Interlayer effects of Van der Waals interactions on transverse vibrational behavior of bilayer graphene sheets

This study focuses only on the interlayer effects of van der Waals (VdWs) interactions (including simultaneous effects of shear and tensile-compressive effects) on the free transverse vibrational behavior of bilayer graphene sheets by implementing the classical continuum mechanics theory. To this end, the classical sandwich plate theory and the Hamilton’s principle are involved to obtain the governing equations and the harmonic differential quadrature method is employed to calculate the natural frequencies and related mode shapes. The results show the shear effect of VdWs interactions has significant influences on primary natural frequencies and mode shapes. Therefore it is a main determinant and can safely assume the pure shear effect while designing sensors, actuators, accelerometers and resonators. Finally, the potential depth parameter is introduced to consider the simultaneous effects of shear and tensile-compressive forces.