Optical excitation and detection of ZGV Lamb waves

Our proposal deals with non-contact excitation and detection of a Lamb wave in a particular point of the dispersion relation. By using spatially and temporally modulated laser-ultrasound we want to utilize the zero group velocity (ZGV) point of the first order symmetrical mode Lamb wave to characterize isotropic plates non-destructively. It is wellknown that for certain wave modes within the Lamb wave dispersion relation segments with negative group velocity exist. The turning points of these curves between negative and positive slope and positive group velocity are of significant interest as here the group velocity becomes zero. As the energy propagation of a wave packet is related to the group velocity at this point of the dispersion relation a strong well-detectable resonance occurs. In contrast to thickness resonances in plates which occur with k=0, where k denotes the wave number, this mode is associated with a finite wave number. Earlier works made use of local, non-contact pulse-echo measurements by using laser-ultrasonic techniques and evaluation of the temporal frequencies of the thickness and ZGV resonances. These methods provide high accuracy for the evaluation of the material properties (longitudinal and shear wave velocities cL, cS) compared to conventional time-of-flight pulse-echo measurements, but do not deliver additional information, like the plate thickness h, for instance: either the material properties or the plate thickness must be known or evaluated by independent measurements. We propose to measure also the wave number, i.e. the wavelength, of the ZGV resonance to gain this information. Since in this point the group velocity must vanish, it defines an additional, unique relationship between the temporal-spatial ZGV frequencies (fZGV, kZGV), material properties (cL, cS) and plate thickness (h). Hence, the temporal and spatial frequencies of the ZGV resonance combined with a frequency scan by the temporally modulated laser-source allows the unique determination of these unknowns. Such measurements are feasible using temporally modulated laser sources in combination with a Spatial Light Modulator (SLM). It allows to measure an arbitrary part of the dispersion relation, e.g. the ZGV point. Temporally modulated laser-ultrasound also allows the evaluation of both thickness and ZGV temporal resonance frequencies. The proposed setup allows arbitrary temporal and spatial frequency resolution. The latter is achieved by using a combination of SLM and tunable magnification optics to fine-tune the size and line-distance of the excitation pattern.

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