The simpler, the better: Analytical methods for nonlinear oscillators and fractional oscillators

The simpler, the better: Analytical methods for nonlinear oscillators and fractional oscillators

In engineering, a fast estimation of the periodic property of a nonlinear oscillator is much needed. This paper reviews some simplest methods for nonlinear oscillators, including He’s frequency formulation, the max-min approach and the homotopy perturbation method. A mathematical insight into He’s f...

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Main Author: Ji-Huan He
Format: Article
Language:English
Published: SAGE Publishing 2019-12-01
Series:Journal of Low Frequency Noise, Vibration and Active Control
Online Access:https://doi.org/10.1177/1461348419844145
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spelling doaj-bab7f0dbd5194e83aa4c25300fcfe2732020-11-25T03:57:06ZengSAGE PublishingJournal of Low Frequency Noise, Vibration and Active Control1461-34842048-40462019-12-013810.1177/1461348419844145The simpler, the better: Analytical methods for nonlinear oscillators and fractional oscillatorsJi-Huan HeIn engineering, a fast estimation of the periodic property of a nonlinear oscillator is much needed. This paper reviews some simplest methods for nonlinear oscillators, including He’s frequency formulation, the max-min approach and the homotopy perturbation method. A mathematical insight into He’s frequency formulation is given, and the weighted average is introduced to further improve the estimated accuracy of the frequency. Fractional oscillators are also discussed.https://doi.org/10.1177/1461348419844145
collection DOAJ
language English
format Article
sources DOAJ
author Ji-Huan He
spellingShingle Ji-Huan He
The simpler, the better: Analytical methods for nonlinear oscillators and fractional oscillators
Journal of Low Frequency Noise, Vibration and Active Control
author_facet Ji-Huan He
author_sort Ji-Huan He
title The simpler, the better: Analytical methods for nonlinear oscillators and fractional oscillators
title_short The simpler, the better: Analytical methods for nonlinear oscillators and fractional oscillators
title_full The simpler, the better: Analytical methods for nonlinear oscillators and fractional oscillators
title_fullStr The simpler, the better: Analytical methods for nonlinear oscillators and fractional oscillators
title_full_unstemmed The simpler, the better: Analytical methods for nonlinear oscillators and fractional oscillators
title_sort simpler, the better: analytical methods for nonlinear oscillators and fractional oscillators
publisher SAGE Publishing
series Journal of Low Frequency Noise, Vibration and Active Control
issn 1461-3484
2048-4046
publishDate 2019-12-01
description In engineering, a fast estimation of the periodic property of a nonlinear oscillator is much needed. This paper reviews some simplest methods for nonlinear oscillators, including He’s frequency formulation, the max-min approach and the homotopy perturbation method. A mathematical insight into He’s frequency formulation is given, and the weighted average is introduced to further improve the estimated accuracy of the frequency. Fractional oscillators are also discussed.
url https://doi.org/10.1177/1461348419844145
work_keys_str_mv AT jihuanhe thesimplerthebetteranalyticalmethodsfornonlinearoscillatorsandfractionaloscillators
AT jihuanhe simplerthebetteranalyticalmethodsfornonlinearoscillatorsandfractionaloscillators
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