Propagation of High-Frequency Elastic Surface Waves Along Cylinders With Various Cross-Sectional Shapes

Elastic surface waves, or Rayleigh waves, are disturbances that travel over the stress-free surface of an elastic solid, and whose amplitudes decay rapidly with depth into the solid. In a series of earlier papers, 1-3 we developed and applied some mathematical techniques to describe the propagation of high-frequency elastic surface waves along cylinders of general cross section. Our intent was to learn more about the properties of such waves traveling down cylindrical objects that might be used as acoustic topographic waveguides. In this paper, we use our earlier mathematical results to study numerically the properties of elastic surface waves on certain specific cylindrical objects of interest. We treat 77 cylinders roughly corresponding to an elliptical bore, an elliptical rod, a wedge with a rounded tip, and a flat plane with a rounded ridge on it. The elastic medium is assumed to be homogeneous and isotropic. The earlier papers discussed two approximate high-frequency descriptions of the surface-wave behavior: an asymptotic approximation and one which we termed a surface-wave approximation. The analysis involved a scalar wave equation, a vector wave equation, and rather complicated boundary conditions. Since the analysis was cumbersome, a simpler scalar "model problem" was first investigated by Morrison. 1 The techniques he developed had counterparts in the full elastic problem, which was treated by Wilson and Morrison 2 in the high-frequency asymptotic approximation, designated by A (as depicted in Fig.