Free Vibrations of Laminated Composite Hyperbolic Shells of Revolution Via GDQ Method

In this paper, the Generalized Differential Quadrature (GDQ) Method is applied to study the dynamic behaviour of laminated composite hyperbolic shells of revolution. The First-order Shear Deformation Theory (FSDT) is used to analyze the above moderately thick structural elements. The governing equations of motion, written in terms of internal resultants, are expressed as functions of five kinematic parameters, by using the constitutive and the congruence 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. The results are obtained taking the meridional and the circumferential co-ordinates into account, without using the Fourier modal expansion methodology. Examples of hyperbolic shell elements are presented to illustrate the validity and the accuracy of GDQ method. GDQ results are compared with the ones obtained using commercial programs such as Abaqus, Ansys, Nastran, Straus, Pro/Mechanica. Very good agreement is observed.