载电流夹紧杆的非线性稳定性分析<sup>*</sup>

程昌钧; 杨骁

载电流夹紧杆的非线性稳定性分析^*

程昌钧^1,2,
杨骁²

1.
上海大学, 上海市应用数学和力学研究所, 上海 200072;
2.
兰州大学力学系, 兰州 730000

基金项目: * 国家教委博士点基金;甘肃省自然科学基金

计量
- 文章访问数: 2171
- HTML全文浏览量: 102
- PDF下载量: 526
- 被引次数: 0
出版历程
- 收稿日期: 1996-03-08
- 刊出日期: 1997-09-15

Nonlinear Stability Analysis of a Clamped Rod Carrying Electric Current

Cheng Changiun^1,2,
Yang Xiao²

1.
Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, P. R. China;
2.
Department of Mechanics, Lanzhou University, Lanzhou 730000, P. R. China

摘要

摘要: 本文研究了载电流夹紧杆在磁场作用下的非线性稳定性,其磁场由两根无限长相互平行的刚性直导线产生.杆的自然状态在刚性导线所在的平面内,并且与两刚性导线等距.首先,在空间变形的假定下,给出了问题的数学描述,讨论了线性化问题和临界电流.其次,证明了杆的过屈曲状态总是平面的.最后,数值计算了分支解的全局响应,得到了杆过屈曲状态的挠度、内力和弯矩的分布.结果表明,载电流杆既可发生超临界屈曲,又可发生次临屈界曲,其性态依赖于杆与导线间的距离;同时,在超临界的过屈曲状态上还存在极限点型的失稳,这与通常的压杆失稳有着本质的区别.
- 磁弹性 /
- 分支 /
- 极限点 /
- 载电流直杆 /
- 数值方法
Abstract: This paper is devoted to the analysis of the nonlinear Stability of a clamped rodcarrying electric current in the magnetic field which is produced by the current frowingin a pair of inifinitely long parallel rigid wires. The natural State of the rod is in theplane of the wires and is equidistant from them.Firstly under the assumption of apatial deformation, the governing equations of the problem are derived, and the linearizedproblem and critical currents are discussed. Secondly, it ls proved that the buckledstates of the rod are always in planes. Finally. the global responses of the bifurcationproblem of the rod are compuled numerically and the distributions of the deflections.axial forces and bending monents are obtained. The results show that the buckledslates of the rod may be either supercritical or Subcritical. depending on the distancebetween the rod and the wires. Furthermore, it is found that-there exists a limit pointon the branch solution of the supercritical buckled State. This is distinctively differentfrom the buckled slate of the elastic compressive rods.
- magnetoelasticity /
- bifurcation /
- limit point /
- numerical method /
- straight rod carrying electric current

HTML全文

参考文献(10)

[1]	H.H.Woodson and J.R.Melcher,Electromechanical Dynamics.John Wiley and Sons.New York(1968).
[2]	P.Wolfe.Equilibrum states of an elastic conductor in a magnetic field:a paradigm ofbifurcation,Trans.Amer.Math.Soc.,278(1983),377～387.
[3]	P.Wolfe.Bifurcation theory of an elastic conducting wires subjected magnetic forces,J.Elasticity,,23,2～3(1990),201～217.
[4]	T.J.Healey,Large rotating states of a conducting elastic wire in a magnetic field:subtlesymmetry and multiparameter bifurcation.J.of Elasticity,24(1990),211～227.
[5]	T.I.Seidman and P.Wolfe,Equilibrium states of an elastic conducting rod in amagnetic field.Arch.Ralional Mech.Anal.,102,4(1988),3O7～329.
[6]	P.Wolfe,Bifurcation theory of an elastic conducting rod in a magnetic field,QuartMech.APPl.Math.41,2(1988),265～279.
[7]	P.Wolfe,Bifurcation theory of a conducting rod subjected to magnetic forces,Int.JNonlinear Mechanics,25,5(1990),597～604.
[8]	S.S.Antman.Ordinary differential equations of one dimensional nonlinear e1asticity.Arch.Rational Mech.Anal.61(1976),3O7～393.
[9]	E.Bujano,G.Geymoat and T.Poston,Post-buckling behavionar of nonlinearyhyperelastic thin rod with cross-section invariant under the dihedral group Dn.,Arch.Rational thech.Anal,.89(1985),307～388.
[10]	朱正佑、程昌钧,《分支问题的数值计算方法》,兰州大学出版社,兰州(1989).