Plane Progressive Waves in constrained anisotropic solids with an application to Kirchhoff plate-like bodies

In previous papers by Podio-Guidugli and Lembo the equations governing the static and dynamic of Kirchhoff plates were obtained from the three-dimensional linear elasticity under the assumptions that the material was both anisotropic and internally constrained; here we apply the same assumptions to obtain, from three-dimensional elasticity an exact theory of the propagation of plane progressive waves into these plates. In order to get this result we first describe the acoustic tensor for an unconstrained monoclinic material whose symmetry group contains simply the reflections on the middle surface of the plate, then we deal with the propagation condition in an internally constrained anisotropic material. This approach differs from that proposed by Chadwick, because we use the constrained elasticity tensor introduced by Podio-Guidugli and Vianello, 1992, instead of the unconstrained one used therein: such a choice leads to the same propagation condition, but to different reactive stresses. Finally, for Kirchhoff plates, we find the admissible waves together with the corresponding stress and couple resultants and the reflection conditions at the boundary.