Free vibration analysis of multi-layer graphene nanoribbons incorporating interlayer shear effect via molecular dynamics simulations and nonlocal elasticity

• Nonlocal parameter is calibrated for vibration of multi-layer graphene nanoribbons.
• Interlayer shear effect between GNR layers is also considered.
• Two first nonlocal frequencies are obtained using sandwich formulation.
• Molecular dynamics simulations are done for nonlocal parameter calibration.

Free vibration of cantilever multi-layer graphene nanoribbons (MLGNRs) with interlayer shear effect is investigated using molecular dynamics simulations (MD) and nonlocal elasticity. Because of similarity of MLGNRs to sandwich structures, sandwich formulations are expressed in the nonlocal form. By comparing the first two frequencies of MLGNRs with various layers and lengths obtained using MD simulations with those of the nonlocal sandwich formulation; the nonlocal parameter is calibrated to match the results of two methods. The results reveal that the calibrated nonlocal parameter for predicting the second frequencies is dependent on the number of MLGNR layers, and it increases by increasing the number of layers.