磁场对不同温度场中输流悬臂碳纳米管动态特性的影响

本文在采用经典欧拉-伯努利梁模型的基础上，引入考虑小尺度效应的非局部弹性理论，着重研究不同温度场中输流悬臂单层碳纳米管系统（SWCNT）在外加纵向磁场作用下的颤振失稳问题。基于哈密顿原理获得了该流固耦合系统的振动控制方程及相应的边界条件，应用微分变换法（DTM法）求解此高阶偏微分方程，通过数值计算研究了不同温度场中施加纵向磁场对系统动力学特性的影响。结果表明：施加纵向磁场在不同温度场中都将增强输流悬臂碳纳米管的动态稳定性。然而，这种增强程度却与温度场的变化量有关，在不同温度变化量下，磁场对系统稳定性的增强程度有一个峰值，这意味着，实际应用中，为了提高这类流固耦合系统的动态稳定性，一味提高纵向磁场强度并不可取。

Magnetic Field Effect on Flutter Stability of a Fluid-conveying Cantilevered Carbon Nanotube under Different Temperature Fields

CNT (Carbon nanotube)-based fluidic systems hold a great potential for emerging medical applications and nano-electromechanical systems (NEMS). One of the critical issues in designing such fluid structure interaction (FSI) systems is how to avoid the vibration induced by the fluid flow, which is undesirable and may even promote the dynamic structural instability. The main objective of the present research is to investigate the flutter instability of a cantilevered single-walled carbon nanotube (SWCNT) induced by fluid flow under a longitudinal magnetic field and different temperature fields. To obtain a dynamical model for the system, the CNTs are modeled as nonlocal Euler–Bernoulli beams. The governing partial differential equations of the transverse vibration and associated boundary conditions are derived by Hamilton’s principle. Then, the differential transformation method (DTM) is applied to solve the governing equations of the FSI systems, and some numerical examples are presented to investigate the effects of nonlocal parameters, temperature and longitudinal magnetic field on the critical flow velocity at which flutter may occur. Numerical results show that the nonlocal small-scale parameter makes the fluid-conveying CNT more flexible, and the addition of a temperature field leads to much richer dynamic behaviors of the CNT system. The above analytical results obtained are found to be in good agreement with those presented in the literature. More importantly, it can be concluded that no matter what the temperature field is, the critical flutter velocity will be improved significantly by applying a longitudinal magnetic field, although there exists an upper limit for this enhancement, which is dependent on temperature variation. The numerical results demonstrate that to improve the dynamic stability of the nanoscale FSI systems, it is not reasonable to just increase the intensity of the axial magnetic field. Thus, the results of the present study may facilitate further analysis of nonlocal vibration, and the design of nanotubes in the presence of multi-physics fields.