a novel method for considering interlayer effects between graphene nanoribbons and elastic medium in free vibration analysis

A complete inspectation on the free vibration of bilayer graphene nanoribbons (blgnrs) modeled as sandwich beams considered tensile-compressive, and shear effects of van der waals (vdws) interactions between adjacent graphene nanoribbons (gnrs) as well as between gnrs and polymer matrix is performed in this research. in this modeling, nanoribbon layers play the role of sandwich beam layers and are modeled based upon the euler-bernoulli theory. in order to deliberate effects of vdws interactions between adjacent gnrs as well as between gnrs and polymer matrix, their equivalent tensile-compressive and shear moduli are contemplated and applied in derivation of governing equations instead of employing conventional winkler and pasternak effects for elastic medium. the governing equations of motion are derived by considering the assumptions and employing sandwich beam theory, and natural frequencies are acquired by implementing harmonic differential quadrature method (hdqm). a detailed study is performed to examine the influences of the tensile-compressive and shear effects of vdws interactions between adjacent gnrs as well as between gnrs and polymer matrix on the free vibration of blgnrs.