Analytical approximations for the oscillators with anti-symmetric quadratic nonlinearity
A second-order ordinary differential equation involving anti-symmetric quadratic nonlinearity changes sign. The behaviour of the oscillators with an anti-symmetric quadratic nonlinearity is assumed to oscillate different in the positive and negative directions. In this reason, Harmonic Balance Me...
| Main Authors: | , , , |
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| Format: | Proceeding Paper |
| Language: | English English |
| Published: |
IOP Publishing
2018
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| Subjects: | |
| Online Access: | http://irep.iium.edu.my/61802/ http://irep.iium.edu.my/61802/7/61802-Analytical%20approximations%20for%20the%20oscillators.pdf http://irep.iium.edu.my/61802/13/61802%20Analytical%20approximations%20for%20the%20oscillators%20with%20anti-symmetric%20SCOPUS.pdf |
| _version_ | 1848785736444149760 |
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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 | A second-order ordinary differential equation involving anti-symmetric quadratic
nonlinearity changes sign. The behaviour of the oscillators with an anti-symmetric quadratic
nonlinearity is assumed to oscillate different in the positive and negative directions. In this
reason, Harmonic Balance Method (HBM) cannot be directly applied. The main purpose of the
present paper is to propose an analytical approximation technique based on the HBM for
obtaining approximate angular frequencies and the corresponding periodic solutions of the
oscillators with anti-symmetric quadratic nonlinearity. After applying HBM, a set of
complicated nonlinear algebraic equations is found. Analytical approach is not always fruitful
for solving such kinds of nonlinear algebraic equations. In this article, two small parameters
are found, for which the power series solution produces desired results. Moreover, the
amplitude-frequency relationship has also been determined in a novel analytical way. The
presented technique gives excellent results as compared with the corresponding numerical
results and is better than the existing ones. |
| first_indexed | 2025-11-14T16:57:53Z |
| format | Proceeding Paper |
| id | iium-61802 |
| institution | International Islamic University Malaysia |
| institution_category | Local University |
| language | English English |
| last_indexed | 2025-11-14T16:57:53Z |
| publishDate | 2018 |
| publisher | IOP Publishing |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | iium-618022018-06-26T07:03:36Z http://irep.iium.edu.my/61802/ Analytical approximations for the oscillators with anti-symmetric quadratic nonlinearity Hosen, Md. Alal Chowdhury, Md. Sazzad Hossien Ali, Mohammad Yeakub Ismail, Ahmad Faris QA297 Numerical Analysis A second-order ordinary differential equation involving anti-symmetric quadratic nonlinearity changes sign. The behaviour of the oscillators with an anti-symmetric quadratic nonlinearity is assumed to oscillate different in the positive and negative directions. In this reason, Harmonic Balance Method (HBM) cannot be directly applied. The main purpose of the present paper is to propose an analytical approximation technique based on the HBM for obtaining approximate angular frequencies and the corresponding periodic solutions of the oscillators with anti-symmetric quadratic nonlinearity. After applying HBM, a set of complicated nonlinear algebraic equations is found. Analytical approach is not always fruitful for solving such kinds of nonlinear algebraic equations. In this article, two small parameters are found, for which the power series solution produces desired results. Moreover, the amplitude-frequency relationship has also been determined in a novel analytical way. The presented technique gives excellent results as compared with the corresponding numerical results and is better than the existing ones. IOP Publishing 2018-01-02 Proceeding Paper PeerReviewed application/pdf en http://irep.iium.edu.my/61802/7/61802-Analytical%20approximations%20for%20the%20oscillators.pdf application/pdf en http://irep.iium.edu.my/61802/13/61802%20Analytical%20approximations%20for%20the%20oscillators%20with%20anti-symmetric%20SCOPUS.pdf Hosen, Md. Alal and Chowdhury, Md. Sazzad Hossien and Ali, Mohammad Yeakub and Ismail, Ahmad Faris (2018) Analytical approximations for the oscillators with anti-symmetric quadratic nonlinearity. In: 4th International Conference on Mathematical Applications in Engineering 2017 (ICMAE'17), 8th–9th August 2017, Kuala Lumpur, Malaysia. http://iopscience.iop.org/article/10.1088/1742-6596/949/1/012006/pdf 10.1088/1742-6596/949/1/012006 |
| spellingShingle | QA297 Numerical Analysis Hosen, Md. Alal Chowdhury, Md. Sazzad Hossien Ali, Mohammad Yeakub Ismail, Ahmad Faris Analytical approximations for the oscillators with anti-symmetric quadratic nonlinearity |
| title | Analytical approximations for the oscillators with anti-symmetric quadratic nonlinearity |
| title_full | Analytical approximations for the oscillators with anti-symmetric quadratic nonlinearity |
| title_fullStr | Analytical approximations for the oscillators with anti-symmetric quadratic nonlinearity |
| title_full_unstemmed | Analytical approximations for the oscillators with anti-symmetric quadratic nonlinearity |
| title_short | Analytical approximations for the oscillators with anti-symmetric quadratic nonlinearity |
| title_sort | analytical approximations for the oscillators with anti-symmetric quadratic nonlinearity |
| topic | QA297 Numerical Analysis |
| url | http://irep.iium.edu.my/61802/ http://irep.iium.edu.my/61802/ http://irep.iium.edu.my/61802/ http://irep.iium.edu.my/61802/7/61802-Analytical%20approximations%20for%20the%20oscillators.pdf http://irep.iium.edu.my/61802/13/61802%20Analytical%20approximations%20for%20the%20oscillators%20with%20anti-symmetric%20SCOPUS.pdf |