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Discontinuous dynamical behaviors in a 2-DOF friction collision system with asymmetric damping

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  • Cao, Jing
  • Fan, Jinjun

Abstract

By using the flow switchability theory in discontinuous dynamical systems, this paper deals with the discontinuous dynamical behaviors of a two degrees of freedom system with asymmetric damping, where considering that friction and impact coexist and the static and dynamic friction coefficients are different. Because of the particularity of friction force, the flow barriers on the velocity boundary that affect the leaving flow are considered in this paper. Based on discontinuity that is caused by the sudden change of friction force or the collision between two objects, the phase space of motion for the object is divided into several different domains and boundaries; and with the help of the analysis of vector fields and G-functions on the corresponding discontinuous boundaries or in domains, the analytical conditions for all possible motions are obtained, which is used to determine the switching of motion state in this system. Finally, numerical simulations are presented to better understand the analytical conditions of the stick, grazing, impact, stuck and periodic motions.

Suggested Citation

  • Cao, Jing & Fan, Jinjun, 2021. "Discontinuous dynamical behaviors in a 2-DOF friction collision system with asymmetric damping," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).
    • Handle: RePEc:eee:chsofr:v:142:y:2021:i:c:s0960077920307980
    DOI: 10.1016/j.chaos.2020.110405
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    References listed on IDEAS

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    1. Fan, Jinjun & Yang, Zhaoxia, 2018. "Analysis of dynamical behaviors of a 2-DOF vibro-impact system with dry friction," Chaos, Solitons & Fractals, Elsevier, vol. 116(C), pages 176-201.
    2. Jinjun Fan & Liqing Li, 2013. "Existence of Positive Solutions for - Laplacian Dynamic Equations with Derivative on Time Scales," Journal of Applied Mathematics, Hindawi, vol. 2013, pages 1-7, February.
    3. Li, Xiaodi & Shen, Jianhua & Rakkiyappan, R., 2018. "Persistent impulsive effects on stability of functional differential equations with finite or infinite delay," Applied Mathematics and Computation, Elsevier, vol. 329(C), pages 14-22.
    4. Fan, Jinjun & Xue, Shan & Chen, Ge, 2018. "On discontinuous dynamics of a periodically forced double-belt friction oscillator," Chaos, Solitons & Fractals, Elsevier, vol. 109(C), pages 280-302.
    5. Li, Xiaodi & Yang, Xueyan & Huang, Tingwen, 2019. "Persistence of delayed cooperative models: Impulsive control method," Applied Mathematics and Computation, Elsevier, vol. 342(C), pages 130-146.
    6. Li, Haitao & Xu, Xiaojing & Ding, Xueying, 2019. "Finite-time stability analysis of stochastic switched boolean networks with impulsive effect," Applied Mathematics and Computation, Elsevier, vol. 347(C), pages 557-565.
    7. Li, Liping & Luo, Albert C.J., 2018. "On periodic solutions of a second-order, time-delayed, discontinuous dynamical system," Chaos, Solitons & Fractals, Elsevier, vol. 114(C), pages 216-229.
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