He's frequency formulation for fractal nonlinear oscillator arising in a microgravity space

At a microgravity condition, a spaceflight might be subject to a microgravity‐induced vibration. There is no theory so far to study the effect of microgravity on the vibration property. Here we give a fractal vibration model by the two‐scale thermodynamics. The fractal oscillator in the microgravity...

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Bibliographic Details
Published inNumerical methods for partial differential equations Vol. 37; no. 2; pp. 1374 - 1384
Main Author Wang, KangLe
Format Journal Article
LanguageEnglish
Published Hoboken, USA John Wiley & Sons, Inc 01.03.2021
Wiley Subscription Services, Inc
Subjects
fractal derivative
Fractal models
Fractals
fractional differential equation
frequency formulation
Gravitational effects
Inverse method
Microgravity
microgravity space
Space flight
two‐scale transform method
Vibration
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Summary:At a microgravity condition, a spaceflight might be subject to a microgravity‐induced vibration. There is no theory so far to study the effect of microgravity on the vibration property. Here we give a fractal vibration model by the two‐scale thermodynamics. The fractal oscillator in the microgravity space is modeled by using the fractal derivative, and its frequency is obtained by He's frequency formula. The variational principle of the fractal model is established by the fractal semi‐inverse method. The example shows that the proposed method is simple, efficient, and accurate. The frequency‐amplitude relationship is elucidated and the effect of the microgravity condition on vibration property is discussed.
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content type line 14
ISSN:0749-159X
1098-2426
DOI:10.1002/num.22584