| 随岁寒1,2,3
，刘金建4*.流动石墨烯增强薄板的模态分析[J].海南师范大学学报自科版,2025,38(1):72-83 |
| 流动石墨烯增强薄板的模态分析 |
| Mode Analysis on Flowing Graphene Reinforced Thin Plates |
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| DOI：10.12051/j.issn.1674-4942.2025.01.010 |
| 中文关键词: 流动连续体力学 石墨烯增强薄板 模态分析 有限差分法 二维节点编号法 |
| 英文关键词: mechanics of flowing continua graphene reinforced thin plate modal analysis finite difference method twodimensional node numbering method |
| 基金项目:国家自然科学基金项目（12272064）；河南省高等学校重点科研项目（23B130002）；河南省科技攻关项目
（222102210147）；商丘工学院校级科研项目（2023KYXM01） |
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| 中文摘要: |
| 结合科氏加速度和离心加速度，提出了流动连续体力学的概念，兼顾了轴向运动结构
力学和管道输流结构力学2类典型力学问题。在四边固支边界内，通过欧拉描述建立流动石墨烯
增强薄板的动力学方程。应用有限差分法求解动力学方程时，为克服传统一维节点编号方法带来
的编程困难，开发了二维节点编号法，在此基础上给出了前四阶导数的差分公式。通过与ANSYS
软件对比发现，本文算法能够在较少的节点数量条件下获得很高的计算精度。将广义特征值方程
转换为标准特征值方程，求解得到的特征值和特征向量分别代表固有频率和模态，给出了固有频
率实部和虚部与流速的关系，其中实部用于表征振动稳定性。利用特征值矩阵拟合出前两阶模态
的三维图，给出了各个流速条件下的模态正视图和斜视图，呈现了模态的阶跃特性。研究还发现：
随着石墨烯含量的增加，各阶频率相应增大，但趋势渐缓；科氏加速度和离心加速度都是流动石墨
烯增强薄板振动的重要影响因素，各自贡献大小与振动阶次相关。 |
| 英文摘要: |
| Combinining Coriolis acceleration and centrifugal acceleration, the concept of mechanics of flowing continua was put
forward, which takes into account the typical mechanical problems of the axial motion structure and the pipeline structure. The dy⁃
namic equation of the flowing graphene reinforced thin plate was established by the Eulerian description within the boundary of
four fixed edges. In order to overcome the programming difficulties caused by the traditional one-dimensional node numbering
method, the two-dimensional node numbering method was developed and the difference formulas of the first four derivatives were
given. By comparing with ANSYS software, it was found that the proposed algorithm can obtain high calculation accuracy under
the condition of fewer nodes. The eigenvalues and eigenvectors obtained by solving the standard eigenvalue equation represent the natural frequency and the mode respectively, and the relationship between the real and imaginary parts of the natural frequency
and the flowing velocity was given. The eigenvalue matrix was innovatively used to fit the three dimensional graph of the first two
modes, and the top and side views of the modes under each speed condition were given, showing the step characteristics of the
modes. The study also found that with the increase of volume fraction, the frequencies of each order increased correspondingly,
but the trend slowed down, and Coriolis acceleration and centrifugal acceleration are both key factors affecting the vibration of
flowing graphene reinforced thin plates, and their contributions are related to the vibration order. |
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