A new analytical technique for solving nonlinear non-smooth oscillators based on the rational harmonic balance method
In the present paper, a new analytical technique based on the rational harmonic balance method (RHBM) has been introduced to determine approximate periodic solutions for the nonlinear non-smooth oscillator. A frequency–amplitude relationship has also been obtained by a novel analytical way. The stan...
| Main Authors: | , , , |
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| Format: | Proceeding Paper |
| Language: | English |
| Published: |
Springer Nature Singapore Pte Ltd.
2018
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| Subjects: | |
| Online Access: | http://irep.iium.edu.my/64006/ http://irep.iium.edu.my/64006/8/64006%20A%20New%20Analytical%20Technique%20for%20Solving%20Nonlinear.pdf |
| _version_ | 1848786130492719104 |
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| 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 | In the present paper, a new analytical technique based on the rational harmonic balance method (RHBM) has been introduced to determine approximate periodic solutions for the nonlinear non-smooth oscillator. A frequency–amplitude relationship has also been obtained by a novel analytical way. The standard rational harmonic balance method (SRHBM) cannot be used directly; it is possible if we rewrite the nonlinear differential equations (NDEs). To overcome this previously stated issue, we offered a modified rational harmonic balance method (MRHBM). It is noticed that a MRHBM works very well for the whole range of initial amplitudes and the excellent agreement of the approximate frequencies as well as the corresponding periodic solutions with its exact ones. The method is basically illustrated by the nonlinear non-smooth oscillators, but it is additionally useful for other nonlinear oscillatory problems with mixed parity arising in recent development of nonlinear sciences and engineering. |
| first_indexed | 2025-11-14T17:04:09Z |
| format | Proceeding Paper |
| id | iium-64006 |
| institution | International Islamic University Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-14T17:04:09Z |
| publishDate | 2018 |
| publisher | Springer Nature Singapore Pte Ltd. |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | iium-640062018-06-07T01:12:43Z http://irep.iium.edu.my/64006/ A new analytical technique for solving nonlinear non-smooth oscillators based on the rational harmonic balance method Hosen, Md. Alal Chowdhury, Md. Sazzad Hossien Ali, Mohammad Yeakub Ismail, Ahmad Faris T Technology (General) T55.4 Industrial engineering.Management engineering. TJ Mechanical engineering and machinery TS Manufactures In the present paper, a new analytical technique based on the rational harmonic balance method (RHBM) has been introduced to determine approximate periodic solutions for the nonlinear non-smooth oscillator. A frequency–amplitude relationship has also been obtained by a novel analytical way. The standard rational harmonic balance method (SRHBM) cannot be used directly; it is possible if we rewrite the nonlinear differential equations (NDEs). To overcome this previously stated issue, we offered a modified rational harmonic balance method (MRHBM). It is noticed that a MRHBM works very well for the whole range of initial amplitudes and the excellent agreement of the approximate frequencies as well as the corresponding periodic solutions with its exact ones. The method is basically illustrated by the nonlinear non-smooth oscillators, but it is additionally useful for other nonlinear oscillatory problems with mixed parity arising in recent development of nonlinear sciences and engineering. Springer Nature Singapore Pte Ltd. 2018 Proceeding Paper PeerReviewed application/pdf en http://irep.iium.edu.my/64006/8/64006%20A%20New%20Analytical%20Technique%20for%20Solving%20Nonlinear.pdf Hosen, Md. Alal and Chowdhury, Md. Sazzad Hossien and Ali, Mohammad Yeakub and Ismail, Ahmad Faris (2018) A new analytical technique for solving nonlinear non-smooth oscillators based on the rational harmonic balance method. In: Second International Conference on the Future of ASEAN (ICoFA) 2017, 15-16 August 2017, Kangar, Perlis. https://link.springer.com/chapter/10.1007/978-981-10-8471-3_45 10.1007/978-981-10-8471-3_45 |
| spellingShingle | T Technology (General) T55.4 Industrial engineering.Management engineering. TJ Mechanical engineering and machinery TS Manufactures Hosen, Md. Alal Chowdhury, Md. Sazzad Hossien Ali, Mohammad Yeakub Ismail, Ahmad Faris A new analytical technique for solving nonlinear non-smooth oscillators based on the rational harmonic balance method |
| title | A new analytical technique for solving nonlinear non-smooth oscillators based on the rational harmonic balance method |
| title_full | A new analytical technique for solving nonlinear non-smooth oscillators based on the rational harmonic balance method |
| title_fullStr | A new analytical technique for solving nonlinear non-smooth oscillators based on the rational harmonic balance method |
| title_full_unstemmed | A new analytical technique for solving nonlinear non-smooth oscillators based on the rational harmonic balance method |
| title_short | A new analytical technique for solving nonlinear non-smooth oscillators based on the rational harmonic balance method |
| title_sort | new analytical technique for solving nonlinear non-smooth oscillators based on the rational harmonic balance method |
| topic | T Technology (General) T55.4 Industrial engineering.Management engineering. TJ Mechanical engineering and machinery TS Manufactures |
| url | http://irep.iium.edu.my/64006/ http://irep.iium.edu.my/64006/ http://irep.iium.edu.my/64006/ http://irep.iium.edu.my/64006/8/64006%20A%20New%20Analytical%20Technique%20for%20Solving%20Nonlinear.pdf |