Determination of thickness and bulk sound velocities of isotropic plates using zero-group-velocity Lamb waves

Abstract

We propose a method to simultaneously determine the thickness of an isotropic plate together with the longitudinal and shear elastic wave velocities of its material. The method requires knowledge of the frequencies of two zero-group-velocity Lamb modes and one respective wavenumber. These quantities are defined by the Rayleigh-Lamb equations, which we use in an inverse problem to obtain the properties of the plate. Experimentally, the frequencies of zero-group-velocity 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 homogeneous tungsten and an aluminium plate.