Influence of in-plane pre-load on the vibration frequency of circular graphene sheet via nonlocal continuum theory

In this study, the free vibration behavior of circular graphene sheet under in-plane pre-load is studied. By using the nonlocal elasticity theory and Kirchhoff plate theory, the governing equation is derived for single-layered graphene sheets (SLGSs). The closed-form solution for frequency vibration of circular graphene sheets under in-plane pre-load has been obtained and nonlocal parameter appears into arguments of Bessel functions. The results are subsequently compared with valid result reported in the literature. The effects of the small scale, pre-load, mode number and boundary conditions on natural frequencies are investigated. The results are shown that at smaller radius of circular nanoplate, the effect of in-plane pre-loads is more importance.