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Discontinuous dynamics of an asymmetric 2-DOF friction oscillator with elastic and rigid impacts

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  • Peng, Yuanyuan
  • Fan, Jinjun
  • Gao, Min
  • Li, Jianping

Abstract

In this paper, by using flow switching theory of discontinuous dynamical systems, the discontinuous dynamic behavior of a 2-DOF (two-degree-of-freedom) friction oscillator with elastic impact and rigid impact on different sides is investigated. For the 2-DOF friction oscillator, when the direction of object’s velocity changes, the negative feedback works and the inequality of maximum static friction force and kinetic friction force leads to the existence of flow barriers. In addition, the elastic impact and rigid impact can change motion states of object, resulting in the discontinuity of this 2-DOF system. Considering the multiple motion states of object and better analyzing the equation of object’s motion, the phase space of each object is divided into different motion domains and boundaries in relative and absolute coordinates by means of the discontinuities resulted from the friction and impact. Moreover, because the elastic impact exists in a time period, there will be a variety of motion behaviors coexisting, such as elastic and rigid impacts occur simultaneously. With that in mind, in absolute coordinate system, the phase space of the system is divided in six cases according to whether there are stick motion and stuck motion. Based on flow switching theory, the switching conditions at discontinuous boundaries for all possible motions are given by using G-functions, and it should be noted that the vanishing conditions of the sliding motion become more complicated due to the existence of flow barriers at speed boundaries. Through defining the switching sets on separation boundaries, the mapping structures are further introduced to demonstrate the global dynamic behavior and periodic motions. For a better understanding of the object’s motion and the switching criteria at separation boundaries, the numerical simulation method is used to demonstrate several typical motions such as passable motion, sliding motion, grazing motion, stick motion (elastic impact), rigid impact and periodic motions etc. The results obtained have reference value for the optimization design and noise control of mechanical systems with gap couplings and negative feedbacks.

Suggested Citation

  • Peng, Yuanyuan & Fan, Jinjun & Gao, Min & Li, Jianping, 2021. "Discontinuous dynamics of an asymmetric 2-DOF friction oscillator with elastic and rigid impacts," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).
    • Handle: RePEc:eee:chsofr:v:150:y:2021:i:c:s096007792100549x
    DOI: 10.1016/j.chaos.2021.111195
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. Li, Xiaodi & Shen, Jianhua & Akca, Haydar & Rakkiyappan, R., 2015. "LMI-based stability for singularly perturbed nonlinear impulsive differential systems with delays of small parameter," Applied Mathematics and Computation, Elsevier, vol. 250(C), pages 798-804.
    4. Luo, Albert C.J. & Chen, Lidi, 2005. "Periodic motions and grazing in a harmonically forced, piecewise, linear oscillator with impacts," Chaos, Solitons & Fractals, Elsevier, vol. 24(2), pages 567-578.
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    Cited by:

    1. Peng, Ruyue & Li, Qunhong & Zhang, Wei, 2024. "Homoclinic bifurcation analysis of a class of conveyor belt systems with dry friction and impact," Chaos, Solitons & Fractals, Elsevier, vol. 180(C).
    2. Guo, Xiuying & Tian, Ruilan & Xue, Qiang & Zhang, Xiaolong, 2022. "Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).
    3. Zheng, Yanxiao & Li, Qunhong & Zhang, Wei & Lei, Jinfeng, 2023. "Three-dimensional mapping analysis of a capsule system with bilateral elastic constraints," Chaos, Solitons & Fractals, Elsevier, vol. 172(C).

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