Periodic Solutions of the Duffing Harmonic Oscillator by He's Energy Balance Method
Duffing harmonic oscillator is a common model for nonlinear phenomena in science and engineering. This paper presents He´s Energy Balance Method (EBM) for solving nonlinear differential equations. Two strong nonlinear cases have been studied analytically. Analytical results of the EBM are compared w...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Shahid Chamran University of Ahvaz
2015-11-01
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| Series: | Journal of Applied and Computational Mechanics |
| Online Access: | http://jacm.scu.ac.ir/article_12269.html |
| _version_ | 1818700560225796096 |
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| author | A. M. El-Naggar Gamal Ismail |
| author_facet | A. M. El-Naggar Gamal Ismail |
| author_sort | A. M. El-Naggar |
| collection | DOAJ |
| description | Duffing harmonic oscillator is a common model for nonlinear phenomena in science and engineering. This paper presents He´s Energy Balance Method (EBM) for solving nonlinear differential equations. Two strong nonlinear cases have been studied analytically. Analytical results of the EBM are compared with the solutions obtained by using He´s Frequency Amplitude Formulation (FAF) and numerical solutions using Runge-Kutta method. The results show the presented method is potentially to solve high nonlinear oscillator equations. |
| first_indexed | 2024-12-17T15:06:53Z |
| format | Article |
| id | doaj.art-5bf25dc38d6e45d0b998ff9196e6e229 |
| institution | Directory Open Access Journal |
| issn | 2383-4536 2383-4536 |
| language | English |
| last_indexed | 2024-12-17T15:06:53Z |
| publishDate | 2015-11-01 |
| publisher | Shahid Chamran University of Ahvaz |
| record_format | Article |
| series | Journal of Applied and Computational Mechanics |
| spelling | doaj.art-5bf25dc38d6e45d0b998ff9196e6e2292022-12-21T21:43:47ZengShahid Chamran University of AhvazJournal of Applied and Computational Mechanics2383-45362383-45362015-11-012110.22055/jacm.2016.12269Periodic Solutions of the Duffing Harmonic Oscillator by He's Energy Balance MethodA. M. El-NaggarGamal IsmailDuffing harmonic oscillator is a common model for nonlinear phenomena in science and engineering. This paper presents He´s Energy Balance Method (EBM) for solving nonlinear differential equations. Two strong nonlinear cases have been studied analytically. Analytical results of the EBM are compared with the solutions obtained by using He´s Frequency Amplitude Formulation (FAF) and numerical solutions using Runge-Kutta method. The results show the presented method is potentially to solve high nonlinear oscillator equations.http://jacm.scu.ac.ir/article_12269.html |
| spellingShingle | A. M. El-Naggar Gamal Ismail Periodic Solutions of the Duffing Harmonic Oscillator by He's Energy Balance Method Journal of Applied and Computational Mechanics |
| title | Periodic Solutions of the Duffing Harmonic Oscillator by He's Energy Balance Method |
| title_full | Periodic Solutions of the Duffing Harmonic Oscillator by He's Energy Balance Method |
| title_fullStr | Periodic Solutions of the Duffing Harmonic Oscillator by He's Energy Balance Method |
| title_full_unstemmed | Periodic Solutions of the Duffing Harmonic Oscillator by He's Energy Balance Method |
| title_short | Periodic Solutions of the Duffing Harmonic Oscillator by He's Energy Balance Method |
| title_sort | periodic solutions of the duffing harmonic oscillator by he s energy balance method |
| url | http://jacm.scu.ac.ir/article_12269.html |
| work_keys_str_mv | AT amelnaggar periodicsolutionsoftheduffingharmonicoscillatorbyhesenergybalancemethod AT gamalismail periodicsolutionsoftheduffingharmonicoscillatorbyhesenergybalancemethod |