A novel model for analysis of multilayer graphene sheets taking into account the interlayer shear effect

In this study, a multiplate shear model is developed for dynamic analysis of multilayer graphene sheets with arbitrary shapes considering the interlayer shear effect. By utilizing the model, then some free-vibration analysis is presented. According to the experimental results, the weak interlayer van der Waals interaction cannot maintain the integrity of carbon atoms in adjacent layers. Therefore, it is required that the interlayer shear effect is accounted to study multilayer graphene mechanical behavior. The governing differential equation of motion is derived for the multilayer graphene sheets utilizing a variational approach based on the Kirchhoff plate model. The essential and natural boundary conditions are also obtained at both the smooth periphery parts of the multilayer graphene sheets and the possible sharp corners. By considering cantilever and simply supported multilayer rectangular graphene sheets as two case studies, the results for the free-vibration analysis are presented based on the developed model, and these results are compared with those of molecular dynamics simulations as some sort of verification. These results show that when the layers number increases, the natural frequency also increases up to a specific number, and afterward the influence of layers number on the natural frequency significantly decreases. Moreover, the natural frequency decreases with increase in the sheet aspect ratio up to a specific value, then the changes in the aspect ratio have no considerable effect in the natural frequency.