Acoustic waves in random distributions of double porosity cylinders

Abstract

Effective quantities – wavenumber, bulk modulus and mass density – are sought for a random distribution of double porosity parallel circular cylinders saturated by the surrounded fluid. For this purpose, a Generalized Self Consistent Method (GSCM) is applied to Linton and Martin’s formula for the wavenumber, which accounts for multiple scattering between cylinders. Since Linton and Martin’s formula contains the Independent Scattering Approximation (ISA), the simplest case of GSCM applied to ISA is also examined. The analysis is restricted to low frequencies where the implicit equations derived from generalized self consistent schemes can be solved analytically. The study focuses especially on the dependence of the effective quantities with the P1, P2, P3 and S waves propagating in the double porosity domains of the heterogeneous medium. Influence of volume fraction of scatterers and of porosity is illustrated.