A dynamical model for multilayered plates with independent shear deformations

In this paper a dynamic model for an $n$-layered plate is developed based upon the assumptions of Reissner-Mindlin plate theory. Each plate layer is assumed to be transversely isotropic, transversely homogeneous and of a uniform thickness; however, no symmetry in the material properties or thicknesses of each plate is assumed. The layers are assumed to be perfectly bonded so that no slip occurs along the interface. No additional a priori kinematic restrictions are imposed upon the motion of the plates. The equations of motion are derived by the principle of virtual work. Existence and uniqueness results are obtained. In the case where the layers are symmetric we show that all solutions decouple into a bending solution (with antisymmetric displacements about the mid-plane) and an in-plane solution (with symmetric displacements).