Vibration Analysis of an Imperfect Single-Layer Graphene Sheet using Quasi-3d Theory and Isogeometric Approach

In this study, the size-dependent free vibration analysis of a geometrically imperfect single-layer graphene sheet (SLGS) is studied by an isogeometric approach along with the quasi-3D shear and normal deformation theory. Initial geometric imperfections alter the natural frequencies of the graphene sheets that may exist inherently or purposely created by researchers. The initial curvature is modelled by an analytical function in the governing Equations of the plate. A 4-variable quasi-3D theory with a seventh-order distribution function is used to include both shear deformation and thickness stretching influences. A weak form of a nonlocal plate for free vibration analysis is derived that requires the first-order continuity of the displacement fields. Inherent high-order continuity of non-uniform rational B-spline (NURBS) basis functions in isogeometric analysis can meet this condition. A comparison between the present study and other published works reveals the efficiency and accuracy of the proposed method in imperfect SLGS. The results of the present study show a significant effect of initial geometric imperfection on the natural frequency of single-layer graphene sheets.