Natural vibration analysis of symmetrical cross-ply laminated plates using a mixed variational formulation

A mixed variational formulation based upon Hamiltonʹs principle and Lagrangeʹs multipliers is generally obtained to deduce the governing equations of laminated composite structures. The additional work, as a function of stresses only, is introduced in the variational statement by using Legendreʹs transformation. A rational higher-order displacement-based two-dimensional theory for the analysis of laminated plates is presented. This theory is established using the mixed variational formulation to study the vibration behaviour of symmetric laminated orthotropic plates subjected to normal traction fields. The accuracy of the present theory is demonstrated via a bending problem for which the exact solution is available. Natural frequencies are obtained according to the classical, first- and higher-order plate theories. The effects of boundary conditions, transverse shear, aspect ratio, orthotropy ratio, and number of layers on natural frequencies are investigated. The obtained results are compared with other exact results available in the field literature.