Free Vibration Analysis of Functionally Graded Doubly Curved Shell Structures Using GDQ Method

In this paper, the Generalized Differential Quadrature (GDQ) Method is applied to analyze the dynamic behaviour of functionally graded doubly curved shells of revolution. The First-order Shear Deformation Theory (FSDT) is used to study these moderately thick structural elements. The treatment is developed within the theory of linear elasticity, when the materials are assumed to be isotropic and inhomogeneous through the thickness direction. The two-constituent functionally graded shell consists of ceramic and metal that are graded through the thickness, from one surface of the shell to the other. Two different power-law distributions are considered for the ceramic volume fraction. 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 the 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 numerical results illustrate the influence of the power-law exponent and of the power-law distribution choice on the mechanical behaviour of functionally graded doubly curved shells.