Waves and statics for functionally graded materials and laminates

It is shown here that, for any laminated stacking of elastic materials which are transversely isotropic with respect to an axis OzOz, having elastic moduli which may depend either continuously or discontinuously on the coordinate z, surface-guided disturbances at any frequency are governed by the reduced membrane equation. An analogous treatment of the statics of plates having the same structure, yields the static theory of functionally graded plates due originally to Spencer et al. Thus, for functionally graded transversely isotropic plates with traction-free surfaces, displacements have a structure closely analogous to dynamic disturbances and are represented in terms of solutions to the biharmonic equation.