Antiplane coherent scattering from a slab containing a random distributionof cavities

The scattering of antiplane waves from a slab region containing a random di stribution of cylindrical cavities is investigated. The cavities have a uni form probability density in the slab region and the solid is homogeneous an d 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 displaceme nt near a fixed cavity. As in Foldy's approach, if is assumed here that the average exciting displacement near a fixed cavity is equal to the average total displacement. With this assumption, the equation for the coherent mot ion reduces to an integrodifferential equation, which is solved in closed f orm by using a Fourier transform technique. The closed-form solution greatl y reduces the computational costs, and allows more direct investigation of the multiple scattering than is dolls elsewhere, Results for the amplitudes and phases of the reflected and transmitted waves outside the slab are plo tted versus the frequency for several values of the cavity density and slab thickness. These results are expected to be valid for low cavity density.