FRACTAL OSCILLATION AND ITS FREQUENCY-AMPLITUDE PROPERTY

Ji-Huan He, Shuai-Jia Kou, Chun-Hui He, Zuo-Wei Zhang and Khaled A. Gepreel
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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

FRACTALS (fractals), 2021, vol. 29, issue 04, 1-9

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.

Keywords: He’s Frequency Formulation; Two-Scale Fractal Calculus; Porous Medium; Fractal Duffing Oscillator; Low Frequency; Acoustic Metamaterial; Sound and Vibration Attenuation (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1142/S0218348X2150105X

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