A Self-Adaptive Umbrella Model for Vibration Analysis of Graphene

The beam finite element and molecular dynamics models are two popular methods to represent the reaction of carbon-carbon bonds in graphene. However, the wrinkles and ripples in geometrical characteristics are difficult take into consideration. The out-planar mechanical properties are neglected in classical models of graphene. This paper proposes a self-adaptive umbrella model for vibration analysis of graphene. The parameters in the umbrella model are flexible to adapting the geometrical and material characteristics of graphene. The umbrella model consists of shell and beam elements. The honeycomb beam and planar shell model of graphene are included in the self-adaptive umbrella model as particular cases. The sensitivity analysis and results confirmed the rationality and feasibility of the self-adaptive umbrella model.