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

Abstract

The complex eigenfrequencies of an evacuated, fluid-immersed infinite cylindrical shell, when plotted in the complex frequency plane, have been grouped into families corresponding to different types of circumferential waves. The real parts of these eigenfrequencies have been used to obtain dispersion curves versus frequency of the phase velocities of these circumferential waves, which are analogous to those of the Lamb waves on an elastic plate in vacuo labeled A0,A1,... and S0,S1,..., but which contain an additional branch reminiscent of the fluid-borne Scholte–Stoneley wave. This branch forms together with the A0-analog an interacting pair of dispersion curves which will be called A0+ (upper branch) and A0− (lower branch). These exhibit a repulsion phenomenon near the ambient fluid sound speech analogous to that in perturbed, quasi-degenerate atomic levels. This is explained here by perturbation theory, showing that during repulsion the wave character gets exchanged so that at frequencies above the repulsion point A0+ is a flexural and A0− a fluid-borne wave, and vice versa below the repulsion point.