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.
Keywords
elastic waves, periodic cracks, anisotropy, spring boundary
conditions, plate equations
