Propagation of Rayleigh waves at the boundary of an orthotropic elastic solid: Influence of initial stress and gravity

Propagation of harmonic plane waves is considered in an orthotropic elastic medium in the presence of initial stress and gravity. Roots of a quadratic equation define the propagation of one quasi-longitudinal wave and one quasi-transverse wave in a symmetry plane in this medium. These two waves are coupled in the identical phase to define the propagation of Rayleigh waves at the boundary of the medium. Two conditions at the stress-free boundary translate into a complex frequency equation, which explains the dispersive behavior of this Rayleigh wave. For the presence of radical terms, this complex equation is rationalized into a real algebraic equation. Only one root of this algebraic equation satisfies the mother frequency equation and hence represents the propagation of dispersive Rayleigh waves at the boundary of the orthotropic solid. The influence of initial stress and gravity on velocity and polarization of Rayleigh waves is observed through a numerical example.