Rayleigh wave propagation in deformed orthotropic materials

A perturbation method is described for the investigation of the propagation of Rayleigh waves on the surface of a homogeneous anisotropic initially deformed material plate. Our perturbation formalism is quite general and can also be applied when other small effects, like slight temperature changes or external magnetic fields, affect the Rayleigh wave propagation velocity. The special cases of slight orthotropy and initial deformations are analyzed in detail. For these cases we derive the Rayleigh wave phase velocity as a function of the propagation direction, the elastic constants, and the initial stresses. The linearity of our formulas suggests that Rayleigh waves can be conveniently used as an experimental technique for the solution of the inverse problem of determining the elastic constants and/or the initial stresses in a material.