Stability and nonplanar buckling analysis of a current-carrying mircowire in three-dimensional magnetic field
Stability and nonplanar buckling analysis of a current-carrying mircowire in three-dimensional magnetic field
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三维磁场中载流微线的稳定性和非平面屈曲分析
DOI：
10.1007/s00542-019-04330-5
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发表时间：
2019
期刊：
影响因子：
--
通讯作者：
Wang Lin
中科院分区：
文献类型：
--
作者：
Hong Yuanzhuo;Wang Lin
基于修正耦合应力理论和欧拉-伯努利梁假设，研究了载流微导线在三维磁场中的稳定性和非平面屈曲问题。利用哈密顿原理，推导了载流微导线三维振动的偏微分控制方程。然后通过伽辽金方法对这些控制方程进行离散，并用四阶龙格-库塔法求解。数值结果表明，长细比和磁场对微丝的稳定性有明显影响。当外加磁场沿未变形微丝的轴向方向作用时，微丝屈曲后结构的形状对所采用的初始条件非常敏感。然而，如果磁场偏离未变形微丝的轴向，有趣的是，即使三维磁场强度的-和/或z分量足够小，屈曲后构型的形状也与初始条件无关。该结果的另一个吸引人的特点是，通过改变每个方向的磁场强度可以调节微线的横向偏转，这可能在微机电系统（MEMS）中具有潜在的应用前景。最后，分析了三维磁场对微丝轴向位移的影响，表明在实际应用中，微丝的轴向运动可以忽略不计。
This paper investigates the stability and nonplanar buckling of a current-carrying microwire immersed in a three-dimensional (3D) magnetic field based on modified coupled stress theory and Euler–Bernoulli beam assumptions. Utilizing Hamilton’s principle, the partial differential governing equations for 3D vibrations of the current-carrying microwire are derived. These governing equations are then discretized via the Galerkin’s approach and solved by a fourth-order Runge–Kutta method. Numerical results show that the slenderness ratio and magnetic field have obvious effect on the stability of the microwire. When the applied magnetic field is along the axial direction of the undeformed microwire, the shape of the postbuckling configuration of the microwire is very sensitive to initial conditions employed. If, however, the magnetic field is deviated from the axial direction of the undeformed microwire, it is interesting that the shape of the postbuckling configuration is independent of initial conditions even if they- and/orz-component of the 3D magnetic field strength is sufficiently small. Another attractive feature of the results is that the lateral deflection of the microwire can be adjusted by changing the magnetic field strength in each direction, which may have potential application to the microelectromechanical systems (MEMS). Finally, the influence of a 3D magnetic field on the axial displacement of the microwire is analyzed, and it is demonstrated that in practice the axial motion of the microwire may be considered negligible.