Vibration Analysis of Cross-Ply Laminated Plates Using the Multilayer Theory

This paper presents the vibration analysis of a cross-ply laminated rectangular plate simply supported at all edges by using the multilayer theory. In the multilayer theory, in-plane and out-of-plane displacements are independently expressed as polynomial forms of third and second order, respectively, for each layer of the plate. A set of governing equations for the laminated plate is derived from the equations of motion, the free surface conditions and the continuity of displacements and stresses along the interfaces between adjacent layers. In contrast, the lamination theory uses only a single displacement field for the whole laminated plate. In numerical examples, natural frequencies, steady-state responses (compliance) and stress distributions in the thickness direction are obtained from both theories for plates with various thickneses and stacking sequences. Further more, a comparison is made between the two sets of results obtained, and the range of applicability of the theories is discussed.