Numerical study of the effect of shear in-plane load on the vibration analysis of graphene sheet embedded in an elastic medium

In the present work, the free vibration behavior of rectangular graphene sheet under shear in-plane load is studied. Nonlocal elasticity theory has been implemented to study the vibration analysis of orthotropic single-layered graphene sheets (SLGSs) subjected to shear in-plane load. Using the principle of virtual work, the governing equations are derived for the rectangular nanoplates. Differential quadrature method is employed and numerical solutions for the vibration frequency are obtained. To verify the accuracy of the present results, the Galerkin method is also developed. DQM results are successfully verified with those of the Galerkin method. The influence of surrounding elastic medium and effect of boundary conditions on the vibration analysis of orthotropic single-layered graphene sheets (SLGSs) is studied. Six boundary conditions are investigated. Numerical results show that the vibration frequencies of SLGSs are strongly dependent on the small scale coefficient and shear in-plane load.