王宇, 徐自强, 李昊,等.功能梯度石墨烯增强自旋圆柱壳的振动特性[J].河南理工大学学报（自然科学版）,2024,43(3):192-200.

WANG Y, XU Z Q , LI H ,et al.Vibration performance of the rotating FG-GPLRC cylindrical shell[J].Journal of Henan Polytechnic University(Natural Science) ,2024,43(3):192-200.

功能梯度石墨烯增强自旋圆柱壳的振动特性

王宇, 徐自强, 李昊, 王鹏, 徐宏达, 张颖

辽宁科技大学 机械工程与自动化学院，辽宁 鞍山 114051

摘要:  目的 为了研究旋转状态下功能梯度石墨烯增强复合材料（FG-GPLRC）圆柱壳的振动特性， 方法   基于改进的Halpin-Tsai微观力学模型与复合材料夹杂理论预测多种分布模式下石墨烯增强结构的等效材料属性。同时，考虑由旋转引起的科氏力与离心力作用，采用一阶剪切变形理论对FG-GPLRC自旋圆柱壳的能量表达式进行推导。之后，选取切比雪夫多项式构造位移容许函数，基于Rayleigh-Ritz法对FG-GPLRC自旋圆柱壳的行波振动特性进行分析，得到壳体的动力学微分方程进而求解出行波振动频率。最后，通过与现有文献数据进行对比，验证本文方法的准确性，并分析石墨烯片的转速、分层数、质量分数与分布模式等因素对旋转壳体振动特性的影响。 结果   石墨烯片分层数为10层时，即可实现对FG-GPLRC自旋圆柱壳振动特性的预测；石墨烯质量分数小于2%时，每增加0.5%，壳体的前后行波频率明显提高；在不同模态下，GPL-X分布模式的壳体行波频率最高，GPL-O分布模式最低，且行波频率随转速的提高而增大；弹性边界条件下，壳体行波振动频率随轴向半波数的增大而增加。 结论   石墨烯片在GPL-X分布模式下使得FG-GPLRC自旋圆柱壳的等效弹性模量增大，对壳体结构刚度的增强效果最佳，且前后行波频率与壳体转速同步增大。

关键词:石墨烯增强材料;Rayleigh-Ritz法;自旋圆柱壳;Halpin-Tasi微观力学模型;弹性边界

doi:10.16186/j.cnki.1673-9787.2023030066

基金项目:国家自然科学基金资助项目（51775257）；辽宁省高校科研基金资助项目（LJKMZ20220637）

收稿日期:2023/03/27

修回日期:2023/08/10

出版日期:2024/05/15

Vibration performance of the rotating FG-GPLRC cylindrical shell

WANG Yu, XU Ziqiang, LI Hao, WANG Peng, XU Hongda, ZHANG Ying

School of Mechanical Engineering & Automation， University of Science and Technology Liaoning， Anshan 114051， Liaoning，  China

Abstract:  Objectives To investigate the vibration characteristics of functionally graded graphene platelets reinforced composite （FG-GPLRC） rotating cylindrical shell， Methods   the equivalent material properties of graphene-reinforced structures in various distribution modes are predicted using the improved Halpin-Tsai micromechanical model and composite intercalation theory. Meanwhile， the energy expressions for the FG-GPLRC rotating cylindrical shell are derived through the first-order shear deformation theory with the consideration of Coriolis and centrifugal forces caused by the rotation. Furthermore， Chebyshev polynomials are selected to construct the displacement admissible functions， while the traveling wave vibration characteristics of FG-GPLRC shell are analyzed based on the Rayleigh-Ritz method to solve the dynamical differential equations of the shell and then to obtain frequencies. Eventually， the accuracy of the method in this paper is verified by comparing with the existing literature data， and the effects of rotating speed， layers， mass fraction， and distribution modes of graphene platelets on the vibration characteristics of rotating shells are analyzed.    Results  The prediction of vibration characteristics for the FG-GPLRC rotating cylindrical shell can be achieved with 10 layers of graphene platelets. For each 0.5% increase in graphene mass fraction less than 2%， both the forward and backward traveling wave frequencies of the shell were increased significantly. In different modes， the shell traveling wave frequencies were highest in the GPL-X distribution pattern and lowest in the GPL-O distribution pattern， and the traveling wave frequencies increased with the increase of rotating speed. The traveling wave frequencies also increased with the axial half wave number under elastic boundary conditions.   Conclusions   Graphene platelets in the GPL-X distribution pattern led to an increase in the equivalent modulus of elasticity of the FG-GPLRC rotating cylindrical shell， which had the best reinforcement effect on the structural stiffness of the shell， and the forward and backward traveling wave frequencies increased in parallel with the rotating speed of the shell.

Key words:graphene-reinforced material;Rayleigh-Ritz method;rotating cylindrical shell;Halpin-Tsai micromechanical model;elastic boundary