Chapter 5

Abstract

In the last chapter we discussed how to solve the problem of a planar SH-wave incident from a half space onto the bottom of a layer welded on that half space. In this case, there were no post-critical angle reflections in the problem. However, there are instances in which plane waves can travel horizontally such that there is a critical reflection of the wave at the boundary between the layer and the half-space. In this case the waves are totally reflected at the top and the bottom of the layer and it becomes trapped within the layer. This problem is similar to the propagation of planar SH-waves in a plate that was also discussed in the last chapter. However, this problem differs in that the plate problem had traction free boundaries above and below, while the current problem has an elastic half-space below. In order to solve this problem, we must investigate the nature of critically reflected waves. Consider the problem of a planar harmonic SH-wave that is incident on the boundary of two welded spaces, as was shown in Figure 4.2 of the previous chapter. A general expression for such a wave can be written as