Abstract
Based on the cluster model for wave-like motions of a 2D vertically vibrated granular system we established previously (Chin Phys Lett, 2010, 27: 124501), a generalization of the cluster model for a 3D granular system is presented in this paper. The 3D cluster model proposes frustums of pyramids as clusters of the 3D granular system, and explains wave patterns as the result of the cluster-boundary and cluster-plate collisions. By analyzing the movement of one cluster in a collision period, we derive a basic equation, which relates the internal characteristic parameter to the external driving parameters. The theoretical results reproduce the behaviors of wave patterns as changes in the driving parameters, and the 3D dispersion relation, which agree with the experimental results.
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Zhang P. Pattern formation and interior dynamics of a bidimensional granular layer under vertical vibration (in Chinese). Master Dissertation. Nanjing: Nanjing University, 2006. 7–15
Cai H, Miao G Q. Cluster model for wave-like motions of a 2D vertically vibrated granular system. Chin Phys Lett, 2010, 27: 124501
Melo F, Umbanhowar P B, Swinney H L. Hexagons, kinks, and disorder in oscillated granular layers. Phys Rev Lett, 1995, 75: 3838–3841
Bizon C, Shattuck M D, Swift J B, et al. Patterns in 3D vertically oscillated granular layers: Simulation and experiment. Phys Rev Lett, 1998, 80: 57–60
Zhang P, Miao G Q, Huang K, et al. Experimental observation of kink in a perfect bidimensional granular system. Chin Phys Lett, 2005, 22: 1961–1963
Melo F, Umbanhowar P, Swinney H L. Transition to parametric wave pattern in a vertically oscillated granular layer. Phys Rev Lett, 1994, 72: 172–175
Clément E, Vanel L, Rajchenbach J, et al. Pattern formation in a vibrated granular layer. Phys Rev E, 1996, 53: 2972–2975
Aoki K M, Akiyama T. Spontaneous wave pattern formation in vibrated granular materials. Phys Rev Lett, 1996, 77: 4166–4169
Risso D, Soto R, Godoy S, et al. Friction and convection in a vertically vibrated granular system. Phys Rev E, 2005, 72: 011305
Götzendorfer A, Tai C H, Kruelle C A, et al. Fluidization of a vertically vibrated two-dimensional hard sphere packing: A granular meltdown. Phys Rev E, 2006, 74: 011304
McNamara S, Falcon E. Simulations of vibrated granular medium with impact-velocity-dependent restitution coefficient. Phys Rev E, 2005, 71: 031302
Miao G Q, Sui L, Wei R J. Dissipative properties and scaling law for a layer of granular material on a vibrating plate. Phys Rev E, 2001, 63: 031304
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Cai, H., Miao, G. Cluster model for wave patterns of a 3D vertically vibrated granular system. Chin. Sci. Bull. 56, 1340–1347 (2011). https://doi.org/10.1007/s11434-011-4426-y
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DOI: https://doi.org/10.1007/s11434-011-4426-y