Repulsion of phase-velocity dispersion curves and the nature of plate vibrations

Abstract

The Lamb waves propagating in an elastic plate in vacuo generate compressional (L) and shear-type (T) plate vibrations which are coupled due to the boundary conditions. Without such coupling, their phase-velocity dispersion curves would form two intersecting families, which at high frequency, tend toward the elastic-wave speeds CL and CT, respectively. It is shown that the coupling causes a repulsion of the dispersion curves similar to that encountered in atomic physics for the energy levels of atoms combining into molecules, which prevents their intersection and at the same time exchanges the nature (L⇆T) of the underlying vibrations. However, in the repulsion regions a succession of dispersion curves combines to asymptotically approach the uncoupled L or T dispersion curves, respectively. For the case of a plate bounded by fluid on one side, and vacuum on the other, the dispersion curves of the fluid-borne (Stoneley–Scholte-type) wave which is known from the studies of Grabowska and Talmant to be present in this case, and of the usual A0 Lamb wave exhibit a similar repulsion phenomenon.