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Phys. Rev. E 74, 046602 (2006) [10 pages]

Theoretical model for the pulse dynamics in a long granular chain

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Wei Ma, Caishan Liu, Bin Chen, and Lin Huang
College of Engineering, State Key Laboratory for Turbulence and Complex Systems, Peking University, Beijing, China

Received 29 May 2006; published 3 October 2006

Whena long line of initially stationary and unstressed touching particlesis hit on one end by another particle, dynamical self-organizedimpulsive waves will be generated and propagating through the granularchain. In this paper we develop a continuous function torepresent the initial impulse wave. Then the partial differential waveequations for chains of cylindrical granules, which can take suchfunction as one of its solutions, are constructed and exactlycoincided with the wave equation obtained by using Taylor seriesexpansion. The properties of the impulse wave propagating, such asthe attenuation of the wave and the forward momentum transferare studied in detail based on our theoretical model, andthe analytical solutions are supported by numerical simulations.

©2006 The American Physical Society

URL:	http://link.aps.org/doi/10.1103/PhysRevE.74.046602
DOI:	10.1103/PhysRevE.74.046602
PACS:	46.40.-f; 45.05.+x; 45.70.-n 46.40.-f Vibrations and mechanical waves 45.05.+x General theory of classical mechanics of discrete systems 45.70.-n Granular systems YEAR: 2006
KEYWORDS:	granular materials, wave propagation, wave equations

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