Studying graphene electromechanical behavior based on the elastic plates moment-membrane theory

Graphene being a two-dimensional nanomaterial created a new research area - its use as a functional element in various modern technology nanodevices. To open the way for such an application, it is necessary, first of all, to study the mechanical properties and its behavior under various conditions and learn how to manipulate them in a controlled way. All this necessitates an adequate graphene deformation simulations, the construction of an appropriate continuum theory that takes into account scale effects, microstructure and graphene crystal lattice physical parameters. This work aims at studying a rectangular graphene sheet in an electric field. For graphene deformations, the application of the transverse bending model of the elastic plates of the moment-membrane linear theory is justified. Forces of the electrical origin are modeled by means of a normal load applied to the front plate surface. A study was made of the influence of boundary conditions, the gap between the plate and the gate, the potential difference, and linear dimensions on the graphene sheet static transverse bending. The problem of graphene sheet natural vibrations is also solved. The graphene sheet vibration frequency lies in the GHz range. In the clamped boundary conditions case, the natural oscillations frequency is much higher than in the hinged supported case. Even at small deflections, a change in the constant voltage value has a significant effect on the graphene sheet natural frequency.