Determination of longitudinal waves in elastic media with distributed thin inclusions of low contrast

An algorithm is proposed to study the effective velocities of longitudinal waves propagation in an unbounded isotropic elastic medium with a system of randomly distributed thin penny-shaped elastic inclusions of variable thickness. It is assumed that inclusions of low contrast, i. e. mechanical parameters of composites components differ unessentially in comparison with little relative thickness of inhomogeneities. The averaged dynamic parameters of such media are determined using the Foldy dispersive relation during the previous analysis of the problem of elastic waves scattering by the corresponding local scatterer.