Free vibration of functionally graded carbon nanotube reinforced composite annular sector plate with general boundary supports

In this paper, an efficient and unified approach for free vibration analysis of the moderately thick functionally graded carbon nanotube reinforced composite annular sector plate with general boundary supports is presented by using the Ritz method and the first-order shear deformation theory. For the distribution of the carbon nanotubes in thickness direction, it may be uniform or functionally graded. Properties of the composite media are based on a refined rule of the mixture approach which contains the efficiency parameters. A modified Fourier series is chosen as the basic function of the admissible function to eliminate all the relevant discontinuities of the displacements and their derivatives at the edges. To establish the general boundary supports of the annular sector plate, the artificial spring boundary technique is implemented at all edges. The desired solutions are obtained through the Ritz-variational energy method. Some numerical examples are considered to check the accuracy, convergence and reliability of the present method. In addition, the parameter studies of the functionally graded carbon nanotube reinforced composite annular sector plate are carried out as well.