温度场作用下输流悬臂碳纳米管的颤振失稳分析

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输流悬臂单层碳纳米管（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。

Analysis of flutter instability of cantilever carbon nanotubes conveying fluid

Fluid-conveying carbon nanotubes (CNTs) have attracted much attention and they are used in nano-electromechanical systems (NEMS) and biomedical applications. In this work 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, taking into account the flow-induced inertia, Coriolis and centrifugal forces along the nanotube, an elastic nonlocal Bernoulli-Euler beam model is developed for thermal-mechanical vibration and instability of a cantilever single-walled carbon nanotube (SWCNT) conveying fluid. The governing partial differential equations of motion and 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 system. 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 dynamical behaviors of the CNT system. It can be concluded that the temperature change can shift the unstable mode in which flutter instability occurs first at sufficiently high flow velocity from one to another. Furthermore, detailed results are demonstrated that at low or room temperature, for the SWCNT, the critical flutter flow velocity increases as the temperature change increases, on the other hand, while at high temperature the critical flow velocity decrease as the temperature change increases. Thus, the results of the present study may facilitate further analyses of nonlocal vibration, and thus the design of nanotubes in the presence of a temperature field. Our results maybe beneficial for the fabrication of smart nanostructures that can be employed to transport fluidic drug to diseased areas, where a low temperature field may help the fluid to flow in a suitable stream.