Vibration analysis of circular and square single-layered graphene sheets: An accurate spring mass model

The free vibration characteristics of circular and square single-layered graphene sheets (SLGSs) are investigated by developing a finite element formulation based on an accurate spring mass model. According to the present atomistic structural model, nodes are defined at the atom locations and suitable three-dimensional spring-type elements are employed to connect these nodes which are representing interatomic interactions. Natural frequencies and their associated vibration modes are obtained for SLGSs of different geometries. Molecular dynamics simulations are also conducted to validate the results obtained from the finite element model developed herein and excellent agreement has been found. It is shown that in the case of rectangular SLGSs, the frequency will be independent of area when the width becomes very small.