Vibration and stability of cross-ply laminated composite shallow shells subjected to in-plane stresses

Natural frequencies and buckling stresses of cross-ply laminated composite shallow shells are analyzed by taking into account the effects of transverse shear and normal deformations, and rotatory inertia. By using the method of power series expansion of displacement components, a set of fundamental dynamic equations of a two-dimensional higher-order theory for rectangular laminated shells made of elastic and orthotropic materials is derived through Hamilton’s principle. Several sets of truncated approximate theories which can take into account the complete effects of higher-order deformations such as shear deformations with thickness changes and rotatory inertia are applied to solve the vibration and stability problems of laminated composite shallow shells. Three types of simply supported shallow shells with positive, zero and negative Gaussian curvature are considered. The total number of unknowns does not depend on the number of layers in any multilayered shells. In order to assure the accuracy of the present theory, convergence properties of the lowest natural frequency for the fundamental mode r = s = 1 are examined in detail. Numerical results are compared with those of the published three-dimensional models and the extended two-dimensional model in which both in-plane and normal displacements are assumed to be C0 continuous in the continuity conditions at the interface between layers. It is noticed that the present global higher-order approximate theories can predict accurately the natural frequencies and buckling stresses of simply supported laminated composite shallow shells within small number of unknowns.