Free vibration analysis of functionally graded cylindrical shells reinforced with graphene platelets

Abstract

This research investigates the free vibrations of graphene platelet reinforced composite (GPLRC) cylindrical shells. Composite cylindrical shell is composed of a number of layers, each layer of composite shell has a different amount of graphene reinforcement, which leads to functionally graded (FG) distribution of the reinforcements. For this purpose, the first-order shear deformation theory of shells and Donnell kinematic relations have been used. To estimate the elastic properties of the composite material, Halpin-Tsai micro-mechanical relationship has been used where the effects of nanofillers is also included. On the other hand to obtain the mass density and Poisson's ratio of the media, the simple rule of mixtures approach is adopted. The Hamilton principle has been used to derive the governing equations for the free vibrations of shells as well as the boundary conditions. The obtained equations are five in number which are coupled in terms of displacements and rotations. Suitable for simply supported boundary conditions of the shell, Fourier expansions have been used as the conventional Navier solution. An analytical solution is provided to obtain the natural frequencies as well as the numbers of their modes. The results of this study at first are compared with the known data for isotropic homogeneous shells and after that novel results are provided for FG-GPLRC cylindrical shells. The results of the present study show that the weight fraction and the distribution of GPLs are two important factors on the natural frequencies of the shell, so that with increasing the weight fraction of GPLs, the natural frequencies of the shell are strongly increased. Also when the inner and outer layers of the shell have the maximum amount of reinforcements, maximum frequencies are achieved.