On vibration and stability problems of laminated plates and shells using shear deformation theories

This study deals with the vibration and stability analyses of laminated plates and shells, using classical, first-order and third-order equivalent single-layer theories and the layer-wise theory of Reddy. Analytical solutions of these theories for natural frequencies and critical buckling loads of plates and shells under various boundary conditions are developed using an improved analytical procedure. A solution for the transient response of viscously damped cross-ply laminated plates, subjected to a sonic-boom type loading, is developed using the third-order shear deformation plate theory of Reddy and the first-order shear deformation plate theory.

The nonlinear dynamic equations of the first-order shear deformation plate theory and the third-order shear deformation plate theory of Reddy are reformulated in terms of a pair of equations describing the interior and the edge-zone problems of rectangular plates laminated of transversely isotropic layers. The pure—shear frequencies of the plate in linear and nonlinear problems are identified from the edge—zone equation. For certain boundary conditions the original system of equations are reduced to three in number, as in the classical plate theory.

The frequency and buckling equations of symmetric plates laminated of transversely isotropic layers are obtained using the Levinson’s third—order shear deformation plate theory. Using the interior and the edge—zone equations, the frequency and buckling equations are also obtained according to the first—order shear deformation plate theory. The solution contribution of the edge—zone equation is analyzed. By introducing a mixed approach, the bending problem of laminated plates with various boundary conditions is studied according to the first—order and Reddy’s third-order shear deformation plate theories.