Acoustic of Sound Propagation in Granular Materials in One, Two, and Three Dimensions

Abstract

We investigate the sound velocity of assemblies of granular particles. Computationally, we investigate regular polygons with various corner numbers in two dimensions with the discrete element method and compare the results for large corner numbers with experiments on soft air-gun beads. The sound velocity for one-dimensional granular chains of spherical particles is about one order of magnitude less than the sound velocity of the bulk material, both in the simulation as well as in the experiment. For twodimensional simulations, the results are comparable to that for one-dimensional chains, but vary with the packing. For the experiments in three dimensions, we find that the sound velocity is two orders of magnitude less than that of the bulk, or one order of magnitude less than that for one-or two-dimensional systems. This result is consistent with the group velocity reported by Liu and Nagel, but well below their reported ''sound velocity''. The latter was in all likelihood not a linear (amplitude-independent) sound wave but one for which the sound-velocity was already affected by non-linear effects, as we elaborate on experimental, theoretical and computational considerations.