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 towards the elastic-wave speeds C_L and C_T, 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.