Conical dispersion of Lamb waves in elastic plates

Guided elastic waves in homogeneous isotropic plates exhibit conical dispersion at zero wave number for discrete values of Poisson's ratio where accidental degeneracy between longitudinal and transverse thickness resonances occur. Waves excited at the coincidence frequency have the infinite phase velocity associated with thickness mode resonances, but the group velocity remains finite. This leads to propagating waves that oscillate in time but are spatially uniform over the plate surface. Here, accidental degeneracy is induced in an aluminum plate by cooling the plate to tune the Poisson's ratio through the degenerate point. We measure linear dispersion in the transition from forward to backward propagating waves near zero wave number. In addition, we demonstrate that waves generated near the coincidence frequency exhibit spatially uniform phase over the plate surface, and show angle independent mode conversion upon encountering the free edge of the plate. We propose that elastic plates offer a simple system to explore the physics of conical dispersion at zero wave number, and that this phenomenon may find application in acoustic devices and nondestructive testing.