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

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

MMC.
2023;
Volume 10, Number 1
: pp. 10–29
https://doi.org/10.23939/mmc2023.01.010
Received: August 04, 2022
Accepted: November 09, 2022

Mathematical Modeling and Computing, Vol. 10, No. 1, pp. 10–29 (2023)

Authors:
  1. R. Belemou
  2. A. Sbitti
  3. J.-J. Marigo
  4. A. Tsouli
1
University Hassan II, Ens
2
University Mohammed V, Ensam
3
Solid Mechanics Laboratory, Ecole Polytechnique
4
University Hassan II, Ensam

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 displacement fields are obtained in closed forms and their validity is inspected by comparison with direct numerics in the case of layers associated with Neumann boundary conditions.

homogenization
matched asymptotic expansion
reflection of waves
viscoelastic
stratified media
effective jump conditions
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