磁偶分布下基尔霍夫棒的平衡
Equilibrium of Kirchhoff's rods subject to a distribution of magnetic couples
摘要：
研究了均匀磁场中磁弹性杆的平衡问题。导出的非线性平衡方程与基尔霍夫理论在同一数量级上是完全一致的。这些方程的Weierstrass椭圆函数的精确解的参考磁弹性悬臂梁进行平面变形的终端力和磁场的作用下，其方向是平行的或正交的。精确解被应用于杆的远程控制变形问题的研究和分支问题，其中端部力和磁场分别作为缺陷参数和分支参数。
英文摘要：
The equilibrium of magneto-elastic rods, formed of an elastic matrix containing a uniform distribution of paramagnetic particles, that are subject to terminal loads and are immersed in a uniform magnetic field, is studied. The deduced nonlinear equilibrium equations are fully consistent with Kirchhoff's theory in the sense that they hold at the same order of magnitude. Exact solutions of those equations in terms of Weierstrass elliptic functions are presented with reference to magneto-elastic cantilevers that undergo planar deformations under the action of a terminal force and a magnetic field whose directions are either parallel or orthogonal. The exact solutions are applied to the study of a problem of remotely controlled deformation of a rod and to a bifurcation problem in which the end force and the magnetic field act as an imperfection parameter and a bifurcation parameter, respectively.
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