NONLINEAR STABILITY ANALYSIS OF A CLAMPED ROD CARRYING ELECTRIC-CURRENT

This paper is devoted to the analysis of the nonlinear stability of a clamped rod carrying electric current in the magnetic field which is p roduced by the current flowing in a pair of infinitely long parallel r igid wires. The natural state of the rod is in the plane of the wires and is equidistant from them. Firstly under the assumption of spatial deformation, the governing equations of the problem are derived, and t he linearized problem and critical currents are discussed. Secondly, i t is proved that the buckled states of the rod are always in planes. F inally, the global responses of the bifurcation problem of the rod are computed numerically and the distributions of the deflections, axial forces and bending moments are obtained. The results show that the buc kled states of the rod and the wires. Furthermore, it is found that th ere exists a limit point on the branch solution of the supercritical b uckled state. This is distinctively different from the buckled state o f the elastic compressive rods.