Propagation of leaky Rayleigh waves along a curved fluid-solid interface

A characteristic equation is derived for a leaky Rayleigh wave (LRW), propagating on a curved fluid-solid interface. The equations of motion for the curved solid and fluid are formulated using the constitutive equations of a homogenous isotropic curved solid and an inviscid fluid, respectively. The displacement potential functions are used to simplify the derivation. The interface conditions are used to ensure continuities of the mass, momentum, and energy across the interface. Then, with the consideration of the interface radius of the curvature, the characteristic equation for the LRW is established and solved numerically by Muller's method. One important outcome is that there is weaker directional dependence for the velocity of the LRWs on the radius of curvature in comparison with the Rayleigh waves at an air-solid interface. However, the numerical results show a strong directional dependence for the attenuation due to the LRW leakage on the complex curvatures. Moreover, a quantitative relation between the curvature and attenuation caused by the leakage for different materials is shown. The results are significant especially with respect to relevant future applications of ultrasonic testing.