Chaos of a class of piecewise Duffing oscillator with fractional-order derivative term

被引：0

作者：

Wang J. ^{[1
]}

Shen Y. ^{[1
]}

Zhang J. ^{[1
]}

Wang X. ^{[2
]}

机构：

[1] State Key Lab for Mechanical Behavior and System Safety of Traffic Engineering Structures, Shijiazhuang Tiedao University, Shijiazhuang

[2] Department of Mechanical and Electrical Engineering, Hebei Vocational College of Rail Transportation, Shijiazhuang

来源：

Zhendong yu Chongji/Journal of Vibration and Shock | 2022年 / 41卷 / 13期

关键词：

chaos; fractional-order derivative; Melnikov method; piecewise Duffing oscillator;

D O I：

10.13465/j.cnki.jvs.2022.13.002

中图分类号：

学科分类号：

摘要：

Here, chaotic motion of a piecewise Duffing oscillator with fractional-order derivative term under harmonic excitation was studied. The fractional-order differential term was calculated using Caputo definition and treated using concepts of equivalent stiffness and equivalent damping. Using Melnikov method，necessary conditions for chaotic motion in the sense of Smale horseshoe were established and critical conditions for the system to have chaotic motion were obtained. The system' s analytical solution and numerical solution were compared. The results verified the correctness of analytical necessary conditions. Finally, numerical simulation was used to study effects of the system' s linear stiffness coefficient, damping coefficient, order number of fractional-order, fractional-order coefficient and piecewise Duffing stiffness coefficient on the system' s chaotic motion. © 2022 Chinese Vibration Engineering Society. All rights reserved.

引用

页码：8 / 16

页数：8

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