He’s frequency formula to fractal undamped Duffing equation

He’s frequency formula to fractal undamped Duffing equation

Nonlinear oscillation is an increasingly important and extremely interesting topic in engineering. This article completely reviews a simple method proposed by Ji-Huan He and successfully establishes a fractal undamped Duffing equation through the two-scale fractal derivative in a fractal space. Its...

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Autor principal: Guang-Qing Feng
Formato: article
Lenguaje:EN
Publicado: SAGE Publishing 2021
Materias:
Control engineering systems. Automatic machinery (General)
TJ212-225
Acoustics. Sound
QC221-246
Acceso en línea:https://doaj.org/article/47403c1750244fa096e7d8bfda9b99c6
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spelling oai:doaj.org-article:47403c1750244fa096e7d8bfda9b99c62021-12-02T01:34:41ZHe’s frequency formula to fractal undamped Duffing equation1461-34842048-404610.1177/1461348421992608https://doaj.org/article/47403c1750244fa096e7d8bfda9b99c62021-12-01T00:00:00Zhttps://doi.org/10.1177/1461348421992608https://doaj.org/toc/1461-3484https://doaj.org/toc/2048-4046Nonlinear oscillation is an increasingly important and extremely interesting topic in engineering. This article completely reviews a simple method proposed by Ji-Huan He and successfully establishes a fractal undamped Duffing equation through the two-scale fractal derivative in a fractal space. Its variational principle is established, and the two-scale transform method and the fractal frequency formula are adopted to find the approximate frequency of the fractal oscillator. The numerical result shows that He’s frequency formula is a unique tool for the fractal equations.Guang-Qing FengSAGE PublishingarticleControl engineering systems. Automatic machinery (General)TJ212-225Acoustics. SoundQC221-246ENJournal of Low Frequency Noise, Vibration and Active Control, Vol 40 (2021)
institution DOAJ
collection DOAJ
language EN
topic Control engineering systems. Automatic machinery (General)
TJ212-225
Acoustics. Sound
QC221-246
spellingShingle Control engineering systems. Automatic machinery (General)
TJ212-225
Acoustics. Sound
QC221-246
Guang-Qing Feng
He’s frequency formula to fractal undamped Duffing equation
description Nonlinear oscillation is an increasingly important and extremely interesting topic in engineering. This article completely reviews a simple method proposed by Ji-Huan He and successfully establishes a fractal undamped Duffing equation through the two-scale fractal derivative in a fractal space. Its variational principle is established, and the two-scale transform method and the fractal frequency formula are adopted to find the approximate frequency of the fractal oscillator. The numerical result shows that He’s frequency formula is a unique tool for the fractal equations.
format article
author Guang-Qing Feng
author_facet Guang-Qing Feng
author_sort Guang-Qing Feng
title He’s frequency formula to fractal undamped Duffing equation
title_short He’s frequency formula to fractal undamped Duffing equation
title_full He’s frequency formula to fractal undamped Duffing equation
title_fullStr He’s frequency formula to fractal undamped Duffing equation
title_full_unstemmed He’s frequency formula to fractal undamped Duffing equation
title_sort he’s frequency formula to fractal undamped duffing equation
publisher SAGE Publishing
publishDate 2021
url https://doaj.org/article/47403c1750244fa096e7d8bfda9b99c6
work_keys_str_mv AT guangqingfeng hesfrequencyformulatofractalundampedduffingequation
_version_ 1718402955035541504

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