Free vibration analysis of bilayer graphenes with interlayer shear effect

In this paper, for the free vibration analysis of bilayer graphenes with interlayer shear effect the sandwich beam model is introduced. Because of the similarity between the bilayer graphene and the sandwich structures, in which at the top and the bottom of the bilayer graphene there is a single layer graphene and between them there is Vander walls bindings, the bilayer graphene is modeled as a sandwich beam and its free vibration is investigated for free-clamp end condition. To obtain the governing equations, each graphene layer is modeled based on the Euler-Bernoulli theory and in-plane displacements are also considered in addition to the transverse displacement. It is also assumed that the graphene layers do not have relative displacement during vibration. The effect of the Vander walls bindings is introduced in the governing equations as the shear modulus. The results obtained by the sandwich beam model, presented in this paper for the first time, include the first five natural frequencies of the bilayer graphenes with 7 to 20 nanometer lengths. These results are validated by the molecular dynamic and the Multi-Beam-Shear model results.