Resonance analysis of multi-layered graphene sheets used as nanoscale resonators

A stacked plate model for the vibration of multi-layered graphene sheets (MLGSs), in which the van der Waals (vdW) interaction between layers is described by an explicit formula, is presented. Explicit formulae are derived for predicting the natural frequencies of double- and triple-layered graphene sheets, and they clearly indicate the effect of vdW interaction on the natural frequencies. The natural frequencies are calculated for various numbers of layered graphene sheets, and the results show that the vdW interaction has no influence on the lowest natural frequency (classical frequency) of an MLGS but plays a significant role in all higher natural frequencies (resonant frequencies) for a given combination of m and n. The vibration modes that are associated with the classical frequencies for each sheet of an MLGS are identical. In contrast, the vibration modes that are associated with the resonant frequencies are non-identical and give various vibration patterns, which indicates that MLGSs are highly suited to use as high frequency resonators.