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.