A numerical study of the dynamics of the surface grain in a granular chain and the role of gravity

We revisit the dynamical behavior of particles in a chain of spherical elastic grains, where the system is assumed to be placed in such a way that the grains suffer progressive loading as function of depth due to the presence of the gravitational acceleration g. Here we address, for the first time, the dynamics of the surface grain in this rather well studied problem (see [R.S. Sinkovits, S. Sen, Phys. Rev. Lett. 74 (1995) 2686; J. Hong, J.Y. Ji, H. Kim, Phys. Rev. Lett. 82 (1999) 3058]) and make predictions that may be verified experimentally by monitoring the dynamics of a single edge grain. When g ! 0, the surface grain dynamics can be associated with the problem of propagation of solitary waves in the chain. When g > 0, the dynamics of the surface grain turns out to be dramatically different, reflective of the very different dynamics exhibited by the grains in a gravitationally loaded chain. As we shall see, these studies provide a necessary first step towards developing an understanding of a difficult but important problem in physics and engineering — namely, the dynamics of the surface grains of a gravitationally loaded close-packed granular bed. c 2006 Elsevier B.V. All rights reserved.

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