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

A mixed variational formulation based upon Hamilton's principle and Lagrang e's multipliers is generally obtained to deduce the governing equations of laminated composite structures. The additional work, as a function of stres ses only, is introduced in the variational statement by using Legendre's tr ansformation. A rational higher-order displacement-based two-dimensional th eory for the analysis of laminated plates is presented. This theory is esta blished using the mixed variational formulation to study the vibration beha viour of symmetric laminated orthotropic plates subjected to normal tractio n 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, ortho tropy ratio, and number of layers on natural frequencies are investigated. The obtained results are compared with other exact results available in the field literature. (C) 2000 Editions scientifiques et medicales Elsevier SA S.