Analytical and molecular dynamics simulation approaches to study behavior of multilayer graphene-based nanoresonators incorporating interlayer shear effect

Analytical and molecular dynamics simulation approaches are used in this paper to study free-vibration behavior of multilayer graphene-based nanoresonators considering interlayer shear effect. According to experimental observations, the weak interlayer van der Waals interaction cannot maintain the integrity of carbon atoms in the adjacent layers. Hence, it is vital that the interlayer shear effect is taken into account to design and analyze multilayer graphene-based nanoresonators. The differential equation of motion and the general form of boundary conditions are first derived for multilayer graphene sheets with rectangular shape using the Hamilton's principle. Then, by pursuing an analytical approach, closed-form results for the natural frequencies are obtained in the case of simply supported boundary conditions. Molecular dynamics (MD) simulations of the graphene sheets are also accomplished to evaluate the accuracy of the presented analytical model's results. The numerical results indicate that by increasing the layers number, the natural frequency also increases until a specific number of layers, then the effect of layers number on the natural frequency significantly decreases. Moreover, by a rise in aspect ratio of the multilayer graphene sheet, the natural frequency decreases until a specific aspect ratio, next, the changes in the sheet aspect ratio have no considerable effect on the natural frequency.