Free vibration and buckling of shear-deformable cross-ply laminated plates using the state-space concept

Abstract

Generalized Levy-type solutions are obtained for the problems of linear vibration and stability of cross-ply laminated plates. The governing equations, which are derived by using the principle of virtual displacement and a third-order shear-deformation plate theory, are transformed into a set of first-order linear ordinary differential equations with constant coefficients. The general solution of these equations can be obtained by using the state-space concept. Then, application of the boundary conditions yields equations for the natural frequencies and buckling loads. Unfortunately, a straightforward application of the state-space concept yields numerically ill-conditioned problems as the plate thickness is reduced. Various methods for overcoming this problem are discussed. A combination of an initial-value method and the modified Gram-Schmidt orthonormalization procedure is used to overcome this problem. It is shown that this method not only yields results that are in excellent agreement with the results in the literature, but also it converges fast and gives all the frequencies and buckling loads regardless of the plate thickness.