Transverse elastic waves in periodically layered infinite and semi-infinite media

The propagation of transverse elastic waves both perpendicular and parallel to the laminations of infinite and semi-infinite periodically layered media is studied. The displacement fields and the dispersion relations for such waves are obtained analytically, and the latter are solved numerically to yield the corresponding dispersion curves. It is shown that a semi-infinite medium layered periodically parallel to its stress-free surface can support shear horizontal surface acoustic waves that have no counterpart in a homogeneous medium. Finally, the dynamical elastic Green's function for a semi-infinite medium layered periodically parallel to its stress-free surface is obtained, and its possible application to Brillouin scattering studies of the surface acoustic waves on such a medium is discussed.