Sound wave propagation in dry granular materials : simulations, theory and experiments

Abstract

In this study sound wave propagation through different types of dry confined granular systems is studied. With three-dimensional discrete element simulations, theory and experiments, the influence of several micro-scale properties: friction, dissipation, particle rotation, and contact disorder, on the macro-scale sound wave propagation characteristics are investigated. Experiments, analyzed with the “Spectral Ratio Technique”, make it possible to extract frequency-dependent propagation velocities and attenuation. An improved set-up for future investigations is proposed in order to better understand dispersion and propagation of sound in granular materials. The full dispersion relation of a Face-Centered-Cubic lattice is derived from a theoretical analysis that involves translations, tangential elasticity, and rotations. The additional displacement and rotation modes and the energy conversion between them is studied using discrete element simulations. Simulations and theory are in perfect quantitative agreement for the regular lattices examined. As a first small step away from order, systems with weak geometrical disorder (system structure) but strong contact disorder, i.e. with an inhomogeneous contact force distribution, are studied next. They reveal nicely the dispersive nature of granular materials and show strong frequency filtering. Low frequencies propagate, whereas high frequencies vanish exponentially. A more detailed study of how energy is transfered between different wavenumber bands shows linearly increasing transfer rates for increasing wavenumbers. A first theoretical approach using a linear Master Equation leads to a quantitative prediction of the energy evolution per band for short times. A bigger second step in complexity is made by investigating the sound propagation in a realistic tablet made of a sintered frictional and cohesive polydisperse powder and prepared in different ways. These simulations nicely display history dependence and the effect of different material parameters. As a conclusion, simulations were found to be a valuable tool to complement theoretical and experimental approaches towards the understanding of complex phenomena, such as sound propagation in (dry) granular materials. However, many open issues, in particular concerning the modeling, still remain.