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A Modified Frequency–Amplitude Formulation For Fractal Vibration Systems

Author

Listed:
  • CHUN-HUI HE

    (School of Civil Engineering, Xi’an University of Architecture and Technology, Xi’an, Shaanxi, P. R. China)

  • CHAO LIU

    (School of Civil Engineering, Xi’an University of Architecture and Technology, Xi’an, Shaanxi, P. R. China†School of Science, Xi’an University of Architecture and Technology, Xi’an, Shaanxi, P. R. China)

Abstract

The simplest frequency formulation for nonlinear oscillators is introduced and proved, and a modification is suggested. A fractal vibration in a porous medium is introduced, and its low-frequency property is elucidated by the frequency formulation. It reveals that the inertia force in a fractal space is equivalent to a couple of the inertia force and the damping force for the traditional differential model.

Suggested Citation

  • Chun-Hui He & Chao Liu, 2022. "A Modified Frequency–Amplitude Formulation For Fractal Vibration Systems," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 30(03), pages 1-8, May.
    • Handle: RePEc:wsi:fracta:v:30:y:2022:i:03:n:s0218348x22500463
    DOI: 10.1142/S0218348X22500463
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    Citations

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    Cited by:

    1. El-Dib, Yusry O. & Elgazery, Nasser S., 2022. "A novel pattern in a class of fractal models with the non-perturbative approach," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).
    2. He, Ji-Huan & Jiao, Man-Li & Gepreel, Khaled A. & Khan, Yasir, 2023. "Homotopy perturbation method for strongly nonlinear oscillators," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 204(C), pages 243-258.
    3. He, Chun-Hui & Liu, Chao, 2023. "Variational principle for singular waves," Chaos, Solitons & Fractals, Elsevier, vol. 172(C).

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