Vibration Analysis of Circular Single-Layer Graphene Sheet Using Finite Element Method

Graphene sheets are combined of Honeycombs lattice carbon-carbon bonds which have high natural frequencies, high strength, and high conductivity. Due to important applications of the graphene sheets particularly at higher frequencies, the study of their dynamic behavior is important in this frequency range. From Molecular Dynamics (MD) point of view as the dimensions of graphene sheet incline, the number of atoms increases, and as a result, its modeling becomes more time-consuming. Besides the experimental methods in small dimensions are difficult to conduct and not economical. In this research Finite Element Method (FEM) is used for frequency analysis of graphene sheets in various dimensions in order to study the capability of FEM in simulating the dynamic behavior of graphene sheets at small scales. In this research, the objective function is to find the minimum size of the sheet in which both methods have good convergence. Also, the time-consuming for the simulation is investigated. The time-consuming for analysis in the Finite Element Method is less than other methods, including Molecular Dynamics (MD), Generalized Differential Quadrature (GDQ), etc. Also, The results indicated that for circular single-layer graphene sheets simulation, using Finite Element Method (FEM) is in good agreement with the results obtained from the Molecular Dynamics (MD) simulation, in the radius more than 100 nm. In this research, the ABAQUS has been used for Finite Element Method (FEM) simulation.