Parameters Approach Applied on Nonlinear Oscillators
We applied an approach to obtain the natural frequency of the generalized Duffing oscillator u¨ + u + α3u3 + α5u5 + α7u7 + ⋯ + αnun=0 and a nonlinear oscillator with a restoring force which is the function of a noninteger power exponent of deflection u¨+αu|u|n−1=0. This approach is based on involve...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Shock and Vibration |
| Online Access: | http://dx.doi.org/10.1155/2014/624147 |
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| author | Najeeb Alam Khan Fatima Riaz Nadeem Alam Khan |
| author_facet | Najeeb Alam Khan Fatima Riaz Nadeem Alam Khan |
| author_sort | Najeeb Alam Khan |
| collection | DOAJ |
| description | We applied an approach to obtain the natural frequency of the generalized Duffing oscillator u¨ + u + α3u3 + α5u5 + α7u7 + ⋯ + αnun=0 and a nonlinear oscillator with a restoring force which is the function of a noninteger power exponent of deflection u¨+αu|u|n−1=0. This approach is based on involved parameters, initial conditions, and collocation points. For any arbitrary power of n, the approximate frequency analysis is carried out between the natural frequency and amplitude. The solution procedure is simple, and the results obtained are valid for the whole solution domain. |
| format | Article |
| id | doaj-art-bcb01d6e013b44b398af88da7789254d |
| institution | Kabale University |
| issn | 1070-9622 1875-9203 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Shock and Vibration |
| spelling | doaj-art-bcb01d6e013b44b398af88da7789254d2025-02-03T06:12:40ZengWileyShock and Vibration1070-96221875-92032014-01-01201410.1155/2014/624147624147Parameters Approach Applied on Nonlinear OscillatorsNajeeb Alam Khan0Fatima Riaz1Nadeem Alam Khan2Department of Mathematical Sciences, University of Karachi, Karachi 75270, PakistanDepartment of Mathematical Sciences, University of Karachi, Karachi 75270, PakistanDepartment of Mathematical Sciences, University of Karachi, Karachi 75270, PakistanWe applied an approach to obtain the natural frequency of the generalized Duffing oscillator u¨ + u + α3u3 + α5u5 + α7u7 + ⋯ + αnun=0 and a nonlinear oscillator with a restoring force which is the function of a noninteger power exponent of deflection u¨+αu|u|n−1=0. This approach is based on involved parameters, initial conditions, and collocation points. For any arbitrary power of n, the approximate frequency analysis is carried out between the natural frequency and amplitude. The solution procedure is simple, and the results obtained are valid for the whole solution domain.http://dx.doi.org/10.1155/2014/624147 |
| spellingShingle | Najeeb Alam Khan Fatima Riaz Nadeem Alam Khan Parameters Approach Applied on Nonlinear Oscillators Shock and Vibration |
| title | Parameters Approach Applied on Nonlinear Oscillators |
| title_full | Parameters Approach Applied on Nonlinear Oscillators |
| title_fullStr | Parameters Approach Applied on Nonlinear Oscillators |
| title_full_unstemmed | Parameters Approach Applied on Nonlinear Oscillators |
| title_short | Parameters Approach Applied on Nonlinear Oscillators |
| title_sort | parameters approach applied on nonlinear oscillators |
| url | http://dx.doi.org/10.1155/2014/624147 |
| work_keys_str_mv | AT najeebalamkhan parametersapproachappliedonnonlinearoscillators AT fatimariaz parametersapproachappliedonnonlinearoscillators AT nadeemalamkhan parametersapproachappliedonnonlinearoscillators |