Vibrational dynamics of confined granular materials.

By means of two-dimensional contact dynamics simulations, we analyze the vibrational dynamics of a confined granular layer in response to harmonic forcing. We use irregular polygonal grains allowing for strong variability of solid fraction. The system involves a jammed state separating passive (loading) and active (unloading) states. We show that an approximate expression of the packing resistance force as a function of the displacement of the free retaining wall from the jamming position provides a good description of the dynamics. We study in detail the scaling of displacements and velocities with loading parameters. In particular, we find that, for a wide range of frequencies, the data collapse by scaling the displacements with the inverse square of frequency, the inverse of the force amplitude, and the square of gravity. Interestingly, compaction occurs during the extension of the packing, followed by decompaction in the contraction phase. We show that the mean compaction rate increases linearly with frequency up to a characteristic frequency and then it declines in inverse proportion to frequency. The characteristic frequency is interpreted in terms of the time required for the relaxation of the packing through collective grain rearrangements between two equilibrium states.