Insightful and comprehensive formularization of frequency–amplitude formula for strong or singular nonlinear oscillators
The comprehensive formularization of the frequency–amplitude formula is the main interest in this work to cover higher powers of the restoring force which are not limited to cubic powers. Three equivalent styles of the generalized frequency amplitude have been performed. In addition, the restoring f...
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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/10.1177/14613484221118177 |
| _version_ | 1797905113062309888 |
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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 comprehensive formularization of the frequency–amplitude formula is the main interest in this work to cover higher powers of the restoring force which are not limited to cubic powers. Three equivalent styles of the generalized frequency amplitude have been performed. In addition, the restoring force is not restricted to an odd function in which the non-secular forces are included. Three forms of the non-secular forces have been formulated for the first time and treated as non-homogenous of the linearized Duffing oscillator. The modified style of He’s formula has been applied to the singular oscillator using the enhanced potential function. The simplicity of the present approach provides extra advantages for high nonlinearity vibration. This method enriches the analysis with more details in new dimensions. |
| first_indexed | 2024-04-10T09:59:52Z |
| format | Article |
| id | doaj.art-4655ff16d3114ff7bb66e0a065b27c9e |
| institution | Directory Open Access Journal |
| issn | 1461-3484 2048-4046 |
| language | English |
| last_indexed | 2024-04-10T09:59:52Z |
| publishDate | 2023-03-01 |
| publisher | SAGE Publishing |
| record_format | Article |
| series | Journal of Low Frequency Noise, Vibration and Active Control |
| spelling | doaj.art-4655ff16d3114ff7bb66e0a065b27c9e2023-02-16T09:33:51ZengSAGE PublishingJournal of Low Frequency Noise, Vibration and Active Control1461-34842048-40462023-03-014210.1177/14613484221118177Insightful and comprehensive formularization of frequency–amplitude formula for strong or singular nonlinear oscillatorsYusry O El-DibThe comprehensive formularization of the frequency–amplitude formula is the main interest in this work to cover higher powers of the restoring force which are not limited to cubic powers. Three equivalent styles of the generalized frequency amplitude have been performed. In addition, the restoring force is not restricted to an odd function in which the non-secular forces are included. Three forms of the non-secular forces have been formulated for the first time and treated as non-homogenous of the linearized Duffing oscillator. The modified style of He’s formula has been applied to the singular oscillator using the enhanced potential function. The simplicity of the present approach provides extra advantages for high nonlinearity vibration. This method enriches the analysis with more details in new dimensions.https://doi.org/10.1177/14613484221118177 |
| spellingShingle | Yusry O El-Dib Insightful and comprehensive formularization of frequency–amplitude formula for strong or singular nonlinear oscillators Journal of Low Frequency Noise, Vibration and Active Control |
| title | Insightful and comprehensive formularization of frequency–amplitude formula for strong or singular nonlinear oscillators |
| title_full | Insightful and comprehensive formularization of frequency–amplitude formula for strong or singular nonlinear oscillators |
| title_fullStr | Insightful and comprehensive formularization of frequency–amplitude formula for strong or singular nonlinear oscillators |
| title_full_unstemmed | Insightful and comprehensive formularization of frequency–amplitude formula for strong or singular nonlinear oscillators |
| title_short | Insightful and comprehensive formularization of frequency–amplitude formula for strong or singular nonlinear oscillators |
| title_sort | insightful and comprehensive formularization of frequency amplitude formula for strong or singular nonlinear oscillators |
| url | https://doi.org/10.1177/14613484221118177 |
| work_keys_str_mv | AT yusryoeldib insightfulandcomprehensiveformularizationoffrequencyamplitudeformulaforstrongorsingularnonlinearoscillators |