纵向磁场中载流单层碳纳米管的振动与失稳  

Vibration and instability of single-walled carbon nanotubes conveying fluid in a longitudinal magnetic field

作　　者：李明[1] 周攀峰[1] 郑华升[1] Li Ming Zhou Panfeng Zheng Huasheng(Hubei Province Key Laboratory of Systems Science in Metallurgical Process, Wuhan University of Science and Technology, Wuhan 430065, Chin)

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,湖北武汉430065

出　　处：《武汉科技大学学报》2017年第1期27-31,共5页Journal of Wuhan University of Science and Technology

基　　金：国家自然科学基金资助项目(51608401);武汉科技大学冶金工业过程系统科学湖北省重点实验室开放基金资助项目(Y201520)

摘　　要：以非局部弹性理论为基础,采用Euler-Bernoulli梁模型,并考虑纳米管管形区域内滑移边界条件以及小尺度效应,研究了纵向磁场中单层载流碳纳米管的振动与失稳问题。根据哈密顿原理获得碳纳米管的横向振动方程和边界条件。应用微分变换法(DTM)对此高阶偏微分方程进行求解,通过数值计算分析磁场强度、小尺度参数和Knudsen数对单层载流碳纳米管振动频率和稳定性的影响。结果表明,小尺度参数和Knudsen数越大,系统基频及临界流速就越低,系统的稳定区域也越小;纵向磁场强度增加到一定程度后,磁场作用将明显提高系统的基频及临界流速,也即增大了系统的稳定区域。On the basis of nonlocal elastic theory and with the slip boundary conditions and small scale effect of nanotubes considered, this paper uses Euler-Bernoulli beam model to investigate the vibration and instability of a simply-supported single-walled carbon nanotube （SWCNT） conveying fluid in a longitudinal magnetic field. Transverse vibration equation and its boundary conditions of the SWCNT are derived according to Hamilton＇s principle. Differential transformation method （DTM） is adopted to solve this high-order partial differential equation. Effects of magnetic field intensity, small scale parameter and Knudsen number on vibration frequency and stability of fluid-conveying SWCNT are analyzed by numerical calculation. The results show that with the increase of small scale parameter and Knudsen number, the fundamental frequency and critical flow velocity of the SWCNT decrease and the system＇s stable region is reduced~ when its intensity increases to a certain degree, the longi- tudinal magnetic field can obviously raise the fundamental frequency and critical flow velocity, i.e. enlarge the system＇s stable region.

关 键 词：碳纳米管 纵向磁场 载流 微分变换法 振动 失稳 临界流速 

分 类 号：O353.1[理学—流体力学]