Nonlinear Stability Analysis of a Clamped Rod Carrying Electric Current

Cheng Changiun; Yang Xiao

Article Contents

Article Navigation > Applied Mathematics and Mechanics > 1997 > 18(9): 769-777

Cheng Changiun, Yang Xiao. Nonlinear Stability Analysis of a Clamped Rod Carrying Electric Current[J]. Applied Mathematics and Mechanics, 1997, 18(9): 769-777.

Citation:

Cheng Changiun, Yang Xiao. Nonlinear Stability Analysis of a Clamped Rod Carrying Electric Current[J]. Applied Mathematics and Mechanics, 1997, 18(9): 769-777.

Citation:

Cheng Changiun, Yang Xiao. Nonlinear Stability Analysis of a Clamped Rod Carrying Electric Current[J]. Applied Mathematics and Mechanics, 1997, 18(9): 769-777.

PDF( 569 KB)

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

Received Date: 1996-03-08
Publish Date: 1997-09-15

Abstract

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

FullText(HTML)

References(10)

References

[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).