Shi Jiajia, Chu Liu, Ma Chao, Braun Robin
School of Transportation and Civil Engineering, Nantong University, Nantong 226019, China.
School of Information Science and Technology, Nantong University, Nantong 226019, China.
Materials (Basel). 2022 May 20;15(10):3679. doi: 10.3390/ma15103679.
Graphene is one of the most promising two-dimensional nanomaterials with broad applications in many fields. However, the variations and fluctuations in the material and geometrical properties are challenging issues that require more concern. In order to quantify uncertainty and analyze the impacts of uncertainty, a stochastic finite element model (SFEM) is proposed to propagate uncertainty for carbon atomic interactions under resonant vibration. Compared with the conventional truss or beam finite element models, both carbon atoms and carbon covalent bonds are considered by introducing plane elements. In addition, the determined values of the material and geometrical parameters are expanded into the related interval ranges with uniform probability density distributions. Based on the SFEM, the uncertainty propagation is performed by the Monte Carlo stochastic sampling process, and the resonant frequencies of graphene are provided by finite element computation. Furthermore, the correlation coefficients of characteristic parameters are computed based on the database of SFEM. The vibration modes of graphene with the extreme geometrical values are also provided and analyzed. According to the computed results, the minimum and maximum values of the first resonant frequency are 0.2131 and 16.894 THz, respectively, and the variance is 2.5899 THz. The proposed SFEM is an effective method to propagate uncertainty and analyze the impacts of uncertainty in the carbon atomic interactions of graphene. The work in this paper provides an important supplement to the atomic interaction modeling in nanomaterials.
石墨烯是最具前景的二维纳米材料之一，在许多领域有着广泛应用。然而，材料和几何特性的变化与波动是具有挑战性的问题，需要更多关注。为了量化不确定性并分析不确定性的影响，提出了一种随机有限元模型（SFEM）来传播共振振动下碳原子相互作用的不确定性。与传统的桁架或梁有限元模型相比，通过引入平面单元同时考虑了碳原子和碳共价键。此外，将材料和几何参数的确定值扩展到具有均匀概率密度分布的相关区间范围。基于SFEM，通过蒙特卡罗随机抽样过程进行不确定性传播，并通过有限元计算得到石墨烯的共振频率。此外，基于SFEM数据库计算特征参数的相关系数。还给出并分析了具有极端几何值的石墨烯的振动模式。根据计算结果，第一共振频率的最小值和最大值分别为0.2131和16.894太赫兹，方差为2.5899太赫兹。所提出的SFEM是传播不确定性和分析石墨烯中碳原子相互作用不确定性影响的有效方法。本文的工作为纳米材料中的原子相互作用建模提供了重要补充。
