Surface waves on the periodic boundary of an elastic half space

The existence of free surface waves on the periodic boundary of an elastic half space is established. These waves are a generalization of Rayleigh waves, and they can propagate both along and — at low frequencies and small profile heights — normal to the ridges of the periodic surface (periodic in one direction and constant in the other). It is shown how the wave number depends on the height and shape of the periodic surface, the frequency, and the direction of propagation. To give a further insight into behaviour of the surface waves some computations of surface displacements are given.