He’s multiple scales method for nonlinear vibrations
He’s multiple scales method is a couple of the homotopy perturbation method and the multiple scales technology in the classic perturbation method. This method has been proved to be a powerful mathematical tool to various nonlinear equations, and it is extremely effective for forced nonlinear oscilla...
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2019-12-01
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Series: | Journal of Low Frequency Noise, Vibration and Active Control |
Online Access: | https://doi.org/10.1177/1461348419861450 |
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doaj-bf6952ef1417452ab5acb43174a4a2af2020-11-25T03:49:38ZengSAGE PublishingJournal of Low Frequency Noise, Vibration and Active Control1461-34842048-40462019-12-013810.1177/1461348419861450He’s multiple scales method for nonlinear vibrationsZhong-Fu RenShao-Wen YaoJi-Huan HeHe’s multiple scales method is a couple of the homotopy perturbation method and the multiple scales technology in the classic perturbation method. This method has been proved to be a powerful mathematical tool to various nonlinear equations, and it is extremely effective for forced nonlinear oscillators. This paper shows that the method can be further improved by incorporating some known technologies, e.g., the parameter-expanding technology, the enhanced perturbation method and the homotopy perturbation method with an auxiliary term. Due to the wide application of the homotopy perturbation method, He’s multiple scales method cleans solutions of nonlinear equations while the classic perturbation method fails.https://doi.org/10.1177/1461348419861450 |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Zhong-Fu Ren Shao-Wen Yao Ji-Huan He |
spellingShingle |
Zhong-Fu Ren Shao-Wen Yao Ji-Huan He He’s multiple scales method for nonlinear vibrations Journal of Low Frequency Noise, Vibration and Active Control |
author_facet |
Zhong-Fu Ren Shao-Wen Yao Ji-Huan He |
author_sort |
Zhong-Fu Ren |
title |
He’s multiple scales method for nonlinear vibrations |
title_short |
He’s multiple scales method for nonlinear vibrations |
title_full |
He’s multiple scales method for nonlinear vibrations |
title_fullStr |
He’s multiple scales method for nonlinear vibrations |
title_full_unstemmed |
He’s multiple scales method for nonlinear vibrations |
title_sort |
he’s multiple scales method for nonlinear vibrations |
publisher |
SAGE Publishing |
series |
Journal of Low Frequency Noise, Vibration and Active Control |
issn |
1461-3484 2048-4046 |
publishDate |
2019-12-01 |
description |
He’s multiple scales method is a couple of the homotopy perturbation method and the multiple scales technology in the classic perturbation method. This method has been proved to be a powerful mathematical tool to various nonlinear equations, and it is extremely effective for forced nonlinear oscillators. This paper shows that the method can be further improved by incorporating some known technologies, e.g., the parameter-expanding technology, the enhanced perturbation method and the homotopy perturbation method with an auxiliary term. Due to the wide application of the homotopy perturbation method, He’s multiple scales method cleans solutions of nonlinear equations while the classic perturbation method fails. |
url |
https://doi.org/10.1177/1461348419861450 |
work_keys_str_mv |
AT zhongfuren hesmultiplescalesmethodfornonlinearvibrations AT shaowenyao hesmultiplescalesmethodfornonlinearvibrations AT jihuanhe hesmultiplescalesmethodfornonlinearvibrations |
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1724494313058992128 |