2-D GDQ solution for free vibrations of anisotropic doubly-curved shells and panels of revolution

In this paper, the Generalized Differential Quadrature (GDQ) method is applied to study the dynamic behaviour of laminated composite doubly-curved shells of revolution. The First-order Shear Deformation Theory (FSDT) is used to analyse the above mentioned moderately thick structural elements. In order to include the effect of the initial curvature a generalization of the Reissner–Mindlin theory, proposed by Toorani and Lakis, is adopted. The governing equations of motion, written in terms of stress resultants, are expressed as functions of five kinematic parameters, by using the constitutive and kinematic relationships. The solution is given in terms of generalized displacement components of points lying on the middle surface of the shell. The discretization of the system by means of the Differential Quadrature (DQ) technique leads to a standard linear eigenvalue problem, where two independent variables are involved. Results are obtained taking the meridional and circumferential co-ordinates into account, without using the Fourier modal expansion methodology. Comparisons between the Reissner–Mindlin and Toorani–Lakis theory are presented. Furthermore, GDQ results are compared with those presented in literature and the ones obtained by using commercial programs such as Abaqus, Ansys, Nastran, Straus and Pro/Mechanica. Very good agreement is observed.