This paper deals with the scattering of plane longitudinal and shear waves by a distribution of elastic ellipsoidal inclusions. The scattered field is determined correct to O(ε3) where ε is a nondimensional wave number, assumed small. Assuming then that the distribution of scatterer centers is random homogeneous function of position and using a self-consistent (“quasi-crystalline”) approximation effective wave speeds are determined for the case of preferred orientation. Various limiting cases, viz., spherical inclusions and voids, elliptic and penny-shaped cracks, and fluid-filled cavities, are derived.

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