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Dynamic model of vibrating plate coupled with a granule bed

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  • Dong, Jinlu
  • Fang, Jianhong
  • Pan, Jingwu
  • Hong, Guangyang
  • Li, Jian

Abstract

A dynamic model is proposed to study the nonlinear behavior of a granule-bed–vibrating-plate coupling system based on the theory of a completely inelastic bouncing ball. The process of interactions between the ball and plate is divided into three stages: synchronized motion, separation, and impact. The discrete-element method is used to obtain the form of the impact function inspired by the bird impact model, and the analytical solutions of the overall process are derived. Furthermore, parametric research is performed to demonstrate the influence on the motion of the plate of system parameters including the amplitude of the excitation force, particle mass, and damping. The calculation results indicate that the model can be used to analyze the coupling dynamic behaviors of particles and plates, and abundant nonlinear phenomena, such as period-doubling bifurcations, can be observed. The motion of the plate always shows chaos in particular frequency bands (the ratio of external excitation frequency to natural frequency was between 0.63 and 0.75 for the conditions in this study).

Suggested Citation

  • Dong, Jinlu & Fang, Jianhong & Pan, Jingwu & Hong, Guangyang & Li, Jian, 2022. "Dynamic model of vibrating plate coupled with a granule bed," Chaos, Solitons & Fractals, Elsevier, vol. 156(C).
    • Handle: RePEc:eee:chsofr:v:156:y:2022:i:c:s0960077922000686
    DOI: 10.1016/j.chaos.2022.111857
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    References listed on IDEAS

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    1. Mátyás, L. & Barna, I.F., 2011. "Geometrical origin of chaoticity in the bouncing ball billiard," Chaos, Solitons & Fractals, Elsevier, vol. 44(12), pages 1111-1116.
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    4. Khan, Arif Ullah & Al-Zubaidi, A. & Munir, Shahid & Saleem, S. & Duraihem, Faisal Z., 2021. "Closed form solutions of cross flows of Casson fluid over a stretching surface," Chaos, Solitons & Fractals, Elsevier, vol. 149(C).
    5. Hong Han & Zehui Jiang & Rui Zhang & Jing Lyu, 2013. "Subharmonic bifurcations and chaotic dynamics of an air damping completely inelastic bouncing ball," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 86(12), pages 1-7, December.
    6. Han, Hong & Jiang, Ze Hui & Zhang, Rui & Lyu, Jing, 2014. "The influence of air on period doubling motion in vertically vibrated grains beds," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 403(C), pages 265-275.
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