Rayleigh waves with impedance boundary conditions in incompressible anisotropic half-spaces

In this paper, the propagation of Rayleigh waves in an incompressible elastic half-space with impedance boundary conditions is investigated. The half-space is assumed to be orthotropic and monoclinic with the symmetry plane x3 = 0 . The main aim of the paper is to derive explicit secular equations of the wave. For the orthotropic case, the secular equation is obtained by employing the traditional approach. It is an irrational equation. For the monoclinic case, the method of polarization vector is used for deriving the secular equation. This is an algebraic equation of eighth-order. When the impedance parameters vanish, the equations obtained coincide with the corresponding secular equations of Rayleigh waves with traction-free boundary conditions. "