多场作用下输流单层碳纳米管的动力学特性  

Dynamic Characteristics of Carbon Nanotubes Conveying FIuid in Multi-physics Fields

作　　者：李明[1] 周攀峰[1] 郑慧明[2] Ming Li Panfeng Zhou Huiming Zheng(Hubei Province Key Laboratory of Systems Science in Metallurgical Process, Wuhan University of Science and Technology, Wuhan , 430081 Department of Mechanics, Huazhong University of Science and Technology, Wuhan , 430074)

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 [2]华中科技大学土木与力学学院力学系,武汉430074

出　　处：《固体力学学报》2017年第5期426-432,共7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(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：以非局部弹性理论为基础,采用欧拉-伯努利梁模型,考虑管型区域内滑移边界条件以及碳纳米管的小尺度效应,应用哈密顿原理获得了温度场与轴向磁场共同作用下的输流单层固支碳纳米管(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多场中单层固支输流碳纳米管的振动与失稳问题.结果表明:温度场、轴向磁场强度、Knudsen数及小尺度参数都会对系统振动频率以及失稳临界流速产生影响.Fluid-conveying carbon nanotubes（CNTs）have attracted much attention and are used in nano-electromechanical systems（NEMS）and biomedical applications.The free vibration and instability characteristics of single-walled carbon nanotubes（SWCNTs）conveying fluid in magnetic and temperature fields are studied in this paper based upon the nonlocal elastic theory.The SWCNTs are modeled as EulerBernoulli beams.The Knudsen number（Kn）is considered the slip boundary conditions between the flow and wall of nanotube,and the average velocity correction parameter is used to obtain the modified flow velocity of nanoflow.The governing partial differential equations of motion and associated boundary conditions are derived by Hamilton＇s principle.The differential transformation method（DTM）is also employed to solve the governing equations under the clamped-clamped end conditions.Then,some numerical examples are presented to investigate the effects of fluid velocity,length scale parameters,Knudsen number,temperature difference and longitudinal magnetic field on the natural frequencies,critical flow velocities and instability of system.It can be concluded that at low or room temperature,the fundamental natural frequency and critical flow velocity for the SWCNT increase as the temperature change increaseswhile at high temperature the fundamental natural frequency and critical flow velocity decrease as the temperature change increases.Both the fundamental natural frequency and critical flow velocity decrease as the nonlocal parameter and the Knudsen number increase.In addition,the stability of the proposed system will be improved significantly by applying a longitudinal magnetic field.Thus,the results of the present study may facilitate further analyses of nonlocal vibration and the design of nanotubes in the presence of a longitudinal magnetic field.Our results be beneficial the fabrication of smart nanostructures employed fluidic drug to diseased areas,where a longitudinal magnetic field may help the fluid to flow i

关 键 词：轴向磁场 温度场 输流碳纳米管 振动 失稳临界流速 

分 类 号：TB383.1[一般工业技术—材料科学与工程]