Effective wave numbers for thermo-viscoelastic media containing random configurations of spherical scatterers

TL;DR

This paper derives a generalized dispersion relation for coherent waves in thermo-viscoelastic media with randomly distributed spherical scatterers, extending previous models to include thermal and viscous effects in three-dimensional settings.

Contribution

It presents a new, generalized formula for wave dispersion in thermo-viscoelastic media with spherical scatterers, broadening the applicability of prior models.

Findings

Derived a comprehensive dispersion relation for thermo-viscoelastic media.

Extended Lloyd and Berry's formula to include thermal and viscous effects.

Provided a three-dimensional counterpart to previous cylindrical scatterer models.

Abstract

The dispersion relation is derived for the coherent waves in fluid or elastic media supporting viscous and thermal effects and containing randomly distributed spherical scatterers. The formula obtained is the generalization of Lloyd and Berry's [Proc. Phys. Soc. Lond. 91, 678-688, 1067], the latter being limited to fluid host media, and it is the three-dimensional counterpart of that derived by Conoir and Norris [Wave Motion 47, 183-197, 2010] for cylindrical scatterers in an elastic host medium.