| FUNDAMENTAL AREAS OF PHENOMENOLOGY(INCLUDING APPLICATIONS) |
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Cluster Model for Wave-Like Motions of a 2D Vertically Vibrated Granular System |
| CAI Hui, MIAO Guo-Qing |
| Institute of Acoustics and Key Laboratory of Modern Acoustics of Ministry of Education, Nanjing University, Nanjing 210093 |
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| Cite this article: |
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CAI Hui, MIAO Guo-Qing 2010 Chin. Phys. Lett. 27 124501 |
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Abstract The fact that trapezoid clusters exist in 2D vertically vibrated granular systems leads us to construct a cluster model, in which wave-like motions are explained as the result of cluster-plate and cluster-cluster collisions. By analyzing the collision of one cluster with the plate in detail, we deduce a basic equation from velocity relationship, which could be separated into two correlative equations: one relates wave-like motion with exciting acceleration, and we call it the excitation condition; the other relates wavelength with exciting frequency, viz., the dispersion relation. The theoretical results are in agreement with the experimental ones, which supports the idea of the cluster model. Moreover, from the cluster model, we also predict a possibility of abnormal dispersion relation of a 2D granular system.
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| Keywords:
45.05.+x
45.70.Qj
05.65.+b
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Received: 30 July 2010
Published: 23 November 2010
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| PACS: |
45.05.+x
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(General theory of classical mechanics of discrete systems)
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45.70.Qj
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(Pattern formation)
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05.65.+b
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(Self-organized systems)
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