Antiplane coherent scattering from a slab containing a random distribution of cavities

The scattering of antiplane waves from a slab region containing a random distribution of cylindrical cavities is investigated. The cavities have a uniform probability density in the slab region and the solid is homogeneous and isotropic on either side of the slab. A general equation for the coherent motion in the solid is derived in terms of the average exciting displacement near a xed cavity. As in Foldy’s approach, it is assumed here that the average exciting displacement near a xed cavity is equal to the average total displacement. With this assumption, the equation for the coherent motion reduces to an integrodi¬erential equation, which is solved in closed form by using a Fourier transform technique. The closed-form solution greatly reduces the computational costs, and allows more direct investigation of the multiple scattering than is done elsewhere. Results for the amplitudes and phases of the re®ected and transmitted waves outside the slab are plotted versus the frequency for several values of the cavity density and slab thickness. These results are expected to be valid for low cavity density