Homogenization of the Helmholtz problem in the presence of a row of viscoelastic inclusions

We propose a homogenization method based on a matched asymptotic expansion technique to obtain the effective behavior of a periodic array of linear viscoelastic inclusions embedded in a linear viscoelastic matrix.  The problem is considered for shear waves and the wave equation in the harmonic regime is considered.  The obtained effective behavior is that of an equivalent interface associated to jump conditions, for the displacement and the normal stress at the interface.  The transmission coefficients and the displacement fields are obtained in closed forms and their validity is inspected

Homogenization of subwavelength free stratified edge of viscoelastic media including finite size effect

This paper proposes the homogenization for a stratified viscoelastic media with free edge.  We consider the effect of two-dimensional periodically stratified slab over a semi-infinite viscoelastic ground on the propagation of shear waves hitting the interface.  Within the harmonic regime, the second order homogenization and matched-asymptotic expansions method is employed to derive an equivalent anisotropic slab associated with effective boundary and jump conditions for the displacement and the normal stress across an interface.  The reflection coefficients and the disp