Modeling and Control of a Smart Single-Layer Graphene Sheet

In this study, a smart single-layer graphene sheet (SLGS) is analytically modeled and its buckling is controlled using coupled polyvinylidene fluoride (PVDF) nanoplates. A voltage is applied to the PVDF nanoplate in thickness direction in order to control the critical load of the SLGS. Electric potential distribution is assumed as a combination of a half-cosine and linear variation in order to satisfy the Maxwell equation. The exact analysis is performed for the case when all four ends are simply supported and in free electrical boundary condition. The nonlocal governing equations are derived through Hamilton’s principle and energy method based on a nonlocal Mindlin plate theory. The detailed mathematical derivations are presented and numerical investigations are performed, while the emphasis is placed on investigating the effect of several parame‐ ters such as small-scale coefficient, stiffness of the internal elastic medium, graphene length, mode number, and external electric voltage on the buckling smart control of the SLGS in detail. It is explicitly shown that the imposed external voltage is an effec‐ tive controlling parameter for buckling of the SLGS. Numerical results are presented to serve as benchmarks for design and smart control of nanodevices.