Scattering of Plane Waves by a Rigid Ribbon in a Solid

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Abstract
The scattering of plane compressional and shearing waves by an infinitely long rigid ribbon with width a in an elastic medium is computed by the use of the Mathieu functions. The diffractionpatterns for ka/2=1,2, and 4 are calculated numerically; the distributions‐in‐angle of the elastic waves bears no resemblance to that of the sound except for the normally incident compressional wave. The expressions for the scattering field and cross section, in powers of ka=h, are obtained in the Rayleigh case. In this case the scattering cross section is of the order of the wavelength, as it is in the case of the scattering of the sound by an absorbing ribbon. Some new expansions of the Mathieu functions in powers of h are listed in the Appendix.

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