Theoretical and Experimental Investigation of Rayleigh Waves on Spherical and Cylindrical Surfaces

Non contact laser ultrasonic methods are appropriated for investigating SAW propagation on curved surfaces. They eliminate coupling issues in the generation and detection of the waves, and their high temporal resolution enables studying the dispersion effect on a large frequency range. We investigate the variations of the phase and group velocities for Rayleigh waves propagating on a sphere or a cylinder. First, a simple expression, giving an approximate value of the phase velocity versus frequency, is derived. The formula needs only two dimensionless coefficients, which can be obtained from the asymptotic behaviour of the phase and group velocities at high frequencies. A second set of coefficients, providing a better approximation, have been determined from characteristic points in the low frequency range of the velocity dispersion curve. These coefficients have been plotted as functions of the material Poison’s ratio. These results provide a means to calculate, with an average error smaller than 1 %, the phase velocity of Rayleigh waves propagating on a sphere or a cylinder made of any isotropic material. Using laser based ultrasonic techniques, the experimental values measured on steel spheres and Duralumin cylinders are in good agreement with the theoretical ones.