Introduction

Many aspects of horizontal shear wave propagation are intriguing and quite valuable for applications involving wave propagation, including ultrasonic NDT. Traditionally, the longitudinal and vertical shear modes of wave propagation have been the most commonly used – probably because they are simple to understand and to generate. Yet horizontal shear waves can also be generated quite easily through a variety of different transducers. This chapter covers the fundamental concepts of such propagation.

Dispersion Curves

In addition to the Lamb wave modes that exist in flat layers, there also exists a set of time-harmonic wave motions known as shear horizontal (SH) modes. The term “horizontal shear” means that the particle vibrations (displacements and velocities) caused by any of the SH modes are in a plane that is parallel to the surfaces of the layer. This is depicted in Figure 14.1, where the wave propagates in the x1 direction and the particle displacements are in the x3 direction.

Physically, any mode in the SH family can be considered as the superposition of up- and down-reflecting bulk shear waves, polarized along x3, with wavevectors lying in the (x1, x2)-plane and inclined at such an angle that the system of waves satisfies traction-free boundary conditions on the surfaces of the layer.

The dispersion equation governing the SH modes can be derived in several ways, including the use of Helmholtz potentials, partial wave analysis, or transverse resonance (Auld 1990). Because of the simple physical nature of the SH modes, the most straightforward way to solve the problem is to deal directly with the displacement equations of motion. This is the approach taken here; for more discussion of this technique, see Achenbach (1984).