Power law decay of zero group velocity Lamb modes

Elastic plates or cylinders can support guided modes with zero group velocity (ZGV) for nonzero wave numbers. At these ZGV-points of the dispersion curves the acoustic energy does not propagate in the waveguide, resulting in sharp resonance effects. In this paper, using laser-based ultrasonic techniques, we investigate the time-decay of the mechanical displacement for ZGV Lamb modes excited by a pulsed laser in various thin metallic plates. In the first microseconds of the local plate vibration, we observed a t-1/2 decay due to the second order term in the dispersion relation. This effect is dominant because the first order term, proportional to the group velocity, vanishes for ZGV-modes. After this power law decay, the mechanical displacement undergoes an exponential decay corresponding to the wave damping. Then, the local attenuation of the plate material can be estimated at the ZGV-resonance frequency.