Elastic waves in a 3D non cohesive granular phononic crystal with rotating particles

The bulk modes of an unconsolidated packing of monodisperse spherical beads, considered as rigid masses connected with springs, arranged in the hexagonal close packed structure are theoretically evaluated. Because of friction, the contacts between spheres are modeled by two springs, one for normal interaction and one for transverse interaction. The existence of the transverse interaction requires to take into account the rotational degrees of freedom of the beads and leads to predict the existence of rotational waves. Theoretical results predict, in the direction perpendicular to the layers plane, the existence of an elastic acoustical-type longitudinal mode, an elastic optical-type longitudinal mode, pure elastic rotational modes and coupled transverse-rotational modes. In the experimental investigations, the dispersion of a pulse is qualitatively observed and show results comparable to the developed theory.