Free vibration of laminated and sandwich plates using enhanced plate theories

In this paper two enhanced plate theories for laminated and sandwich plates are developed via the mixed variational formulation for free vibration studies. A concept presented by the author [J.-S. Kim, Reconstruction of first-order shear deformation theory for laminated and sandwich shells, AIAA Journal 42 (2004) 1685–1697], which includes the displacement and stress recovery procedure, is extended to the mixed variational theorem. By obtaining the transverse shear stresses based on higher-order zig-zag theories, the mixed variational formulation embraces them as the classical FSDT and HSDT. Relationships between the higher-order zig-zag theories and the classical FSDT and HSDT are systematically established via the mixed variational theorem and the generalized definition of the mean displacement. The accuracy and efficiency of the present enhanced plate theories are demonstrated by comparing their results with the reported results in the literature and 3D exact elasticity solutions for the plates vibrating in cylindrical bending.