Vibration of laminated orthotropic composite plates and shells.

Almost all of the analytical solution techniques presented for composite plates and shells deal with either simply supported conditions or boundary conditions with at least a pair of opposite edges simply supported. In the present study, an alternative general approach, combining superposition and state space techniques is developed for the free vibration analysis of laminated orthotropic composite plates and shells having arbitrary boundary conditions. This study concentrates on the antisymmetric angle-ply laminated plates and cross-ply laminated plates and shells. Three commonly adopted theories, i.e., classical theory, first-order shear deformation theory and third-order shear deformation theory, have been employed and compared with one another to investigate the influence of transverse shear deformation, structural aspect ratio, length-to-thickness ratio, degree of anisotropy and the number of layers on natural frequency. Convergence tests have been carried out to guarantee the accuracy of the closed-form solutions. Wherever possible, numerical results generated by the present approach are compared with those reported in the published references. Accurate non-dimensional fundamental frequencies are presented for laminated plates and shells with two adjacent edges, three edges and four edges clamped and other edges simply supported. Such analyses have not been reported in the literature previously. Also, vibration analysis of a cantilever angle-ply antisymmetric plate with a point support is conducted to demonstrate the applicability of the present technique. It has been shown that the method works extremely well and excellent agreements are found between the present results and those generated by previous researchers. It has also been shown that more complicated boundary-value problems can be solved by this technique without any difficulty