Nanoscale vibration characteristics of multi-layered graphene sheets

A continuum-based plate model is proposed to study the nanoscale vibration characteristics of multi-layered graphene sheets (MLGSs) that are increasingly being proposed for important engineering applications such as THz resonators. Generalized Differential Quadrature (GDQ) method is used to predict the natural frequencies and their associated vibration modes of single-layered and triple-layered graphene sheets, as well as general MLGSs. Numerical simulations are carried out to examine the effects of van der Waals (vdW) interactions, which are present as bonding forces between the layers, on nanoscale vibration natural frequencies and their mode shapes. The results show that for a general MLGSs, vibration modes can be classified into 3 families lower classical synchronized modes which are independent of van der Waals forces, middle van der Waals enhanced modes which are largely determined by the presence of van der Waals interactions and higher mixed modes which are combinations of the classical synchronized modes and van der Waals enhanced modes. Detailed characterizations of these modes from their derived mode shapes have been achieved for the typical case of triple-layered GSs, as well as general MLGSs. Effects of different boundary conditions, aspect ratios and the number of layers on nanoscale vibration properties have been examined in detail. The results presented in this paper, for the first time, provide accurate and wholesome studies and characterizations on the interesting nanoscale vibration properties of multi-layered graphene sheets and the results obtained will certainly be useful to those who are concerned with the dynamics of graphene sheets which are increasingly being deployed for various innovative engineering applications. (C) 2012 Elsevier Ltd. All rights reserved.