Free transverse vibration analysis of circular and annular graphene sheets with various boundary conditions using the nonlocal continuum plate model

In this article, the free vibration behavior of circular and annular graphene sheet is studied. Using the nonlocal elasticity theory, the governing equations are derived for single-layered graphene sheets (SLGS) and nonlocal parameter appears into arguments of Bessel functions. Analytical frequency equations for circular and annular graphene sheets are obtained based on different cases of boundary conditions. New version of differential quadrature method has been used to solve the governing equations for circular nanoplate. The results of new version of differential quadrature method are successfully verified with those of the analytical method. The results are subsequently compared with valid results reported in the literature. The effects of the small scale on natural frequencies are investigated considering various parameters such as the radius of the plate, radius ratio, nodal circle, nodal diameter number, boundary conditions and mode numbers.