network (ARPN)
2015
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| Subjects: | |
| Online Access: | http://irep.iium.edu.my/47978/ http://irep.iium.edu.my/47978/1/Analytical_approximate_solutions_for_the_Helmholtz-Duffing_oscillator_-.pdf |
| _version_ | 1848783229885087744 |
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| author | Md. Alal, Hosen Chowdhury, Md. Sazzad Hossien |
| author_facet | Md. Alal, Hosen Chowdhury, Md. Sazzad Hossien |
| author_sort | Md. Alal, Hosen |
| building | IIUM Repository |
| collection | Online Access |
| 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. |
| first_indexed | 2025-11-14T16:18:02Z |
| format | Article |
| id | iium-47978 |
| institution | International Islamic University Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-14T16:18:02Z |
| publishDate | 2015 |
| publisher | Asian Research Publishing Network (ARPN) |
| recordtype | eprints |
| repository_type | Digital Repository |
| 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/ |
| spellingShingle | QA76 Computer software Md. Alal, Hosen Chowdhury, Md. Sazzad Hossien Analytical approximate solutions for the Helmholtz-Duffing oscillator |
| title | 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_short | Analytical approximate solutions for the Helmholtz-Duffing oscillator |
| title_sort | analytical approximate solutions for the helmholtz-duffing oscillator |
| topic | QA76 Computer software |
| 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 |