2D and 3D shell models for the free vibration investigation of functionally graded cylindrical and spherical panels

The paper shows the free vibration investigation of simply supported functionally graded material (FGM) shells. Spherical and cylindrical shell geometries are investigated for two different material configurations which are one-layered FGM structures and sandwich structures embedding an internal FGM core. A three-dimensional (3D) exact shell model and different two-dimensional (2D) computational models are compared in terms of frequencies and vibration modes. The proposed numerical solutions are typical 2D finite elements (FEs), and classical and advanced generalized 2D differential quadrature (GDQ) solutions. High and low frequency orders are investigated for thin and thick simply supported shells. Vibration modes are fundamental to compare the 3D exact shell model and 2D numerical solutions. The 2D finite element results based on the classical Reissner–Mindlin theory are calculated using a typical commercial FE software. Classical and advanced GDQ 2D models use the generalized unified formulation. The 3D exact shell model uses the differential equations of equilibrium written in general orthogonal curvilinear coordinates and developed in layer-wise (LW) form. The differences between 2D numerical results and 3D exact results depend on the thickness ratio and geometry of the structure, the considered mode and the frequency order, the lamination sequence and materials.