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Fractal Oscillation And Its Frequency-Amplitude Property

Author

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  • JI-HUAN HE

    (School of Science, Xi’an University of Architecture and Technology, Xi’an, P. R. China†School of Mathematics and Information Science, Henan Polytechnic University, Jiaozuo, P. R. China‡National Engineering Laboratory for Modern Silk, College of Textile and Clothing Engineering, Soochow University, 199 Ren-Ai Road, Suzhou, P. R. China)

  • SHUAI-JIA KOU

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

  • CHUN-HUI HE

    (�School of Civil Engineering, Xi’an University of Architecture & Technology, Xi’an 710055, P. R. China)

  • ZUO-WEI ZHANG

    (�School of Automation, Northwestern Polytechnical University, Xi’an, P. R. China)

  • KHALED A. GEPREEL

    (��Math. Depart. Faculty of Science, Taif University, P. O. Box 11099, Taif 21944, Saudi Arabia**Mathematics Department, Faculty of Science, Zagazig University, Egypt)

Abstract

When an oscillator vibrates in a porous medium or along an unsmooth surface, a fractal model can be adopted using the two-scale fractal derivative. This paper elucidates a simple but effective method for fast and exclusive insight into the asymptotically periodic property at the initial stage and the extremely low frequency property when time tends to infinity. Some examples are illustrated to show the one-step solution process and the accurate results.

Suggested Citation

  • Ji-Huan He & Shuai-Jia Kou & Chun-Hui He & Zuo-Wei Zhang & Khaled A. Gepreel, 2021. "Fractal Oscillation And Its Frequency-Amplitude Property," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 29(04), pages 1-9, June.
    • Handle: RePEc:wsi:fracta:v:29:y:2021:i:04:n:s0218348x2150105x
    DOI: 10.1142/S0218348X2150105X
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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).

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