Size-Dependent Dynamic Behavior of Axially Moving Graphene Nanosheets using Nonlocal First-Order Shear Deformation Theory

Document Type : Original Article


Beijing Technology and Business University, Fangshan District, China, 102401


Based on the potential applications of graphene nanosheets as super-sensitive sensors, this paper examines the vibrations of graphene nanoplates under the influence of axial motion. For this purpose, Kirchhoff's nonlinear plate model will be used in conjunction with the modified couple stress theory (MCST). Using Hamilton's principle, nonlinear equations governing motion are extracted and then discretized using the Galerkin method. Based on the numerical method, the dynamic response and vibration characteristics of these systems are determined. According to our results, the small size parameter increases the critical speed of the system. The first non-dimensional critical speed of the system at 0, 1.2, and 1.8 is approximately 3.14, 3.18, and 3.42, respectively. A small size parameter also increases the system's oscillation frequency. It is unnecessary to apply the modified stress coupling theory to nanosheets with thicker thicknesses (h > 1.25l) since the effect of the size scale parameter increases with decreasing thickness. In contrast, the frequency increases significantly for thinner nanosheets. Due to the nonlinear behavior of these systems, the instability of the motion of the system can be attributed to chaotic behavior based on the study of the dynamic response. Graphene nanosheets and other plate-like nanostructures may be identified based on the results presented here.