Repulsion phenomena in the phase-velocity dispersion curves of circumferential waves on elastic cylindrical shells

Abstract

The complex eigenfrequencies of a fluid-immersed evacuated infinite cylindrical shell, when plotted in the complex frequency plane, can be grouped into families corresponding to different types of circumferential waves. The dispersion curves versus frequency of the phase velocities of these circumferential waves are analogous to those of the Lamb waves on a plate A0, A1,… and S0, S1,…, but contain an additional branch reminiscent of the fluid-borne Scholte–Stoneley wave. This branch together with the A0-analog forms an interacting pair of dispersion curves A0+ (upper branch) and A0− (lower branch) which exhibit a repulsion phenomenon near the ambient fluid sound speed. Results of a recent numerical study of this phenomenon are here explained by perturbation theory, showing that during repulsion the wave character gets exchanged so that at frequencies above repulsion A0+ is a flexural and A0− a fluid-borne wave, and vice versa below repulsion.