Rayleigh waves with impedance boundary condition: Formula for the velocity, existence and uniqueness

The propagation of Rayleigh waves in an isotropic elastic half-space with impedance boundary conditions was investigated recently by Godoy et al. [Wave Motion 49 (2012), 585-594]. The authors have proved the existence and uniqueness of the wave. However, they were not successful in obtaining an analytical exact formula for the wave velocity. The main purpose of this paper is to find such a formula. By using the complex function method, an analytical exact formula for the velocity of Rayleigh waves has been derived. Furthermore, from the obtained formula, the existence and uniqueness of the wave has been established easily.