Free Vibration of Functionally Graded Variable Thickness Carbon Nanotube Annular Plates

In this paper, free vibration of carbon nanotube-reinforced functionally graded circular plates with hole has been investigated. Distribution of carbon nanotubes are continuous and the gradual and graded changes of materials through the plate thickness are considered as volume fraction. Considering the linear and non-linear variation of circular plates through the radial direction and also considering the proposed function for the thickness, the plate thickness can be convex or concave. Moreover, the motion equations of plate were obtained based on the third-order shear deformation theory. These equations are coupled differential equations which can convert Ordinary Differential Equations (ODE) using the Trigonometric series expansion of displacement fields such that they satisfy the axial symmetry condition. Solving the converted ODE equations is too difficult. For this reason, the differential quadrature method is employed to solve these equations. The obtained results are compared with the results reported by other researchers and an excellent agreement is observed between them. Finally, the effects of different geometric parameters as well as different volume fracture of nanotubes on natural frequency have been studied.