温度场作用下悬臂输流碳纳米管的颤振失稳分析  

Analysis of Flutter Instability of Cantilever Carbon Nanotubes Conveying Fluid in a Temperature Field

作　　者：李明[1] 方康 郑华升 Ming Li;Kang Fang;Huasheng Zheng(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

出　　处：《固体力学学报》2018年第6期634-641,共8页Chinese Journal of Solid Mechanics

基　　金：国家自然科学基金项目(51608401);湖北省自然科学基金项目(2016CFB265);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：以非局部弹性理论为基础,采用欧拉-伯努利梁模型,考虑碳纳米管的小尺度效应,应用哈密顿原理获得了温度场作用下的悬臂输流单层碳纳米管(SWCNT)的振动控制方程以及边界条件,依靠微分变换法(DTM法)对此高阶偏微分方程进行求解,通过数值计算研究了温度场中悬臂单层输流碳纳米管的振动与颤振失稳问题.结果表明:管内流体流速、温度场中温度变化情况与小尺度参数都会对系统振动频率以及颤振失稳临界流速产生影响.其中,小尺度效应将会降低悬臂输流系统的稳定性,使系统更为柔软;而高温场与低温场对系统动态失稳的影响不同,低温场中随温度变化值的增加,系统的稳定性提高;高温场这一作用效果恰好与之相反.Fluid-conveying carbon nanotubes(CNTs)have attracted much attention and are used in nano-electromechanical systems(NEMS)and biomedical applications.In this work,the differential transform method(DTM)is used to study the vibration behavior of fluid-conveying single-walled carbon nanotube(SWCNT).Based on the theories of elasticity mechanics and nonlocal elasticity,by taking into account the flow-induced inertia and the Coriolis and centrifugal forces along the nanotube,an elastic nonlocal Bernoulli-Euler beam model is developed for the thermal-mechanical vibration and instability of a cantilever SWCNT conveying fluid.The governing partial differential equations of motion and the associated boundary conditions are derived by Hamilton’s principle.The resulting eigenvalue problem is then solved,and some numerical examples are presented to investigate the effects of fluid velocity,nonlocal parameter and temperature change on the critical flow velocities and flutter instability of the system.The numerical results show that the nonlocal small-scale parameter makes the fluid-conveying CNT more flexible.More importantly,the addition of a temperature field leads to much richer dynamic behaviors of the CNT system.It can be concluded that the temperature change can shift the unstable mode,in which flutter instability first occurs at a sufficiently high flow velocity,from one to another.Furthermore,detailed results demonstrate that at low or room temperature,for the SWCNT,the critical flutter flow velocity increases as the temperature change increases;while at high temperature,the critical flow velocity decreases as the temperature change increases.Thus,the results of the present study may facilitate further analysis of nonlocal vibration,and thus the design of nanotubes in the presence of a temperature field.Our research can be beneficial to the fabrication of smart nanostructures which can be employed to transport fluidic drug to disease areas,where a low temperature field may help the fluid flow in a suitable stream.

关 键 词：温度场 悬臂输流碳纳米管 振动 颤振失稳临界流速 非局部弹性理论 

分 类 号：O613.71[理学—无机化学] TB383.1[理学—化学]