基于有限元和微分求积法的石墨烯等效纳米板动力特性研究

吴雪彬; 白镇滔; 刘秦龙; 李东波

doi:10.21656/1000-0887.460048

基于有限元和微分求积法的石墨烯等效纳米板动力特性研究

doi: 10.21656/1000-0887.460048

吴雪彬^1,,
白镇滔²,
刘秦龙^{1, 2},
李东波^{1, 2, ,}

1.
西安建筑科技大学理学院，西安 710055
2.
西安建筑科技大学土木工程学院，西安 710055

基金项目:

国家重点研发计划课题 2023YFF0906001

国家自然科学基金 52378195

国家自然科学基金 52008332

详细信息

作者简介:
吴雪彬(2000—)，男，硕士生(E-mail: w2211212321@xauat.edu.cn)

通讯作者:
李东波(1982—)，男，教授，博士，博士生导师(通信作者. E-mail: ldb@xauat.edu.cn)

中图分类号: O34
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- 文章访问数: 147
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- 被引次数: 0
出版历程
- 收稿日期: 2025-03-11
- 修回日期: 2025-04-29
- 刊出日期: 2026-04-01

Dynamic Characteristics Analysis of Equivalent Graphene Nanoplatelets Based on Finite Element and Differential Quadrature Methods

WU Xuebin^1
,,
BAI Zhentao²,
LIU Qinlong^{1, 2},
LI Dongbo^{1, 2
, ,}

1.
School of Science, Xi'an University of Architecture and Technology, Xi'an 710055, P.R.China
2.
College of Civil Engineering, Xi'an University of Architecture and Technology, Xi'an 710055, P.R.China

摘要

摘要: 非局部连续介质理论能充分考虑材料尺寸效应及微观结构对宏观力学性质的影响，是一种解决宏微观关联问题的新途径，但由于其本构关系中嵌入了长程相互作用积分项，控制方程呈现高阶偏积分-微分方程组特征，显著提升了计算复杂度. 为此，本文基于有限元-微分求积(FE-DQ)耦合算法，提出了一种非局部连续介质理论的求解方法，并对石墨烯等效纳米板的自由振动特性进行了研究. 结果表明，FE-DQ数值方法通过分向离散策略将非局部积分-微分方程转化为可解代数系统，从而极大简化求解过程，是一种有效的非局部连续介质理论的求解方法. 基于计算结果，进一步研究了尺寸、非局部参数及振动模态等因素对自由振动频率非局部效应的影响机制. 结果表明，随着尺寸的增大，纳米板自由振动频率的非局部效应呈现出逐渐减弱的趋势；当非局部参数取值逐渐增大，或者振动模态阶数持续升高时，自由振动频率的非局部效应会显著增强. 研究成果可为相关领域纳米尺度下结构动力学特性研究提供参考.
- 非局部连续介质理论 /
- FE-DQ方法 /
- 石墨烯 /
- 等效纳米板 /
- 动力特性
Abstract: The nonlocal continuum theory effectively integrates microscopic structural features and macroscopic mechanical responses by introducing a cross-scale correlation mechanism, providing a new theoretical paradigm for solving multi-scale mechanical problems. However, due to the incorporation of long-range interaction integral terms in the constitutive relationship, its control equations exhibit the characteristics of high-order partial integro-differential equations, and significantly increase the computational complexity. A novel finite element-differential quadrature coupling algorithm (FE-DQ) was established and applied to the study of the free vibration characteristics of graphene equivalent nanoplatelets. Based on the parameterized calculation, the influential mechanisms of key variables such as characteristic sizes and non-local parameters on the non-local effects of buckling loads were revealed through systematic parametric studies. The results show that, the scale effect of buckling loads exhibits a significant nonlinear attenuation characteristic and is positively correlated with the size of the non-local parameter. With the gradual increase of the structural size, the non-local effect on the free vibration frequency will gradually weaken; conversely, with the continuous increase of the non-local parameter value or the rise of the vibration modal order, the non-local effect on the free vibration frequency will intensify significantly. The research provides a reference for the study of structural dynamic characteristics on a nanoscale in related fields.
- dynamic characteristic /
- FE-DQ method /
- graphene /
- equivalent nanoplatelet /
- nonlocal continuum theory

HTML全文

图 1 石墨烯等效的纳米薄板

Figure 1. The equivalent graphene nanoplatelet

下载: 全尺寸图片幻灯片

图 2 不同尺寸下石墨烯等效纳米板自由振动频率比变化柱状图

注为了解释图中的颜色，读者可以参考本文的电子网页版本，后同.

Figure 2. The bar chart of free vibration frequency ratio variations for equivalent graphene nanoplatelets under different sizes

下载: 全尺寸图片幻灯片

图 3 不同非局部参数下石墨烯等效纳米板自由振动频率比变化曲线图

Figure 3. The plot of free vibration frequency ratio variations for equivalent graphene nanoplatelets under different nonlocal parameters

下载: 全尺寸图片幻灯片

图 4 不同振动模态下石墨烯等效纳米板自由振动频率变化曲线

Figure 4. The plot of free vibration frequency variation curves for equivalent graphene nanoplatelets under different vibration modes

下载: 全尺寸图片幻灯片

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