Predicting nanovibration of multi-layered graphene sheets embedded in an elastic matrix

A continuum-based plate model is proposed to study the vibration behavior of multi-layered graphene sheets (MLGSs) that are embedded in an elastic matrix. A set of explicit formulas is derived to predict the natural frequencies and associated vibration modes of double-layered and triple-layered graphene sheets that are embedded in an elastic matrix. Numerical simulations are carried out to examine the effects of the van der Waals (vdW) interaction on the natural frequencies. The results show that for a given combination of wavenumbers (m, n), the lowest natural frequency of a MLGS is independent of the vdW interaction, but all of the other higher natural frequencies depend significantly on the vdW interaction. The influence of the moduli of the surrounding matrix is also investigated, and the results indicate that the classical natural frequency depends significantly on these moduli. For lower-order resonant frequencies, the effect of the surrounding matrix is very small and can be neglected, but the higher-order resonant frequencies depend significantly on the moduli, and the influence of the surrounding matrix must thus be taken into consideration. In addition, the resonance modes of a MLGS system are dominated by the vdW interaction, whereas the moduli of the surrounding matrix only slightly affect the relative amplitude ratios of the sheets and do not change the vibration direction.