超音速FG石墨烯片增强梁的非线性静动态特性  

Nonlinear static and dynamic characteristics of functionally graded graphene platelets reinforced beam in supersonic flow

作　　者：张浩晨 韩明君[1] 冯瑞龙 ZHANG Haochen;HAN Mingjun;FENG Ruilong(School of Science,Lanzhou University of Technology,Lanzhou Gansu 730050)

机构地区：[1]兰州理工大学理学院,甘肃兰州730050

出　　处：《首都师范大学学报(自然科学版)》2025年第2期43-51,共9页Journal of Capital Normal University:Natural Science Edition

基　　金：国家自然科学基金项目(12062010)。

摘　　要：为研究功能梯度石墨烯片增强复合材料(FG-GPLRC)梁在气动载荷和温度共同作用下的非线性静动态特性问题,基于经典梁理论和一阶活塞理论建立超音速流中功能梯度石墨烯片增强梁的非线性振动模型。考虑石墨烯片沿厚度方向呈现3种不同梯度分布(U-GPLRC、O-GPLRC和XGPLRC),由哈密顿原理推导出FG-GPLRC增强梁气动弹性控制微分方程,利用Galerkin法,将其转化为非线性常微分方程,利用Routh-Hurwitz系统稳定性判据,将Hopf分岔化为非线性方程求根问题。通过参数研究,分析温度、石墨烯片质量分数、分布模式对FG-GPLRC增强梁气动弹性的稳定性影响,求解得出无量纲临界流速、临界频率和临界动压,最后通过数值计算进行FG-GPLRC增强梁气动弹性稳定性验证。结果表明:石墨烯片质量分数越大,增强效果越明显,X-GPLRC分布模式增强效果最佳。研究结果将为FG-GPLRC梁的设计优化提供理论参考依据。To investigate the nonlinear static and dynamic characteristics of functionally graded graphene platelets reinforced composite beam(FG-GPLRC)under the combined action of aerodynamic load and temperature.A nonlinear vibration model of functionally graded graphene platelets(GPL)reinforced beam in supersonic flow is established based on the classical beam theory and first-order piston theory.Firstly,considering that GPL presents three different gradient distributions(U-GPLRC,OGPLRC and X-GPLRC)along the thickness direction,deriving the functional gradient graphene platelets reinforced beam aeroelastic control differential equation by applying Hamilton’s principle.Secondly,using the Galliukin method,it is transformed into a nonlinear ordinary differential equation,and then the determination of the Hopf bifurcation is transformed into the root of the nonlinear equation using the stability criterion of the Routh-Hurwitz system.The effects of temperature,GPL mass fraction and distribution pattern on the stability of FG-GPLRC beam aeroelasticity were analyzed by parametric study.The solution yields dimensionless critical flow velocity,dimensionless critical frequency,and dimensionless dynamic pressure.Finally,the aeroelastic stability of the FG-GPLRC beam was verified by numerical calculations.the results show that the higher the mass fraction of gpl,the more significant the enhancement effect,and the x-gplrc distribution pattern has the best enhancement effect.the research results will provide theoretical reference for the design optimization of fg-gplrc beam.

关 键 词：石墨烯片 功能梯度 梁 气动弹性 

分 类 号：O351[理学—流体力学]