Nanoscale vibrational analysis of a multi-layered graphene sheet embedded in an elastic medium

In this paper, nanoscale vibrational analysis of a multi-layered graphene sheet embedded in an elastic medium is investigated and the corresponding natural frequencies and the associated modes are determined. The modeling is based on the fact that the elastic moduli of a graphene sheet in two perpendicular orientations are different, so the plate is considered to be anisotropic. The graphene layers stacking at the top of each other bond with carbon–carbon van der Waals forces between two adjacent ones. Also, the whole multi-layered graphene sheet is influenced by polymer-carbon van der Waals forces from the surrounding elastic medium.