REPULSION OF PHASE-VELOCITY DISPERSION-CURVES AND THE NATURE OF PLATEVIBRATIONS

The Lamb waves propagating in an elastic plate in vacuo generate compr essional (L) and shear type (T) plate vibrations which are coupled due to the boundary conditions. Without such coupling, their phase-veloci ty dispersion curves would form two intersecting families which at hig h frequency tend towards the elastic-wave speeds C(L) and C(T), respec tively. It is shown that the coupling causes a repulsion of the disper sion curves similar to that encountered in atomic physics for the ener gy levels of atoms combining into molecules, which prevents their inte rsection and at the same time exchanges the nature (L <-> T) of the un derlying vibrations. However, in the repulsion regions a succession of dispersion curves combines to asymptotically approach the uncoupled L or T dispersion curves, respectively.