Dynamics of a gravitationally loaded chain of elastic beads.

ABSTRACT

Elastic beads repel in a highly nonlinear fashion, as described by Hertz law, when they are compressed against one another. Vertical stacking results in significant compressions of beads at finite distances from the surface of the stack due to gravity. Analytic studies that have been reported in the literature assume acoustic excitations upon weak perturbation [J. Hong et al., Phys. Rev. Lett. 82, 3058 (1999)] and soliton-like excitations upon strong perturbation [V. Nesterenko, J. Appl. Mech. Tech. Phys. 5, 733 (1983); S. Sen and M. Manciu, Physica A 268, 644 (1999)]. The present study probes the position, velocity and acceleration and selected two-point temporal correlations and their power spectra for individual beads for cases in which the system has been (i) weakly, (ii) strongly, and (iii) moderately perturbed at the surface in the sense specified in the text. Our studies reveal the existence of distinctly different dynamical behavior of the tagged beads, in contrast to conventional acoustic response, as the strength of the perturbation is varied at fixed gravitational loading. We also comment on the effects of polydispersity on system dynamics and probe the relaxation of isolated light and heavy beads in the chain. (c) 2000 American Institute of Physics.