弹性地基上FG-GRC梁的振动

兰州理工大学学报 ›› 2025, Vol. 51 ›› Issue (2): 38-43.

弹性地基上FG-GRC梁的振动

张靖华^*, 姚玉琴

兰州理工大学理学院, 甘肃兰州 730050

收稿日期:2022-12-27 出版日期:2025-04-28 发布日期:2025-04-29
通讯作者: 张靖华(1979-),女,甘肃渭源人,博士,教授,博导.Email:zjhhrb@163.com
基金资助:
国家自然科学基金(12362009),甘肃省科技计划项目(23JRRA775)

Vibration of FG-GRC beam on elastic foundation

ZHANG Jing-hua, YAO Yu-qin

School of Science, Lanzhou University of Technology, Lanzhou 730050, China

Received:2022-12-27 Online:2025-04-28 Published:2025-04-29

摘要/Abstract

摘要： 为了研究置于弹性地基上石墨烯增强功能梯度(FG-GRC)梁的振动问题,首先基于经典梁理论,利用变分原理建立该问题的动力学控制微分方程,其中材料的物性参数基于Halpin-Tsai和混合律模型进行描述;然后,采用分离变量法对控制方程进行精确解析求解,计算得到3种不同边界约束梁在弹性地基上振动的无量纲固有频率;同时,将计算结果退化到无地基的情况,并与文献已有结果进行对比,证明理论推导和数值结果的正确性;最后,通过分析数值结果讨论地基刚度系数、石墨烯含量和几何参数等对FG-GRC梁固有频率的影响.结果表明:虽然弹性地基对梁基频的影响较明显,但随阶数的增加影响减弱;另外,石墨烯片几何形状的变化对固有频率同样具有显著影响.

关键词: 石墨烯增强, 弹性地基, 功能梯度梁, 振动

Abstract: The vibration of a graphene platelets reinforced functionally graded composite (FG-GRC) beam placed on an elastic foundation is studied. Firstly, the dynamic governing differential equations of the problem are established by applying the variational principle based on the classical beam theory, in which the material properties of the composites are described according to the mechanical models of Halpin-Tsai and the rule of mixture. Then, the governing equations are solved analytically by the method of separated variables, yielding the dimensionless natural frequencies of the beam with three kinds of boundary constraints on the elastic foundation. Furthermore, the results are compared with the existing ones in the literatures by reduced to no foundation, which proves correctness of the theoretical derivations and numerical calculations. Finally, effects of foundation stiffness, graphene content and geometric parameters on the natural frequencies of the FG-GRC beam are discussed by analyzing of the numerical results. It is found that the influence of the elastic foundation on the fundamental frequencies is obvious, with the influence diminishing as the mode order increases. In addition, the variations of the geometric shapes of graphene platelets have great influences on the natural frequencies.

Key words: graphene reinforced, functionally graded beam, free vibration, elastic foundation

中图分类号:

TH113.1
O343

张靖华, 姚玉琴. 弹性地基上FG-GRC梁的振动[J]. 兰州理工大学学报, 2025, 51(2): 38-43.

ZHANG Jing-hua, YAO Yu-qin. Vibration of FG-GRC beam on elastic foundation[J]. Journal of Lanzhou University of Technology, 2025, 51(2): 38-43.

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