Vibration analysis of functionally graded carbon nanotube reinforced composites (FG-CNTRC) circular, annular and sector plates

The intent of this paper is to firstly perform the vibration analysis of the functionally graded carbon nanotube reinforced composites (FG-CNTRC) circular, annular and sector plates with arbitrary boundary conditions by means of the semi-analytical method which is proposed by the author's team. In the material model, the distribution of the carbon nanotubes is uniform or functionally graded along with the thickness direction of structures and four types of the CNTs distribution are studied in this paper. The refined rule of mixtures approach containing the efficiency parameters is adopted to determine the properties of the composite media. The admissible displacement functions of the FG-CNTRC circular, annular and sector plates are uniformly expanded as the modified Fourier series which embodies a standard cosine Fourier series and several auxiliary functions which are introduced to eliminate the limit of the boundary conditions. On this foundation, the first-order shear deformation elasticity theory is employed to construct the energy expression of the FG-CNTRC circular, annular and sector plates. Then the Ritz-variational energy method is used to decide the natural frequencies and the associated mode shapes. To examine the convergence, accuracy, stability and efficiency of the computational model, the comprehensive studies are conducted. Based on that, some crucial parametric studies covering the influence of the geometrical parameters, CNTs distributions, volume fraction of CNTs and boundary conditions are also investigated in detail.