Effect of elastic foundation on vibrational behavior of graphene based on first-order shear deformation theory

In this study, an investigation of the free vibrations of hollow circular plates is reported. The study is based on elastic foundation and the results depicted are further extended to study the special case of graphene sheets. The first-order shear deformation theory is applied to study the elastic properties of the material. A hollow circular sheet is modeled and the vibrations are simulated with the aid of finite element method. The results obtained are in good agreement with the theoretical findings. After the validation, a model of graphene is presented. Graphene contains a layer of honeycomb carbon atoms. Inside a layer, each carbon atom C is attached to three other carbon atoms and produces a sheet of hexagonal array. A 25 nm X 25 nm graphene sheet is modeled and simulated using the validated technique, that is, via the first-order shear deformation theory. The key findings of this study are the vibrational frequencies and vibrational mode shapes.