Lamb mode spectra versus the Poisson ratio in a free isotropic elastic plate

Abstract

The variation, with material parameters, of Lamb modes is investigated. Vibration spectra of traction-free elastic plates are generally presented, for a given isotropic material, as a set of dispersion curves corresponding to the various Lamb mode branches. Here, the spectrum variations, with the Poisson ratio nu, are plotted in a dimensionless co-ordinate system in the form of a bundle of curves for each Lamb mode. Except for the fundamental anti-symmetric mode A(0), this representation highlights the same behavior for all Lamb modes. V(T) denoting the shear wave velocity, the (omega,k) plane can be divided into two angular sectors separated by the line of slope V(T) [square root]2. In the upper one, corresponding to a phase velocity V=omega/k larger than V(T)[square root]2, dispersion curves are very sensitive to the plate material parameters. In the lower sector (V<V(T)[square root]2) all the branches, whatever the value of the Poisson ratio (0<or=nu<0.5), are gathered into a thin pencil. Moreover, curves of a given bundle cross the boundary line at coincidence points equally spaced. These properties and a specific behavior observed for nu=0 are explained in terms of Lame wave solutions of the characteristic equations of Lamb modes.