Propagation of coherent transverse waves: Influence of the translational and rotational subwavelength resonances.

The propagation of coherent transverse waves through a homogeneous elastic medium containing a set of spherical dense inclusions is an interesting topic. In such a material, in addition to the coherent longitudinal wave, two coherent transverse waves can propagate. The modeling used is based on the multiple scattering theory, which requires the scattering coefficients of the single scattering problem. These coefficients are calculated for moving rigid particles, leading to approximations of the two subwavelength dipolar resonances, one associated to a translational motion and the other to a rotational motion. Numerical simulations are carried out in order to compare the effective wavenumbers of the coherent elastic waves through the analysis of their phase velocity and attenuation. This comparison is performed for elastic and moving rigid spheres. It is shown that both dipolar resonances may have a great influence on the propagation of coherent transverse waves.