Two dimensional wave problems in rotating elastic media

Abstract

The rotation of an elastic medium makes it act anisotropically and dispersively. The eigenvectors for plane wave propagation are in general complex and thus the waves are elliptically polarized. In general the waves are neither pure shear nor pure compressional waves, and their speeds depend on the ratio of rotational frequency of the medium and the angular frequency of the wave. The class of problems discussed here involves waves propagating perpendicularly to the axis of rotation and in particular we discuss plane strain modes. The reflection and refraction of plane waves is considered. The plane waves are used to construct a general solution in cylindrical coordinates. The solution is given in terms of Bessel functions. The cylindrical solution is applied to scattering by circular cylinders. The problem of free oscillations is mentioned briefly.