Elastic SH wave propagation in a layered anisotropic plate with periodic interface cracks: exact versus spring boundary conditions

The propagating antiplane (SH) modes in a symmetrically three-layered, anisotropic, thick plate with a periodic array of interface cracks are investigated. The exact dispersion relation can be derived with the help of a hypersingular integral equation approach and Floquet's theorem. The interface cracks can be a model for interface damage, but a much simpler model is a recently developed spring boundary condition. This boundary condition is used both for the thick plate and in the derivation of plate equations with the help of power series expansions in the thickness coordinate. For low frequencies (cracks small compared to the wavelength) the three models are shown to give the same results and this is a confirmation that the spring boundary condition is a valid approximation at low frequencies.