Abstract The bending rigidity of two-dimensional (2D) materials is a key parameter for understanding the mechanics of 2D NEMS devices. The apparent bending rigidity of graphene membranes at macroscopic scale differs from theoretical predictions at micro-scale. This difference is believed to originate from thermally induced dynamic ripples in these atomically thin membranes. In this paper, we perform modal analysis to estimate the effective bending rigidity of graphene membranes from the frequency spectrum of their Brownian motion. Our method is based on fitting the resonance frequencies obtained from the Brownian motion in molecular dynamics simulations, to those obtained from a continuum mechanics model, with bending rigidity and pretension as the fit parameters. In this way, the effective bending rigidity of the membrane and its temperature and size dependence, are extracted, while including the effects of dynamic ripples and thermal fluctuations. The proposed method provides a framework for estimating the macroscopic mechanical properties in other 2D nanostructures at finite temperatures.

中文翻译：

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用于确定石墨烯的尺寸和温度相关弯曲刚度的模态分析

摘要 二维 (2D) 材料的弯曲刚度是理解二维 NEMS 器件力学的关键参数。宏观尺度石墨烯膜的表观弯曲刚度与微观尺度的理论预测不同。这种差异被认为源于这些原子级薄膜中的热致动态波纹。在本文中，我们进行模态分析，从布朗运动的频谱估计石墨烯膜的有效弯曲刚度。我们的方法基于将从分子动力学模拟中的布朗运动获得的共振频率拟合到从连续介质力学模型获得的共振频率，以弯曲刚度和预应力作为拟合参数。这样，提取膜的有效弯曲刚度及其温度和尺寸依赖性，同时包括动态波纹和热波动的影响。所提出的方法为在有限温度下估计其他二维纳米结构的宏观力学性能提供了一个框架。