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Nanoscale vibration characteristics of multi-layered graphene sheets

机译：多层石墨烯片的纳米级振动特性

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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.
机译：提出了一种基于连续体的平板模型来研究多层石墨烯片（MLGS）的纳米级振动特性，而多层石墨烯片（MLGS）越来越多地被提出用于重要的工程应用，例如THz谐振器。广义差分正交（GDQ）方法用于预测单层和三层石墨烯片以及常规MLGS的固有频率及其相关的振动模式。进行了数值模拟，以检验范德华力（vdW）相互作用对纳米级振动固有频率及其振型的影响，该相互作用以层之间的结合力形式存在。结果表明，对于一般的MLGS，振动模式可分为3类：较低的经典同步模式，与Van der Waals力无关；中等Van der Waals增强模式，主要由van der Waals相互作用和更高的混合模式，是经典同步模式和范德华增强模式的组合。对于三层GS和一般MLGS的典型情况，已经从其导出的模式形状中获得了这些模式的详细表征。详细检查了不同的边界条件，纵横比和层数对纳米级振动性能的影响。本文首次提出的结果，对多层石墨烯片材的有趣的纳米级振动特性提供了准确，有益的研究和表征，所获得的结果对于那些关注石墨烯片材动力学的人当然是有用的。它们正越来越多地用于各种创新工程应用。

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