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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Main Authors: Seher Durmaz, Metin Orhan Kaya
Format: Article
Language:English
Published: Wiley 2012-01-01
Series:Journal of Applied Mathematics
Online Access:http://dx.doi.org/10.1155/2012/518684
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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.
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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