Abstract The vibration of single-layered graphene sheets (SLGS) is investigated using a new finite element method based on nonlocal continuum plate model with second order strain gradient taken into consideration. The paper starts with dynamic equation of Kirchhoff plate of strain gradient elasticity. Then a 4-node 24-degree of freedom (DOF) plate element is developed to discretize the higher order partial differential equations with the small scale effect taken into consideration. The finite element results are in good agreement with theoretical results in analyzing simply-supported SLGS, which validated the reliability of the finite element method. Finally, the finite element method is used to study the vibration of graphene sheets with different size,wave length，boundary conditions and the nonlocal parameter which show the small scale effects.
2014, Vol. 35 
