Local vibration of an elastic plate and zero-group velocity Lamb modes

Abstract

Elastic plates or cylinders can support guided modes with zero group velocity (ZGV) at a nonzero value of the wave number. Using laser-based ultrasonic techniques, we experimentally investigate some fascinating properties of these ZGV modes: resonance and ringing effects, backward wave propagation, interference between backward and forward modes. Then, the conditions required for the existence of ZGV Lamb modes in isotropic plates are discussed. It is shown that these modes appear in a range of Poisson's ratio about the value for which the cutoff frequency curves of modes belonging to the same family intercept, i.e., for a bulk wave velocity ratio equal to a rational number. An interpretation of this phenomenon in terms of a strong repulsion between a pair of modes having a different parity in the vicinity of the cutoff frequencies is given. Experiments performed with materials of various Poisson's ratio demonstrate that the resonance spectrum of an unloaded elastic plate, locally excited by a laser pulse, is dominated by the ZGV Lamb modes.

Air-coupled ultrasonic through-transmission thickness measurements of steel plates

“…When the Lamb mode group velocity vanishes for non-zero wavenumbers it is referred to as zero group velocity (ZGV) modes. ZGV modes have been identified to exist for symmetrical and antisymmetric modes up to orders 10 and 9, respectively, and for a wide range of Poisson's ratios [40]. One of the modes with an observed ZGV-point is the first symmetrical mode, referred to as S 1 -ZGV.…”

“…A group of non-contact techniques that produce and senses ultrasound in metals and other materials, is the laser-based techniques [50]. The laser based methods have been successful in studying Lamb waves in plates [51,52] and more specifically, the ZGV modes [40].…”

“…Prada et al [40] investigated the ZGV mode and the backward propagating wave both experimentally and theoretically. The temporal behavior of ZGV resonances was studied in [46,47], where a power law and an exponential decay in time of the ZGV resonances were observed.…”

Time-resolved detection of propagating Lamb waves in thin silicon membranes with frequencies up to 197 GHz

“…Compared to surface acoustic waves in bulk silicon twice higher frequencies for Lamb waves (197 GHz with a 100 nm grating) are generated in a membrane at equal grating periods. 4,5 Continuous progress in the development of methods for the fabrication of membranes with a thickness in the nm range for a variety of applications 6 requires the evaluation of their parameters and quality, e.g., their dispersion relation and damping, the development of methods for both the generation and detection of acoustic waves at GHz frequencies.Standing waves in free-standing films of lm thickness have been first detected by Brillouin scattering. 7 Recently, femtosecond lasers have been successfully applied to generate and detect longitudinal acoustic modes in free-standing silicon (Si) membranes with frequencies up to 500 GHz corresponding to 20 nm wavelengths.…”

“…Compared to surface acoustic waves in bulk silicon twice higher frequencies for Lamb waves (197 GHz with a 100 nm grating) are generated in a membrane at equal grating periods. 4,5 Continuous progress in the development of methods for the fabrication of membranes with a thickness in the nm range for a variety of applications 6 requires the evaluation of their parameters and quality, e.g., their dispersion relation and damping, the development of methods for both the generation and detection of acoustic waves at GHz frequencies.…”