Investigation of Functionally Graded Carbon Nanotube Distribution Effect on the Frequency of Annular Sector Plates on Pasternak Elastic Foundation

In this paper, free vibration of functionally graded carbon nanotube annular sector plates is studied. Distribution of carbon nanotubes is continuous and meaningful and gradual changes of materials in the direction of thickness are in the form of volume fraction. Annular sector plate is placed on the Winkler-Pasternak two parameters elastic foundation. The motion equations of plate are derived using the Hamilton principle and the refined plate theory. These coupled differential equations are transformed to ordinary equations using the trigonometric series expansion of space variation functions and then are solved with the help of differential quadrature method. The obtained results are compared with the other researcher’s results and an excellent agreement can be observed between them. Finally, the effects of different geometric parameters, different distributions of carbon nanotubes in the thickness direction, elastic foundation, and also different boundary conditions on the natural frequencies are investigated.