Application of modified couple-stress theory to stability and free vibration analysis of single and multi-layered graphene sheets

With the development of nanotechnology, research activities on carbon nanostructures have increased rapidly. In recent years, due to the extraordinary mechanical properties of graphene sheets, there has been a growing interest in investigating the mechanical response of these carbon nanostructures. In this article, the modified couple-stress theory (MCST) is first employed to study the free vibration and mechanical buckling of single-layered graphene sheets (SLGSs). To this end, SLGS is modeled as a nanoplate and the two-variable refined plate theory (TVRPT) is adopted to extend the finite strip method (FSM) formulation. The natural free vibration frequency and mechanical buckling loads of the sheet are then obtained by solving the proper eigenvalue problems. Mechanical buckling and free vibration of multi-layered graphene sheets (MLGSs) are also investigated considering the effects of van der Waals (vdW) bonds between the layers. Modified couple-stress theory is applied to consider the small-scale effects of the graphene sheets. The results obtained by the proposed method are validated against those available in the literature. Finally, a comprehensive parametric study is performed to investigate the effects of different parameters such as loading schemes, nanoplate dimensions and boundary conditions.