Transverse vibration of single-layer graphene sheet under 2D magnetic field action by differential quadrature method

In this paper, governing equations of transverse vibration of single-layer graphene sheet with different boundary conditions under 2D in-plane magnetic field action, considering its consequent forces and moments, are investigated for the first time using differential quadrature method (DQM). Governing equations of motion are obtained using non-local theory and considering Lorentz's force. The partial differential equations of system are changed to the ordinary differential equations using separation of variables method. Using differential quadrature method, the obtained governing equations are solved for different boundary conditions. The effects of elastic foundation stiffness, non-local parameter, plate aspect ratio and 2D magnetic field effects on the natural frequency of graphene sheet are evaluated. The results show that increase of foundation stiffness, non-local parameter and aspect ratio result in increase of fundamental frequency, in all boundary conditions. But, action of in-plane magnetic field results in decrease of fundamental frequency, because of decreasing flexural stiffness and increasing in-plane pressure loading.