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Global Dynamics of a Vibro-Impact Energy Harvester

Author

Listed:
  • Zhenbang Cao

    (Key Laboratory of Optical Engineering, Chinese Academy of Sciences, Chengdu 610209, China
    The Institute of Optics and Electronics, Chinese Academy of Sciences, Chengdu 610209, China
    University of Chinese Academy of Sciences, Beijing 100039, China
    These authors contributed equally to this work and should be considered co-first authors.)

  • Haotong Ma

    (Key Laboratory of Optical Engineering, Chinese Academy of Sciences, Chengdu 610209, China
    The Institute of Optics and Electronics, Chinese Academy of Sciences, Chengdu 610209, China
    University of Chinese Academy of Sciences, Beijing 100039, China)

  • Xuegang Yu

    (Key Laboratory of Optical Engineering, Chinese Academy of Sciences, Chengdu 610209, China
    The Institute of Optics and Electronics, Chinese Academy of Sciences, Chengdu 610209, China
    University of Chinese Academy of Sciences, Beijing 100039, China
    These authors contributed equally to this work and should be considered co-first authors.)

  • Jianliang Shi

    (Key Laboratory of Optical Engineering, Chinese Academy of Sciences, Chengdu 610209, China
    The Institute of Optics and Electronics, Chinese Academy of Sciences, Chengdu 610209, China
    University of Chinese Academy of Sciences, Beijing 100039, China)

  • Hu Yang

    (Key Laboratory of Optical Engineering, Chinese Academy of Sciences, Chengdu 610209, China
    The Institute of Optics and Electronics, Chinese Academy of Sciences, Chengdu 610209, China
    University of Chinese Academy of Sciences, Beijing 100039, China)

  • Yi Tan

    (Key Laboratory of Optical Engineering, Chinese Academy of Sciences, Chengdu 610209, China
    The Institute of Optics and Electronics, Chinese Academy of Sciences, Chengdu 610209, China
    University of Chinese Academy of Sciences, Beijing 100039, China)

  • Ge Ren

    (Key Laboratory of Optical Engineering, Chinese Academy of Sciences, Chengdu 610209, China
    The Institute of Optics and Electronics, Chinese Academy of Sciences, Chengdu 610209, China
    University of Chinese Academy of Sciences, Beijing 100039, China)

Abstract

In this paper, we consider a two-sided vibro-impact energy harvester described as a forced cylindrical capsule inclined at a horizontal angle, and the motion of the ball inside the capsule follows from the impacts with the capsule ends and gravity. Two distinct cases of dynamical behavior are investigated: the nondissipative and dissipative cases, where the dissipation is given by a restitution coefficient of impacts. We show that the dynamics of the system are described by the use of a 2D implicit map written in terms of the variables’ energy and time when the ball leaves the moving capsule ends. More precisely, in the nondissipative case, we analytically show that this map is area-preserving and the existence of invariant curves for some rotation number with Markoff constant type is proved according to Moser’s twist theorem in high energy. The existence of invariant curves implies that the kinetic energy of the ball is always bounded, and hence, the structure of system is not destroyed by the impacts of the ball. Furthermore, by numerical analysis we also show that the dynamical behavior of this system is regular, mainly containing periodic points, invariant curves and Aubry–Mather sets. After introducing dissipation, the dissipation destroys the regular dynamical behavior of the nondissipative case, and a periodic point with low energy is generated.

Suggested Citation

  • Zhenbang Cao & Haotong Ma & Xuegang Yu & Jianliang Shi & Hu Yang & Yi Tan & Ge Ren, 2022. "Global Dynamics of a Vibro-Impact Energy Harvester," Mathematics, MDPI, vol. 10(3), pages 1-12, February.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:3:p:472-:d:740166
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    References listed on IDEAS

    as
    1. Zhao, Huai & Ouyang, Huajiang, 2021. "A capsule-structured triboelectric energy harvester with stick-slip vibration and vibro-impact," Energy, Elsevier, vol. 235(C).
    2. Carneiro, Pedro & Soares dos Santos, Marco P. & Rodrigues, André & Ferreira, Jorge A.F. & Simões, José A.O. & Marques, A. Torres & Kholkin, Andrei L., 2020. "Electromagnetic energy harvesting using magnetic levitation architectures: A review," Applied Energy, Elsevier, vol. 260(C).
    Full references (including those not matched with items on IDEAS)

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