Finding the dispersion relations for lamb-type waves in a concave piezoelectric plate by optical visualization of the ultrasound field radiated into a fluid

Abstract

We propose and experimentally demonstrate a method for measuring the phase velocities of Lamb waves in concave piezoelectric plates submerged in a fluid. The method is based on the optical shadowgraphy method of visualizing the ultrasound field that occurs in a fluid when Lamb modes are excited in the plate under study. According to the condition of wave resonance, the propagation direction of the waves radiated into the fluid is determined by the phase velocity of a Lamb wave in the plate, which makes it possible to measure the indicated velocity. Proceeding from this, we demonstrate that when spherical concave piezoelectric plates are used, the phase velocities of Lamb waves can be determined by the position of the caustics—areas of acoustic wave focusing in the fluid. We have experimentally measured the dispersion curves of several Lamb modes for a concave piezoelectric plate with a diameter of 100 mm and thickness of around 2 mm, which was submerged in water. Ultrasound waves were optically visualized in the fluid by the schlieren method on a specially designed setup, in which off-axis parabolic mirrors were used to implement the dark-field method. We demonstrated that the measured dispersion curves for low-order Lamb modes are well described by the theoretical dependences calculated using the Rayleigh-Lamb equation.