Transverse waves in anisotropic elastic materials

With few exceptions, a transverse wave can propagate in an anisotropic elastic material along certain directions only. Equations that allow us to compute the direction n, the polarization vector a and the wave speed c are presented for a general anisotropic elastic material. In contrast to longitudinal waves, the directions along which a transverse wave can propagate are not finite isolated directions. There is a one-parameter family of n along which a transverse wave can propagate. On the surface of the unit sphere n12+n22+n33=1, the n along which a transverse wave can propagate traces out at least three curves. The intersection of two or more curves is the direction along which a longitudinal wave can propagate. We present solutions for n, a and c for orthotropic, tetragonal and trigonal materials. The corresponding solutions for hexagonal and cubic materials have been obtained earlier.