Elastic effects on vibration of bilayer graphene sheets incorporating integrated VdWs interactions

The following study addresses the free vibration analysis of a bilayer graphene sheet (BLGS) embedded in an elastic medium in the presence of shear and tensile-compressive effects of van der Waals (vdWs) interactions. To ascertain the contribution of each force, the effects are considered separately and simultaneously. To model the geometry of the BLGS, the sandwich plate theory and the Hamilton's principle are considered to derive the governing equations of motion. The Harmonic differential quadrature method is applied to solve the coupled equations and obtain the natural frequencies and related mode shapes. The results reveal that the contribution of tensile-compressive modulus of elastic medium is the most in changing the frequency of BLGSs. (paper)