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Periodic motions and grazing in a harmonically forced, piecewise, linear oscillator with impacts

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  • Luo, Albert C.J.
  • Chen, Lidi

Abstract

In this paper, an idealized, piecewise linear system is presented to model the vibration of gear transmission systems. Periodic motions in a generalized, piecewise linear oscillator with perfectly plastic impacts are predicted analytically. The analytical predictions of periodic motion are based on the mapping structures, and the generic mappings based on the discontinuous boundaries are developed. This method for the analytical prediction of the periodic motions in non-smooth dynamic systems can give all possible periodic motions based on the adequate mapping structures. The stability and bifurcation conditions for specified periodic motions are obtained. The periodic motions and grazing motion are demonstrated. This model is applicable to prediction of periodic motion in nonlinear dynamics of gear transmission systems.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:chsofr:v:24:y:2005:i:2:p:567-578
    DOI: 10.1016/j.chaos.2004.09.028
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    Cited by:

    1. Wang, Zheng & Luo, Tianqi, 2017. "Multiformity of periodic-impact motions of a harmonically forced soft-impacting system and experimental verification based on an electronic circuit," Chaos, Solitons & Fractals, Elsevier, vol. 94(C), pages 23-36.
    2. Luo, Guanwei & Xie, Jianhua & Zhu, Xifeng & Zhang, Jiangang, 2008. "Periodic motions and bifurcations of a vibro-impact system," Chaos, Solitons & Fractals, Elsevier, vol. 36(5), pages 1340-1347.
    3. Navarro-López, Eva M. & Licéaga-Castro, Eduardo, 2009. "Non-desired transitions and sliding-mode control of a multi-DOF mechanical system with stick-slip oscillations," Chaos, Solitons & Fractals, Elsevier, vol. 41(4), pages 2035-2044.
    4. 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).
    5. 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).
    6. Qin, Weiyang & Su, Hao & Yang, Yongfeng, 2008. "Grazing bifurcation and chaos in response of rubbing rotor," Chaos, Solitons & Fractals, Elsevier, vol. 37(1), pages 166-174.
    7. Yang, Guidong & Xu, Wei & Gu, Xudong & Huang, Dongmei, 2016. "Response analysis for a vibroimpact Duffing system with bilateral barriers under external and parametric Gaussian white noises," Chaos, Solitons & Fractals, Elsevier, vol. 87(C), pages 125-135.

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