Torsional Wave Propagation in a Circular Cylinder with a Periodically Corrugated Outer Surface

Abstract

The paper describes a theoretical study on the speed of torsional elastic waves propagating in a circular cylinder whose outer radius varies periodically as a harmonic function of the axial coordinate. An approximate solution for the phase speed was obtained by using the perturbation technique for sinusoidal modulation of a small amplitude. This shows that the wave speed in the cylinder with a corrugated outer surface is less than that in a smooth cylinder by the square of the amplitude of the surface perturbation. This theoretical prediction reasonably agrees with an experimental observation reported earlier. It is also shown that the wave speed reduction due to the surface corrugation becomes larger for a thinner cylinder and for a bigger density of corrugation.