FRACTAL OSCILLATION AND ITS FREQUENCY-AMPLITUDE PROPERTY

被引：98
作者：
He, Ji-Huan [1 ,2 ,3 ]
Kou, Shuai-Jia [1 ]
He, Chun-Hui [4 ]
Zhang, Zuo-Wei [5 ]
Gepreel, Khaled A. [6 ,7 ]
机构：
[1] Xian Univ Architecture & Technol, Sch Sci, Xian, Peoples R China
[2] Henan Polytech Univ, Sch Math & Informat Sci, Jiaozuo, Henan, Peoples R China
[3] Soochow Univ, Coll Text & Clothing Engn, Natl Engn Lab Modern Silk, 199 Ren Ai Rd, Suzhou, Peoples R China
[4] Xian Univ Architecture & Technol, Sch Civil Engn, Xian 710055, Peoples R China
[5] Northwestern Polytech Univ, Sch Automat, Xian, Peoples R China
[6] Taif Univ, Fac Sci, Math Dept, POB 11099, At Taif 21944, Saudi Arabia
[7] Zagazig Univ, Fac Sci, Math Dept, Zagazig, Egypt
来源：
FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY | 2021年 / 29卷 / 04期
关键词：
He's Frequency Formulation; Two-Scale Fractal Calculus; Porous Medium; Fractal Duffing Oscillator; Low Frequency; Acoustic Metamaterial; Sound and Vibration Attenuation; MODEL; CALCULUS;
D O I：
10.1142/S0218348X2150105X
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
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.
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页数：9
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