Exact treatment of leaky Rayleigh waves in the presence of a layer

Abstract

An exact theory, supported by experimental measurements, of bounded acoustic‐beam reflection near the Rayleigh angle from a fluid‐solid interface loaded by a solid layer is presented. We derive an analytical expression for the reflection coefficient by applying continuity conditions appropriate for the problem geometry to wave potentials in the three media. The reflected field, including leaky Rayleigh‐wave effects, is calculated by evaluating numerically the Fourier integral containing the incident beam transform and the reflection coefficient. The dispersion of the Rayleigh wave speed is deduced from the behavior of the reflection coefficient in the complex plane. We find excellent agreement with measurements of the wave speed over a wide range of frequency and layer thickness in stainless steel samples loaded with copper layers. The beam displacement parameter, which is also deduced from characteristics of the reflection coefficient, displays an unexpected minimum as a function of frequency. Experimental results are compared to theory for the acoustic amplitude distribution in the reflected field, both near and at the Rayleigh angle.