Sandwich beam model for free vibration analysis of bilayer graphene nanoribbons with interlayer shear effect

In this study, sandwich beam model (SM) is proposed for free vibration analysis of bilayer graphene nanoribbons (BLGNRs) with interlayer shear effect. This model also takes into account the intralayer (in-plane) stretch of graphene nanoribbons. The molecular dynamics (MD) simulations using the software LAMMPS and Adaptive Intermolecular Reactive Empirical Bond Order (AIREBO) potential are done to validate the accuracy of the sandwich model results. The MD simulation results include the two first frequencies of cantilever BLGNRs with different lengths and two interlayer shear moduli, i.e., 0.25 and 4.6 GPa. These two interlayer shear moduli, 0.25 and 4.6 GPa, can be obtained by sliding a small flake of graphene on a large graphene substrate when the parameter of E_LJ term in AIREBO potential, epsilon_CC, is set to be 2.84 and 45.44 meV, respectively. The SM results for a wide range of bending rigidity values show that the proposed model, i.e., the SM, predicts much better than the previous beam model in which the intralayer stretch is ignored. In addition, it is observed that the model can properly predict the natural frequencies of BLGNRs for various values of the bending rigidity and the interlayer shear modulus.