Global Dynamics of a Vibro-Impact Energy Harvester

Zhenbang Cao, Haotong Ma, Xuegang Yu, Jianliang Shi, Hu Yang, Yi Tan and Ge Ren
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Zhenbang Cao: Key Laboratory of Optical Engineering, Chinese Academy of Sciences, Chengdu 610209, China
Haotong Ma: Key Laboratory of Optical Engineering, Chinese Academy of Sciences, Chengdu 610209, China
Xuegang Yu: Key Laboratory of Optical Engineering, Chinese Academy of Sciences, Chengdu 610209, China
Jianliang Shi: Key Laboratory of Optical Engineering, Chinese Academy of Sciences, Chengdu 610209, China
Hu Yang: Key Laboratory of Optical Engineering, Chinese Academy of Sciences, Chengdu 610209, China
Yi Tan: Key Laboratory of Optical Engineering, Chinese Academy of Sciences, Chengdu 610209, China
Ge Ren: Key Laboratory of Optical Engineering, Chinese Academy of Sciences, Chengdu 610209, China

Mathematics, 2022, vol. 10, issue 3, 1-12

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.

Keywords: energy harvester; vibro-impact system; invariant curves; global dynamics (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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