磁场对不同温度场中输流悬臂碳纳米管颤振稳定性的影响  

Magnetic Field Effect on Flutter Stability of a Fluid-conveying Cantilevered Carbon Nanotube under Different Temperature Fields

作　　者：李明[1] 吕刘飞 郑华升[1] 方康 Ming Li;Liufei Lv;Huasheng Zheng;Kang Fang(Hubei Province Key Laboratory of Systems Science in Metallurgical Process,Wuhan University of Science and Technology,Wuhan,430081)

机构地区：[1]武汉科技大学冶金工业过程系统科学湖北省重点实验室,武汉430081

出　　处：《固体力学学报》2021年第1期87-93,共7页Chinese Journal of Solid Mechanics

基　　金：国家自然科学基金青年基金项目(51608401);湖北省自然科学基金项目(2015CFB205);冶金工业过程系统科学湖北省重点实验室(武汉科技大学)开放基金项目(Y201520)资助。

摘　　要：论文在采用经典欧拉-伯努利梁模型的基础上,引入考虑小尺度效应的非局部弹性理论,着重研究不同温度场中输流悬臂单层碳纳米管系统(SWCNT)在外加纵向磁场作用下的颤振失稳问题.基于哈密顿原理获得了该流固耦合系统的振动控制方程及相应的边界条件,应用微分变换法(DTM法)求解此高阶偏微分方程,通过数值计算研究了不同温度场中施加纵向磁场对系统动力学特性的影响.结果表明:纵向磁场在不同温度场中都将增强输流悬臂碳纳米管的动态稳定性.然而,这种增强程度却与温度场的变化量有关,在不同温度变化量下,磁场的逐渐增强对系统稳定性的增强程度有一个峰值,这意味着,实际应用中,为了提高这类流固耦合系统的动态稳定性,一味提高纵向磁场强度并不可取.CNT(Carbon nanotube)-based fluidic systems hold a great potential for emerging medical applications and nano-electromechanical systems(NEMS).One of the critical issues in designing such fluid structure interaction(FSI)systems is how to avoid the vibration induced by the fluid flow,which is undesirable and may even promote the dynamic structural instability.The main objective of the present research is to investigate the flutter instability of a cantilevered single-walled carbon nanotube(SWCNT)induced by fluid flow under a longitudinal magnetic field and different temperature fields.To obtain a dynamical model for the system,the CNTs are modeled as nonlocal Euler-Bernoulli beams.The governing partial differential equations of the transverse vibration and associated boundary conditions are derived by Hamilton’s principle.Then,the differential transformation method(DTM)is applied to solve the governing equations of the FSI systems,and some numerical examples are presented to investigate the effects of nonlocal parameters,temperature and longitudinal magnetic field on the critical flow velocity at which flutter may occur.Numerical results show that the nonlocal small-scale parameter makes the fluid-conveying CNT more flexible,and the addition of a temperature field leads to much richer dynamic behaviors of the CNT system.The above analytical results obtained are found to be in good agreement with those presented in the literature.More importantly,it can be concluded that no matter what the temperature field is,the critical flutter velocity will be improved significantly by applying a longitudinal magnetic field,although there exists an upper limit for this enhancement,which is dependent on temperature variation.The numerical results demonstrate that to improve the dynamic stability of the nanoscale FSI systems,it is not reasonable to just increase the intensity of the axial magnetic field.Thus,the results of the present study may facilitate further analysis of nonlocal vibration,and the design of nanotubes in the p

关 键 词：纵向磁场 温度场 输流悬臂碳纳米管 动力学特性 颤振失稳临界流速 

分 类 号：TB383.1[一般工业技术—材料科学与工程] TQ127.11[化学工程—无机化工]