Modeling and Free Vibration Analysis for Bi-directional Functionally Graded Porous 3D Graphene Foams Cylindrical Shells with Arbitrary Boundary Conditions

In this paper, the first investigation of axially functionally graded porous (FGP) configuration of three-dimensional graphene foams (3D-GFs) structures is carried out and the vibration characteristics of conventional radially FGP cylindrical shells are comparatively analyzed. To begin with, predicting equivalent material properties of bi-directional FGP 3D-GFs by utilizing open cell body theory. Moreover, based on the regional decomposition method, the cylindrical shell is divided into a number of segments along the axial direction, and the appropriate artificial spring stiffness values are selected to simulate the connection conditions between each section and the boundary constraints of the shell structure in the actual working conditions. Meanwhile, the vibration characteristics of the shell under arbitrary boundary conditions are explored on the basis of the first-order shear deformation theory (FSDT) and the Gegenbauer-Ritz method. The axially FGP structures are analyzed in comparison with the radial configurations, while the influence of factors such as boundary conditions, FGP types, and geometrical parameters on the natural characteristics of the shell is discussed. The research shows that the framework of 3D-GFs, which is distributed more at the boundary ends and inner and outer surfaces of the shell, has the most reinforcement effect on the overall stiffness of the structure, and the radially FGP configuration is more competitive.