Free vibration of thick laminated cylindrical shells with different boundary conditions using general differential quadrature

Abstract

Equations of motion with required boundary conditions for deep and thick cylindrical composite shells are shown using two First-order Shear Deformation Theories. The difference between them is the inclusion of the effects of curvature in the evaluation of stiffness parameters. Equations of motion with stress resultants lead to a system of fifteen first-order differential equations for dynamics of cylindrical shells. These equations are solved numerically using the General Differential Quadrature method for free vibration of isotropic, cross-ply, angle-ply and general lay-up cylindrical shells with six types of different boundary conditions using the aforementioned theories. The first five frequency parameters and mode shapes which are obtained from both theories are compared with the available results in the literature and those obtained using a three-dimensional finite element analysis to test the accuracy of the shell theories presented here.