Analysis of free vibration of embedded multi-layered graphene sheets

In this paper, the vibrational properties of four- and five-layered graphene sheets (GSs) embedded in the elastic matrix are analyzed based on a multi-layered continuum model with considering the vdW interaction of any two layers of GSs. The influences of vdW interaction and the surrounding matrix on the vibrational properties four- and five-layered GSs embedded in elastic medium are investigated in detail. The results show that the surrounding matrix has a significant effect on the foundational frequency of MLGSs, while these factors are neglectable for the other higher-order frequencies. These results will be helpful for engineering application of four- and five-layered GSs.