Successive approximate solutions for nonlinear oscillation and improvement of the solution accuracy with efficient non-perturbative technique
In the present study, several successive approximate solutions of the nonlinear oscillator are derived by using the efficient frequency formula. A systematical analysis of the formulation of the nonlinear frequency helps to establish a general periodic solution. Each approximation represents, indivi...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
SAGE Publishing
2023-09-01
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| Series: | Journal of Low Frequency Noise, Vibration and Active Control |
| Online Access: | https://doi.org/10.1177/14613484231161425 |
| _version_ | 1797733393127964672 |
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| author | Yusry O El-Dib Haifa A Alyousef |
| author_facet | Yusry O El-Dib Haifa A Alyousef |
| author_sort | Yusry O El-Dib |
| collection | DOAJ |
| description | In the present study, several successive approximate solutions of the nonlinear oscillator are derived by using the efficient frequency formula. A systematical analysis of the formulation of the nonlinear frequency helps to establish a general periodic solution. Each approximation represents, individually, the solution of the nonlinear oscillator. For the optimal design and accurate prediction of structural behavior, a new optimizer is demonstrated for efficient solutions. The classical Duffing frequency formula has been modified. The numerical calculations show high agreement with the exact frequency. The justifiability of the obtained solutions is confirmed by comparison with the numerical solution. It is shown that the enhanced solution is accurate for large amplitudes and is not restricted to oscillations that have small amplitudes. The new approach can provide a perfect approximation for the nonlinear oscillation. |
| first_indexed | 2024-03-12T12:27:30Z |
| format | Article |
| id | doaj.art-25543b6168954860bf1c56a143b4d8c5 |
| institution | Directory Open Access Journal |
| issn | 1461-3484 2048-4046 |
| language | English |
| last_indexed | 2024-03-12T12:27:30Z |
| publishDate | 2023-09-01 |
| publisher | SAGE Publishing |
| record_format | Article |
| series | Journal of Low Frequency Noise, Vibration and Active Control |
| spelling | doaj.art-25543b6168954860bf1c56a143b4d8c52023-08-29T19:21:10ZengSAGE PublishingJournal of Low Frequency Noise, Vibration and Active Control1461-34842048-40462023-09-014210.1177/14613484231161425Successive approximate solutions for nonlinear oscillation and improvement of the solution accuracy with efficient non-perturbative techniqueYusry O El-DibHaifa A AlyousefIn the present study, several successive approximate solutions of the nonlinear oscillator are derived by using the efficient frequency formula. A systematical analysis of the formulation of the nonlinear frequency helps to establish a general periodic solution. Each approximation represents, individually, the solution of the nonlinear oscillator. For the optimal design and accurate prediction of structural behavior, a new optimizer is demonstrated for efficient solutions. The classical Duffing frequency formula has been modified. The numerical calculations show high agreement with the exact frequency. The justifiability of the obtained solutions is confirmed by comparison with the numerical solution. It is shown that the enhanced solution is accurate for large amplitudes and is not restricted to oscillations that have small amplitudes. The new approach can provide a perfect approximation for the nonlinear oscillation.https://doi.org/10.1177/14613484231161425 |
| spellingShingle | Yusry O El-Dib Haifa A Alyousef Successive approximate solutions for nonlinear oscillation and improvement of the solution accuracy with efficient non-perturbative technique Journal of Low Frequency Noise, Vibration and Active Control |
| title | Successive approximate solutions for nonlinear oscillation and improvement of the solution accuracy with efficient non-perturbative technique |
| title_full | Successive approximate solutions for nonlinear oscillation and improvement of the solution accuracy with efficient non-perturbative technique |
| title_fullStr | Successive approximate solutions for nonlinear oscillation and improvement of the solution accuracy with efficient non-perturbative technique |
| title_full_unstemmed | Successive approximate solutions for nonlinear oscillation and improvement of the solution accuracy with efficient non-perturbative technique |
| title_short | Successive approximate solutions for nonlinear oscillation and improvement of the solution accuracy with efficient non-perturbative technique |
| title_sort | successive approximate solutions for nonlinear oscillation and improvement of the solution accuracy with efficient non perturbative technique |
| url | https://doi.org/10.1177/14613484231161425 |
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