Rayleigh waves with impedance boundary conditions in anisotropic solids

• Rayleigh waves with impedance boundary conditions are considered.
• The half-space is orthotropic and monoclinic with the symmetry plane x3=0x3=0.
• The explicit secular equations are obtained.
• They recover the secular equations of classical Rayleigh waves.

The paper is concerned with the propagation of Rayleigh waves in an elastic half-space with impedance boundary conditions. The half-space is assumed to be orthotropic and monoclinic with the symmetry plane x3=0x3=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. From this equation, a new version of the secular equation for isotropic materials is derived. For the monoclinic case, the method of polarization vector is used for deriving the secular equation and it is an algebraic equation of eighth-order. When the impedance parameters vanish, this equation coincides with the secular equation of Rayleigh waves with traction-free boundary conditions.