Estimated the frequencies of a coupled damped nonlinear oscillator with the non-Perturbative method
The current article is concerned with a comprehensive investigation of achieving the simplest solution of non-conservative coupled nonlinear forced oscillators. The article mainly depends on a non-perturbative method. It depends on yielding an equivalent linear system. The advantage of this linear s...
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| Format: | Article |
| Language: | English |
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SAGE Publishing
2023-03-01
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| Series: | Journal of Low Frequency Noise, Vibration and Active Control |
| Online Access: | https://doi.org/10.1177/14613484221130148 |
| _version_ | 1828014306891923456 |
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| author | Yusry O El-Dib |
| author_facet | Yusry O El-Dib |
| author_sort | Yusry O El-Dib |
| collection | DOAJ |
| description | The current article is concerned with a comprehensive investigation of achieving the simplest solution of non-conservative coupled nonlinear forced oscillators. The article mainly depends on a non-perturbative method. It depends on yielding an equivalent linear system. The advantage of this linear system is that its coefficients are easily computed and that they include the effects of the original nonlinear coefficients. This linearization approach allows achieving quasi-exact solutions even in the presence of periodic forces. The relationships of frequencies with amplitudes are easily established. The analytical solution so yielded may serve as a basis for a qualitative understanding of the actual behavior of the coupled nonlinear oscillators. Additionally, numerical calculations are carried out graphically to address the validation of the new approach and to further illustrate the effectiveness and convenience of the method. The results are compared with the exact numerical solutions which show perfect accuracy. The method can be easily extended to other nonlinear systems and can therefore be exceedingly applicable in engineering and other sciences. |
| first_indexed | 2024-04-10T10:00:03Z |
| format | Article |
| id | doaj.art-689b1ab396be4951995ee2227b74d8a4 |
| institution | Directory Open Access Journal |
| issn | 1461-3484 2048-4046 |
| language | English |
| last_indexed | 2024-04-10T10:00:03Z |
| publishDate | 2023-03-01 |
| publisher | SAGE Publishing |
| record_format | Article |
| series | Journal of Low Frequency Noise, Vibration and Active Control |
| spelling | doaj.art-689b1ab396be4951995ee2227b74d8a42023-02-16T09:34:19ZengSAGE PublishingJournal of Low Frequency Noise, Vibration and Active Control1461-34842048-40462023-03-014210.1177/14613484221130148Estimated the frequencies of a coupled damped nonlinear oscillator with the non-Perturbative methodYusry O El-DibThe current article is concerned with a comprehensive investigation of achieving the simplest solution of non-conservative coupled nonlinear forced oscillators. The article mainly depends on a non-perturbative method. It depends on yielding an equivalent linear system. The advantage of this linear system is that its coefficients are easily computed and that they include the effects of the original nonlinear coefficients. This linearization approach allows achieving quasi-exact solutions even in the presence of periodic forces. The relationships of frequencies with amplitudes are easily established. The analytical solution so yielded may serve as a basis for a qualitative understanding of the actual behavior of the coupled nonlinear oscillators. Additionally, numerical calculations are carried out graphically to address the validation of the new approach and to further illustrate the effectiveness and convenience of the method. The results are compared with the exact numerical solutions which show perfect accuracy. The method can be easily extended to other nonlinear systems and can therefore be exceedingly applicable in engineering and other sciences.https://doi.org/10.1177/14613484221130148 |
| spellingShingle | Yusry O El-Dib Estimated the frequencies of a coupled damped nonlinear oscillator with the non-Perturbative method Journal of Low Frequency Noise, Vibration and Active Control |
| title | Estimated the frequencies of a coupled damped nonlinear oscillator with the non-Perturbative method |
| title_full | Estimated the frequencies of a coupled damped nonlinear oscillator with the non-Perturbative method |
| title_fullStr | Estimated the frequencies of a coupled damped nonlinear oscillator with the non-Perturbative method |
| title_full_unstemmed | Estimated the frequencies of a coupled damped nonlinear oscillator with the non-Perturbative method |
| title_short | Estimated the frequencies of a coupled damped nonlinear oscillator with the non-Perturbative method |
| title_sort | estimated the frequencies of a coupled damped nonlinear oscillator with the non perturbative method |
| url | https://doi.org/10.1177/14613484221130148 |
| work_keys_str_mv | AT yusryoeldib estimatedthefrequenciesofacoupleddampednonlinearoscillatorwiththenonperturbativemethod |