Nanoscale Vibrational Analysis of an Embedded Multi-Layered Graphene Sheet

In this paper, nanoscale vibrational analysis of a multilayered graphene sheet embedded in an elastic medium is investigated and the corresponding resonant modes and frequencies are determined. It is known that the elastic moduli of a graphene sheet in two orientations x, y are different, so the graphene sheet is assumed to be a general form of an orthotropic plate. The orthotropic sheets stacking at the top of each other bond with carbon-carbon van der Waals forces, also the whole multi-layered graphene sheet is influenced by polymer-carbon van der Waals forces from the surrounding elastic medium.