四边简支功能梯度石墨烯增强复合材料厚板的自由振动分析

兰州理工大学学报 ›› 2023, Vol. 49 ›› Issue (4): 166-172.

• 数理科学 • 上一篇

四边简支功能梯度石墨烯增强复合材料厚板的自由振动分析

雷芳明^*

兰州理工大学理学院, 甘肃兰州 730050

收稿日期:2022-10-02 出版日期:2023-08-28 发布日期:2023-08-29
通讯作者: 雷芳明(1985-),男,甘肃天水人,讲师. Email:leifm@lut.edu.cn
基金资助:
国家自然科学基金(12062010,11862012)

Free vibration analysis of functionally graded grapheme-reinforced composite thick plates with simply supported on four sides

LEI Fang-ming

School of Science, Lanzhou Univ. of Tech., Lanzhou 730050, China

Received:2022-10-02 Online:2023-08-28 Published:2023-08-29

摘要/Abstract

摘要： 基于准三维板理论,研究了四边简支功能梯度石墨烯增强复合材料(FG-GRC)厚板的自由振动行为.通过改进的Halpin-Tsai模型计算了不同分布模式下FG-GRC厚板的有效性能,利用Hamilton原理构建其控制方程,并根据Navier法求解.通过参数研究部分揭示了石墨烯纳米片(GPLs)的重量分数、FG-GRC板的总层数、GPLs分布模式、宽厚比以及长宽比对四边简支FG-GRC厚板自由振动固有频率的影响.由于准三维板理论考虑了厚度拉伸效应,因此在厚板计算中比经典板理论、一阶板理论和Reddy三阶板理论更为精确.

关键词: 功能梯度石墨烯增强复合材料, 厚板, 准三维板理论, Navier法, 自由振动

Abstract: The vibration characteristic of four-edge simply supported functionally graded graphene reinforced thick plates is investigated by using the quasi-3D plate theory. The main properties of FG-GRC thick plates are calculated for different distributions within the improved Halpin-Tsai model. The governing equations are proposed according to the Hamilton’s principle, and the solutions were obtained by using the Navier’s method. Some parameters are adjusted to clarify the effects of the weight fraction of graphene nanosheets (GPLs), the total number of layers of FG-GRC plate, the distribution pattern of GPLs, and the aspect ratio on the natural frequency of free vibration. The quasi-3D plate theory takes into account the effect of thickness stretching, therefore, it is more accurate than the classical plate theory, first-order plate theory, and Reddy third-order plate theory in the calculation of thick plate.

Key words: functionally graded graphene reinforced composite, thick plate, quasi-3D plate theory, Navier’s method, free vibration

中图分类号:

O343
TB34

雷芳明. 四边简支功能梯度石墨烯增强复合材料厚板的自由振动分析[J]. 兰州理工大学学报, 2023, 49(4): 166-172.

LEI Fang-ming. Free vibration analysis of functionally graded grapheme-reinforced composite thick plates with simply supported on four sides[J]. Journal of Lanzhou University of Technology, 2023, 49(4): 166-172.

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四边简支功能梯度石墨烯增强复合材料厚板的自由振动分析

Free vibration analysis of functionally graded grapheme-reinforced composite thick plates with simply supported on four sides

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