euler-bernoulli theory

A complete investigation on the free vibration of bilayer graphene nanoribbons (BLGNRs) mod-eled as sandwich beams taking into account 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 role of sandwich beam layers and are modeled based upon Euler-Bernoulli theory. To consider effects of vdWs interactions between adjacent GNRs as well as between GNRs and polymer matrix, their equivalent tensile-compressive and shear moduli are considered and utilized 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 obtained 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.