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.

In this project we have optically excited and detected a particular type of guided elastic waves in plates termed as Zero Group Velocity (ZGV) Lamb waves. For zero-group-velocity Lamb waves, the energy is locally trapped which causes large, well-detectable displacements which manifest as sharp peaks in the local response spectrum of a plate. We studied the generation process of these waves and demonstrated their applicability for material characterization and non-destructive testing applications. The main aim of the project was the simultaneous determination of longitudinal and transversal wave velocities as well as the plate thickness using these modes. In addition, we also studied backward propagating Lamb waves, which appear due to the presence of ZGV Lamb waves and possess the intriguing property of having opposite directions for propagation and energy transport.In order to optically excite elastic waves, a laser is pointed on a sample surface, where it is partially absorbed. The material is locally heated by the absorbed energy and the swift thermal expansion generates mechanical waves which propagate in the material. The corresponding displacements at the sample surface are detected with a laser interferometer. In plates the generated waves form guided waves, so-called Lamb waves, propagating harmonically along the plate, with a distinct frequency and wavenumber. Depending on thickness and elastic material properties of the plate, resonant frequencies exist where ZGV Lamb waves which do not carry energy along the plate, arise. We were able to experimentally optimize the coupling of a laser source into these ZGV resonances. Optimum coupling occurs for a diameter of approximately 3 times the plate thickness. In addition, we showed that the decay of the resonant oscillations is affected by the spot diameter only in the first instant after the laser pulse impact, succeeded by a decay sole due to material damping. Progressing in the project we developed a systematic mathematical formulation for an inverse problem to find the elastic properties of a plate by measuring two ZGV frequencies (assuming known plate thickness). The approach also points out that additionally measuring the wavenumber of one ZGV resonance allows to simultaneously determine the elastic properties and thickness of a plate. We achieved this, by extending the measurement of the ZGV frequencies with wavenumber measurements based on laser excitation patterns and demonstrated the simultaneous measurement of longitudinal and transversal wave velocity and the plate thickness.Additionally, we were able to experimentally show the intriguing effect of negative reflection of so called backward Lamb waves at the straight edge of a simple Aluminum plate. Here we selectively excited these special waves which are related to ZGV Lamb waves and detected the 2D wave field reflected from an edge.