Chaos of a class of piecewise Duffing oscillator with fractional-order derivative term
WANG Jun1, SHEN Yongjun1, ZHANG Jianchao1, WANG Xiaona2
1.State Key Lab for Mechanical Behavior and System Safety of Traffic Engineering Structures, Shijiazhuang Tiedao University, Shijiazhuang 050043, China; 2.Department of Mechanical and Electrical Engineering, Hebei Vocational College of Rail Transportation, Shijiazhuang 050021, China
Abstract：This paper presents an investigation of the chaos in a piecewise Duffing oscillator with fractional-order derivative under harmonic excitation. The Caputo definition is used to calculate the fractional-order derivative, and the concepts of equivalent stiffness and equivalent damping are used to process the fractional-order derivative. Based on the Melnikov method, the analytically necessary condition for the chaos in the sense of Smale horseshoes is established and then the chaotic critical condition curve is obtained. The comparison between the analytical solution and the numerical solution is investigated, and the results verify the correctness of the analytically necessary condition. Finally, the influence of linear stiffness coefficient, damping coefficient, fractional-order order, fractional-order coefficient and piecewise Duffing stiffness coefficient on the necessary conditions for chaos are studied by numerical simulation.
Key words：Melnikov method; fractional-order derivative; piecewise Duffing oscillator; chaos
王军1，申永军1，张建超1，王晓娜2. 一类分数阶分段Duffing振子的混沌研究[J]. 振动与冲击, 2022, 41(13): 8-16.
WANG Jun1, SHEN Yongjun1, ZHANG Jianchao1, WANG Xiaona2. Chaos of a class of piecewise Duffing oscillator with fractional-order derivative term. JOURNAL OF VIBRATION AND SHOCK, 2022, 41(13): 8-16.
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