A comparison study on the harmonic balance method and rational harmonic balance method for the Duffing-harmonic oscillator
The Duffing-harmonic oscillator is a common model in nonlinear sciences and engineering. In the present paper, the harmonic balance method and rational harmonic balance method have been introduced to derive the approximate periods of strongly nonlinear Duffing-harmonic oscillator. The comparison of...
| Main Authors: | , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Research India Publications
2016
|
| Subjects: | |
| Online Access: | http://irep.iium.edu.my/51347/ http://irep.iium.edu.my/51347/1/gjpamv12n3_59.pdf |
| _version_ | 1848783835822555136 |
|---|---|
| author | Hosen, Md. Alal Chowdhury, Md. Sazzad Hossien Ali, Mohammad Yeakub Ismail, Ahmad Faris |
| author_facet | Hosen, Md. Alal Chowdhury, Md. Sazzad Hossien Ali, Mohammad Yeakub Ismail, Ahmad Faris |
| author_sort | Hosen, Md. Alal |
| building | IIUM Repository |
| collection | Online Access |
| description | The Duffing-harmonic oscillator is a common model in nonlinear sciences and engineering. In the present paper, the harmonic balance method and rational harmonic balance method have been introduced to derive the approximate
periods of strongly nonlinear Duffing-harmonic oscillator. The comparison of two methods is made to demonstrate that the rational harmonic balance method (RHBM) gives almost similar results to next higher-order approximation results of harmonic balance method (HBM). It is highly remarkable that the solution procedure in both methods are simple and takes less computational effort for determining approximate periods and shows a good agreement compared with the exact ones. |
| first_indexed | 2025-11-14T16:27:40Z |
| format | Article |
| id | iium-51347 |
| institution | International Islamic University Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-14T16:27:40Z |
| publishDate | 2016 |
| publisher | Research India Publications |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | iium-513472017-03-21T08:40:05Z http://irep.iium.edu.my/51347/ A comparison study on the harmonic balance method and rational harmonic balance method for the Duffing-harmonic oscillator Hosen, Md. Alal Chowdhury, Md. Sazzad Hossien Ali, Mohammad Yeakub Ismail, Ahmad Faris QA Mathematics QC Physics The Duffing-harmonic oscillator is a common model in nonlinear sciences and engineering. In the present paper, the harmonic balance method and rational harmonic balance method have been introduced to derive the approximate periods of strongly nonlinear Duffing-harmonic oscillator. The comparison of two methods is made to demonstrate that the rational harmonic balance method (RHBM) gives almost similar results to next higher-order approximation results of harmonic balance method (HBM). It is highly remarkable that the solution procedure in both methods are simple and takes less computational effort for determining approximate periods and shows a good agreement compared with the exact ones. Research India Publications 2016 Article PeerReviewed application/pdf en http://irep.iium.edu.my/51347/1/gjpamv12n3_59.pdf Hosen, Md. Alal and Chowdhury, Md. Sazzad Hossien and Ali, Mohammad Yeakub and Ismail, Ahmad Faris (2016) A comparison study on the harmonic balance method and rational harmonic balance method for the Duffing-harmonic oscillator. Global Journal of Pure and Applied Mathematics, 12 (3). pp. 2721-2732. ISSN 0973-1768 E-ISSN 0973-9750 http://www.ripublication.com/gjpam16/gjpamv12n3_59.pdf |
| spellingShingle | QA Mathematics QC Physics Hosen, Md. Alal Chowdhury, Md. Sazzad Hossien Ali, Mohammad Yeakub Ismail, Ahmad Faris A comparison study on the harmonic balance method and rational harmonic balance method for the Duffing-harmonic oscillator |
| title | A comparison study on the harmonic balance method
and rational harmonic balance method for the
Duffing-harmonic oscillator |
| title_full | A comparison study on the harmonic balance method
and rational harmonic balance method for the
Duffing-harmonic oscillator |
| title_fullStr | A comparison study on the harmonic balance method
and rational harmonic balance method for the
Duffing-harmonic oscillator |
| title_full_unstemmed | A comparison study on the harmonic balance method
and rational harmonic balance method for the
Duffing-harmonic oscillator |
| title_short | A comparison study on the harmonic balance method
and rational harmonic balance method for the
Duffing-harmonic oscillator |
| title_sort | comparison study on the harmonic balance method
and rational harmonic balance method for the
duffing-harmonic oscillator |
| topic | QA Mathematics QC Physics |
| url | http://irep.iium.edu.my/51347/ http://irep.iium.edu.my/51347/ http://irep.iium.edu.my/51347/1/gjpamv12n3_59.pdf |