A simple modified harmonic balance method for strongly nonlinear oscillator with cubic non-linearity and harmonic restoring force
In this article, a very simple modified form of the harmonic balance method is used to solve a strongly nonlinear oscillator with cubic nonlinearity and harmonic restoring force. Taylor series expansion up to third term is considered for the harmonic restoring force. The first approximate solutions...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
SAGE Publishing
2024-03-01
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| Series: | Journal of Low Frequency Noise, Vibration and Active Control |
| Online Access: | https://doi.org/10.1177/14613484231198958 |
| _version_ | 1797304060827664384 |
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| author | Nazmul Sharif Helal Uddin Molla Abdul Alim |
| author_facet | Nazmul Sharif Helal Uddin Molla Abdul Alim |
| author_sort | Nazmul Sharif |
| collection | DOAJ |
| description | In this article, a very simple modified form of the harmonic balance method is used to solve a strongly nonlinear oscillator with cubic nonlinearity and harmonic restoring force. Taylor series expansion up to third term is considered for the harmonic restoring force. The first approximate solutions of the present method pleasantly agree with the numerical solution obtained by Runge–Kutta fourth order method. Accuracy and simplicity of the present method solution is established when compared with the other method solutions. The present method can be utilized to other nonlinear oscillators. |
| first_indexed | 2024-03-08T00:03:58Z |
| format | Article |
| id | doaj.art-47922d7f533949cb9dedd2cba9436b82 |
| institution | Directory Open Access Journal |
| issn | 1461-3484 2048-4046 |
| language | English |
| last_indexed | 2024-03-08T00:03:58Z |
| publishDate | 2024-03-01 |
| publisher | SAGE Publishing |
| record_format | Article |
| series | Journal of Low Frequency Noise, Vibration and Active Control |
| spelling | doaj.art-47922d7f533949cb9dedd2cba9436b822024-02-17T11:05:35ZengSAGE PublishingJournal of Low Frequency Noise, Vibration and Active Control1461-34842048-40462024-03-014310.1177/14613484231198958A simple modified harmonic balance method for strongly nonlinear oscillator with cubic non-linearity and harmonic restoring forceNazmul SharifHelal Uddin MollaAbdul AlimIn this article, a very simple modified form of the harmonic balance method is used to solve a strongly nonlinear oscillator with cubic nonlinearity and harmonic restoring force. Taylor series expansion up to third term is considered for the harmonic restoring force. The first approximate solutions of the present method pleasantly agree with the numerical solution obtained by Runge–Kutta fourth order method. Accuracy and simplicity of the present method solution is established when compared with the other method solutions. The present method can be utilized to other nonlinear oscillators.https://doi.org/10.1177/14613484231198958 |
| spellingShingle | Nazmul Sharif Helal Uddin Molla Abdul Alim A simple modified harmonic balance method for strongly nonlinear oscillator with cubic non-linearity and harmonic restoring force Journal of Low Frequency Noise, Vibration and Active Control |
| title | A simple modified harmonic balance method for strongly nonlinear oscillator with cubic non-linearity and harmonic restoring force |
| title_full | A simple modified harmonic balance method for strongly nonlinear oscillator with cubic non-linearity and harmonic restoring force |
| title_fullStr | A simple modified harmonic balance method for strongly nonlinear oscillator with cubic non-linearity and harmonic restoring force |
| title_full_unstemmed | A simple modified harmonic balance method for strongly nonlinear oscillator with cubic non-linearity and harmonic restoring force |
| title_short | A simple modified harmonic balance method for strongly nonlinear oscillator with cubic non-linearity and harmonic restoring force |
| title_sort | simple modified harmonic balance method for strongly nonlinear oscillator with cubic non linearity and harmonic restoring force |
| url | https://doi.org/10.1177/14613484231198958 |
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