Multiscale Analysis Approach to find the Dynamic Characteristics of Graphene Sheet

The research work addresses question on dynamic characteristic of structure which exhibit periodicity at nano scale viz. single layer graphene sheet using multiscale analysis approach. The carbon-carbon bond of graphene sheet is modeled as space frame element whereas the carbon atom is modeled as 3D-mass element without rotary inertia. Molecular structural mechanics (MSM) model has been used to find the equivalent geometric and elastic properties of space frame element to represent carbon-carbon bond. In molecular structural mechanics model, force field is expressed in the form of steric potential energy by omitting the electrostatic interaction. Sectional stiffness parameters are linked with the force field constants to derive the equivalent elastic and geometric properties of space frame element. This approach is used here to investigate the dynamic behavior of single layer graphene sheet. Simulations have been carried out with different values of aspect ratio to know the effect of variation in length and width on the natural frequencies of graphene structure. Molecular dynamic simulation has also been carried out on the same structure of graphene sheet to validate the results of proposed molecular structural mechanics model.