Computational Methods in Engineering

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.