Continuum model for the vibration of multilayered graphene sheets

TLDR

The study presents a continuum model for analyzing the vibration of multilayered graphene sheets. An explicit van der Waals interaction formula is derived and used to develop a continuum‑plate model that predicts vibration modes of multilayered graphene sheets, with mode shapes examined for double‑ and ten‑layered configurations. The lowest natural frequency of a multilayered graphene sheet is independent of van der Waals interaction, while higher resonant frequencies and their mode shapes vary with layer number, allowing distinct resonance modes by changing the number of layers.

Abstract

The vibration analysis of multilayered graphene sheets (MLGSs) using a continuum model is reported in this paper. An explicit formula is derived to predict the van der Waals (vdW) interaction between any two sheets of a MLGS. Based on the derived formula, a continuum-plate model is developed for the vibration of MLGSs. Our investigation indicates that the lowest natural frequency (classical natural frequency) of a MLGS for a given combination of $m$ and $n$ is independent of the vdW interaction, but that all of the other higher natural frequencies (resonant frequencies) are significantly dependent on this interaction. The mode shapes that are associated with the natural frequencies are investigated for double-layered and ten-layered graphene sheets. We find that the vibration modes that are associated with the classical natural frequency of all the sheets are in the same direction and have the same amplitude, whereas the vibration modes of the sheets that are associated with the resonant frequencies are different due to the influence of the vdW interaction. Thus various resonance modes can be obtained by varying the number of layers of a MLGS.