Zero group velocity Lamb modes and edge resonance in a semi‐infinite plate.

Abstract

The local resonances of an elastic plate with a free edge are investigated using laser ultrasonic techniques. It is known that the long wavelength vibrations of a plate can be interpreted in terms of Lamb modes. Low‐frequency vibrations can be ascribed to the flexural A0 mode, while high‐frequency shear or stretch vibrations occur at the cutoff of higher order Lamb modes. These thickness resonances correspond to an in‐phase motion of the whole plate, associated to vanishing Lamb wave number. An elastic plate can also support local vibrations at nonzero values of the wave number for which Lamb mode dispersion curves undergo a minimum. Recently, experiments using laser ultrasonic techniques demonstrated that the local resonance of an infinite elastic plate is entirely governed by these zero group velocity (ZGV) Lamb modes. For a semi‐infinite plate, ZGV modes can be observed at a distance as close as two thicknesses from the edge. Coming toward the edge, ZGV resonances slowly vanish, whereas the edge mode resonance appears, whose frequency depends on the thickness and on the bulk velocities of the plate. Using a laser excitation on the edge, the amplitude profile of the normal displacement of the edge was determined.