Effective properties of acoustic waves in a poroelastic medium containing spherical cavities randomly distributed within the Rayleigh limit

TL;DR

This paper investigates how acoustic waves propagate in a poroelastic medium with randomly distributed spherical cavities, deriving effective properties and wave numbers in the low frequency limit.

Contribution

It introduces generalized Waterman-Truell and Linton-Martin formulas for poroelastic media, providing explicit expressions for effective wave properties.

Findings

Derived effective mass densities and moduli for the medium.

Obtained wave numbers of coherent waves in the low frequency limit.

Extended formulas to include poroelastic effects.

Abstract

The propagation of acoustic waves in a poro-elastic medium of infinite extension containing spherical cavities randomly distributed is investigated. The scattering coefficients are computed in the low frequency limit using the sealed pore boundary conditions. Also in this limit, using explicit Waterman-Truell (WT) formulas and a generalization of the Linton-Martin (LM) formula to poro-elastic medium, expressions of the wave numbers of the coherent waves are proposed. Expressions of the effective mass densities and moduli are derived from the WT formulas. The effective properties of the coherent wave in an elastic medium are obtained as a limiting case when the porosity tends towards zero.