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Determination of Natural Vibrations of Simply Supported Single Layer Graphene Sheet using Non-Local Kirchhoff Plate Theory

Since the discovery of carbon allotrope called graphene, graphene has attracted strong scientific interest in past decade. Graphene sheets (GS) have enormous potential for application as structural elements in nanoscale devices, owing to their remarkable chemical, physical and mechanical properties for example low weight, high surface area, extremely high stiffness and high sensitivity [1]. Nanoelectromechanical resonator sensors (NEMS) based on graphene sheets (GS) show ultrahigh sensitivity to vibration. Many factors such as dimensions of the GSs will affect the sensor characteristics [2]. The focus of this paper is derivation of analytical model of Simply Supported Single Layer Graphene Sheet which is based on nonlocal Kirchhoff plate theory and this theory incorporates size effects into classical plate theory [3]. After derivation of analytical model, the Galerkin method was applied in order to obtain natural frequencies of simply supported SLGS [4]. The obtained results showed very high sensitivity of SLGS which suggest they are good candidates for a gas sensor detection.

carbon ; graphene ; galerkin method ; kirchhoff plate theory ; natural vibrations ; NEMS ; single layer graphene sheet (SLGS)

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