磁敏固支载流单壁碳纳米管在轴向磁场中的振动特性

Vibration characteristics of magnetically sensitive clamped-clamped carbon nanotubes conveying fI uid subjected to a longitudinal magnetic field

以非局部弹性理论为基础,采用欧拉-伯努利梁模型,考虑了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轴向磁场中磁敏载流单壁碳纳米管(SWCNT)的振动控制方程以及边界条件;依靠微分变换法(DTM)对此高阶偏微分方程进行求解,通过数值计算研究了单壁固支载流碳纳米管的振动与失稳问题。结果表明:轴向磁场强度H_x、克努森数K_n、小尺度参数m都会对系统振动频率以及系统稳定区域产生影响,其中K_n及m越大,系统基频越低,稳定区域越小;而当外加轴向磁场强度达到一定数值后,磁场作用将使系统的稳定性明显加强。

Based on the nonlocal elastic theory, a nonlocal Euler-Bernoulli beam model is utilized to investigate the effect of a longitudinal magnetic field on the transverse vibration of magnetically sensitive clamped-clamped carbon nanotubes(SWCNTs) with conveying fluid. The slip boundary conditions of CNT conveying fluid are considered based on Knudsen number(K_n). The equation of motion and associated boundary conditions are derived by using Hamilton's principle. In the solution part the differential transformation method(DTM) is used to solve the higher-order differential equations of motion. The effects of longitudinal magnetic field, nonlocal parameter and Knudsen number on the vibration frequency and divergence instability of SWCNT conveying fluid are investigated. Numerical results from the model show that the fundamental natural frequency and stability region of the SWCNT are affected by the small scale effect, Knudsen number and longitudinal magnetic field. It is found that with increase in the small scale effect and Knudsen number the fundamental natural frequency and stability become less pronounced, but the good stability are observed when the longitudinal magnetic field increased to a certain degree.