Free vibrations of laminated composite doubly-curved shells and panels of revolution via the GDQ method

摘要

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 analyze the above mentioned moderately thick structural elements. 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. Examples of hyperbolic, catenary, cycloid, parabolic, elliptic and circular shell and panel structures are presented to illustrate the validity and the accuracy of the GDQ method. 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.