Low frequency approximations for effective wavenumbers and moduli of randomly perforated poroelastic media

A random distribution of cylindrical fluid cavities in a poroelastic matrix obeying Biot's theory is considered. Using the Conoir-Norris generalization of the Linton-Martin formula to media sustaining both P and SV waves, we examine successively the incidence of fast, slow and shear waves onto the random medium. Analytical expressions are sought for the effective wavenumbers of the coherent waves in the Rayleigh limit. The estimates for the mass density and moduli of the heterogeneous media are presented up to the order of c2 in concentration. The limiting case of random fluid cavities in an elastic matrix is also discussed.