Approximate solutions for strongly nonlinear oscillators by using Harmonic Balance Method
We introduce an analytical technique to solve strongly nonlinear oscillators with cubic and harmonic restoring force by using harmonic balance method (HBM). A set of nonlinear algebraic equations is appeared when HBM is imposed. In this paper, a power series solutions of these nonlinear algebraic eq...
| Main Authors: | , |
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| Format: | Proceeding Paper |
| Language: | English |
| Published: |
2015
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| Subjects: | |
| Online Access: | http://irep.iium.edu.my/44869/ http://irep.iium.edu.my/44869/1/44869.pdf |
| _version_ | 1848782682587136000 |
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| author | Hosen, Md. Alal Chowdhury, Md. Sazzad Hossien |
| author_facet | Hosen, Md. Alal Chowdhury, Md. Sazzad Hossien |
| author_sort | Hosen, Md. Alal |
| building | IIUM Repository |
| collection | Online Access |
| description | We introduce an analytical technique to solve strongly nonlinear oscillators with cubic and harmonic restoring force by using harmonic balance method (HBM). A set of nonlinear algebraic equations is appeared when HBM is imposed. In this paper, a power series solutions of these nonlinear algebraic equations gives desired results and to avoid numerical complexity. A very good agreement was found between approximate and numerical solutions, which prove that HBM is very efficient and produces high accuracy results. We found that, a second order HBM works very well and the excellent agreement of the approximate solutions with the numerical solutions. The advantage of this method is its simple procedure and applicable for many oscillatory problems arising in science and engineering. |
| first_indexed | 2025-11-14T16:09:20Z |
| format | Proceeding Paper |
| id | iium-44869 |
| institution | International Islamic University Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-14T16:09:20Z |
| publishDate | 2015 |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | iium-448692015-10-05T01:12:49Z http://irep.iium.edu.my/44869/ Approximate solutions for strongly nonlinear oscillators by using Harmonic Balance Method Hosen, Md. Alal Chowdhury, Md. Sazzad Hossien QA Mathematics We introduce an analytical technique to solve strongly nonlinear oscillators with cubic and harmonic restoring force by using harmonic balance method (HBM). A set of nonlinear algebraic equations is appeared when HBM is imposed. In this paper, a power series solutions of these nonlinear algebraic equations gives desired results and to avoid numerical complexity. A very good agreement was found between approximate and numerical solutions, which prove that HBM is very efficient and produces high accuracy results. We found that, a second order HBM works very well and the excellent agreement of the approximate solutions with the numerical solutions. The advantage of this method is its simple procedure and applicable for many oscillatory problems arising in science and engineering. 2015 Proceeding Paper PeerReviewed application/pdf en http://irep.iium.edu.my/44869/1/44869.pdf Hosen, Md. Alal and Chowdhury, Md. Sazzad Hossien (2015) Approximate solutions for strongly nonlinear oscillators by using Harmonic Balance Method. In: 2nd International Conference on Mathematical Sciences & Computer Engineering (ICMSCE 2015), 5th-6th February 2015, Langkawi, Malaysia. (In Press) http://www.icmsce.net/cms/ |
| spellingShingle | QA Mathematics Hosen, Md. Alal Chowdhury, Md. Sazzad Hossien Approximate solutions for strongly nonlinear oscillators by using Harmonic Balance Method |
| title | Approximate solutions for strongly nonlinear oscillators by using Harmonic Balance Method |
| title_full | Approximate solutions for strongly nonlinear oscillators by using Harmonic Balance Method |
| title_fullStr | Approximate solutions for strongly nonlinear oscillators by using Harmonic Balance Method |
| title_full_unstemmed | Approximate solutions for strongly nonlinear oscillators by using Harmonic Balance Method |
| title_short | Approximate solutions for strongly nonlinear oscillators by using Harmonic Balance Method |
| title_sort | approximate solutions for strongly nonlinear oscillators by using harmonic balance method |
| topic | QA Mathematics |
| url | http://irep.iium.edu.my/44869/ http://irep.iium.edu.my/44869/ http://irep.iium.edu.my/44869/1/44869.pdf |