Effective wave numbers for media sustaining the propagation of three types of bulk waves and hosting a random configuration of scatterers

International audienceWave propagation through an isotropic host medium containing a large number of randomly and uniformly located scatterers is considered at low frequency and for low concentrations of spheres, and the dispersion relation of the coherent waves is obtained. The same problem had been addressed by Lloyd and Berry for spheres in an ideal fluid, and more recently by Linton and Martin for cylinders in an ideal fluid, and by Conoir and Norris for cylinders in an elastic solid. Here, the dispersion relation is derived in the case of spheres, and extended to that of cylinders, from the comparison of the 3d and 2d cases in an elastic solid. The host medium considered may support the propagation of P different types of bulk waves, as for example a thermo-visco-elastic medium or a poro-elastic medium (P=3). As in the previous works mentioned above, the hole correction of Fikioris and Waterman is taken into account, along with the quasi-crystalline approximation