Investigating simultaneous effects of tensile-compressive and shear moduli of van der Waals interactions on the vibration of bilayer graphene nanoribbons for different boundary condition

In this study, effects of various boundary conditions on the free vibration of double layer graphene nanoribbons (DLGNRs) are investigated by considering both of tensile-compressive and shear effects of van der Waals (vdWs) interactions. Sandwich beam theory is used to model the DLGNRs. In the references, only one of tensile-compressive or shear effects of vdWs interactions have been considered. Based on sandwich beams theory, vdWs interactions are equivalent to the sandwich core and are modeled in a way that they can withstand the tensile-compressive and shear forces simultaneously. Hamilton’s principle is employed to extract governing equations of motion and boundary conditions. Harmonic differential quadrature method is utilized to investigate natural frequencies and related mode shapes of DLGNRs. In order to verify, results are compared to other literatures in a condition that one of the vdWs effects to be neglected. The effect of boundary condition and interlayer shear direction on the mode shape, sequence and value of DLGNRs natural frequencies are investigated.