Magnetoelastic Buckling and Vibration of a Rod Carrying Electric Current

Abstract

The effect of high electric currents on the stability and dynamics of a circular rod is investigated. A uniform current distribution in the undeformed rod is assumed. The perturbed magnetic field due to bending deformation is shown to set up a system of destabilizing forces. For long wavelength vibrations, a frequency-current dispersion relation is obtained which shows a continuous decrease in the natural frequency of the rod as the current in the rod is increased. At a critical value of current the natural frequency of the rod goes to zero and the rod buckles, which is the solid analog to the “kink instability” in plasma physics. The critical current criteria is applied to find the minimum support distance for a superconducting coil for magnetic levitation of trains. Experiments were conducted on a copper rod to observe the destabilizing effect of the electric currents of up to 400 A. Dynamic tests show that the natural frequencies decrease as the current in the rod increased. The frequency-current dispersion and the estimated critical current agree reasonably with the corresponding theoretical values.