Influence of temperature on the modal behavior of monolayer graphene sheets

Abstract

In this work, the vibrational behavior of rectangular monolayer graphene sheets is predicted at different environmental temperatures. Graphene sheets are modeled according to their molecular structure via finite element analysis. Using molecular mechanics theory, the potential energy of graphene is expressed as temperature-dependent. The graphene interatomic interactions are simulated by spring elements, and the nodes of the model represent the carbon atoms. The carbon atom mass is considered in the assembly and solution of the vibrational problem. The temperature influence is introduced to the model because of its effect on the bond length and stiffness of the spring elements. The eigenvalue problem is solved using appropriate boundary conditions. The solution yields the frequencies and corresponding mode shapes of graphene for all temperatures, sheet dimensions, and orientations under the boundary conditions investigated. The results of this study demonstrate that the bending frequencies are not influenced by temperature, in contrast to the in-plane vibrations. The results demonstrate the accuracy of the proposed method compared with published data in the literature.