Using Zero-Group-Velocity Lamb Waves to Determine Thickness and Bulk Sound Velocities of Isotropic Plates

We present an ultrasound method to simultaneously determine the thickness of a plate together with the longitudinal and shear elastic wave velocities of its material [1]. The method works without assumptions or a priori knowledge of the plate thickness or the sound velocities, which are usually required in order to obtain the other quantity from time of flight measurements. Instead, the method is based on the measurement of the frequencies of two zero-group velocity (ZGV) Lamb modes and one respective wavenumber. ZGV Lamb waves are resonant waves which appear at multiple defined angular frequencies f and wavenumbers k in the Rayleigh-Lamb dispersion spectrum of plates, where the group velocity becomes zero. We use this relation, which depends on the elastic properties and the thickness of the plate in an inverse problem to obtain the properties of the plate. Experimentally, the frequencies of ZGV points can be obtained at high precision by measuring the elastic response spectrum of a plate, using laser-ultrasound techniques. By shaping the excitation laser spot with a spatial light modulator, we extend this to enable measurements of the corresponding wavenumber. The introduced method is demonstrated for a tungsten plate.