High-Order Energy Balance Method to Nonlinear Oscillators
Energy balance method (EBM) is extended for high-order nonlinear oscillators. To illustrate the effectiveness of the method, a cubic-quintic Duffing oscillator was chosen. The maximum relative errors of the frequencies of the oscillator read 1.25% and 0.6% for the first- and second-order approximat...
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2012/518684 |
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| _version_ | 1849692943891300352 |
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| author | Seher Durmaz Metin Orhan Kaya |
| author_facet | Seher Durmaz Metin Orhan Kaya |
| author_sort | Seher Durmaz |
| collection | DOAJ |
| description | Energy balance method (EBM) is extended for high-order nonlinear oscillators. To illustrate the effectiveness of the method, a cubic-quintic Duffing oscillator was chosen. The maximum relative errors of the frequencies of the oscillator read 1.25% and 0.6% for the first- and second-order approximation, respectively. The third-order approximation has an accuracy as high as 0.008%. Excellent agreement of the approximated frequencies and periodic solutions with the exact ones is demonstrated for several values of parameters of the oscillator. |
| format | Article |
| id | doaj-art-95ca5d43178f466cadebe58590bf1422 |
| institution | DOAJ |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-95ca5d43178f466cadebe58590bf14222025-08-20T03:20:34ZengWileyJournal of Applied Mathematics1110-757X1687-00422012-01-01201210.1155/2012/518684518684High-Order Energy Balance Method to Nonlinear OscillatorsSeher Durmaz0Metin Orhan Kaya1Faculty of Aeronautics and Astronautics, Istanbul Technical University, Maslak, 34469 Istanbul, TurkeyFaculty of Aeronautics and Astronautics, Istanbul Technical University, Maslak, 34469 Istanbul, TurkeyEnergy balance method (EBM) is extended for high-order nonlinear oscillators. To illustrate the effectiveness of the method, a cubic-quintic Duffing oscillator was chosen. The maximum relative errors of the frequencies of the oscillator read 1.25% and 0.6% for the first- and second-order approximation, respectively. The third-order approximation has an accuracy as high as 0.008%. Excellent agreement of the approximated frequencies and periodic solutions with the exact ones is demonstrated for several values of parameters of the oscillator.http://dx.doi.org/10.1155/2012/518684 |
| spellingShingle | Seher Durmaz Metin Orhan Kaya High-Order Energy Balance Method to Nonlinear Oscillators Journal of Applied Mathematics |
| title | High-Order Energy Balance Method to Nonlinear Oscillators |
| title_full | High-Order Energy Balance Method to Nonlinear Oscillators |
| title_fullStr | High-Order Energy Balance Method to Nonlinear Oscillators |
| title_full_unstemmed | High-Order Energy Balance Method to Nonlinear Oscillators |
| title_short | High-Order Energy Balance Method to Nonlinear Oscillators |
| title_sort | high order energy balance method to nonlinear oscillators |
| url | http://dx.doi.org/10.1155/2012/518684 |
| work_keys_str_mv | AT seherdurmaz highorderenergybalancemethodtononlinearoscillators AT metinorhankaya highorderenergybalancemethodtononlinearoscillators |