Scattering of Plane Waves by a Cavity Ribbon in a Solid

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Abstract
The scattering of plane compressional or shear waves by a cavity ribbon with width a in an elastic medium is computed by the use of the Mathieu functions when the displacement of the incident wave is in xy plane. The diffraction patterns for kca/2=1, 2, and 4, and for ks=2kc are obtained; the diffraction patterns by a cavity ribbon are similar to those of the sound wave by a perfectly absorbing ribbon only when the incident compressional waves propagate to the direction normal to the plane of the ribbon. The scattering cross sections Q/a are of the order of (ka)3 in the Rayleigh case. These facts support the conclusion of the previous paper (rigid ribbon).