Sound wave propagation in weakly polydisperse granular materials

Dynamic simulations of wave propagation are performed in dense granular media with a narrow polydisperse size-distribution and a linear contact-force law. A small perturbation is created on one side of a static packing and its propagation, for both P- and S-waves, is examined. A size variation comparable to the typical contact deformation already changes sound propagation considerably. The transmission spectrum becomes discontinuous, i.e., a lower frequency band is transmitted well, while higher frequencies are not, possibly due to attenuation and scattering. This behaviour is qualitatively reproduced for (i) Hertz non-linear contacts, for (ii) frictional contacts, (iii) for a range of smaller amplitudes, or (iv) for larger systems. This proves that the observed wave propagation and dispersion behaviour is intrinsic and not just an artifact of (i) a linear model, (ii) a frictionless packing, (iii) a large amplitude non-linear wave, or (iv) a finite size effect.