Dynamic instability of electroconductive cylindrical shell in a magnetic field

Abstract

The dynamic instability of electroconductive cylindrical shells interacting with an external magnetic fields is considered in the paper. Two cases of applied external dynamic loads are discussed, namely (i) a harmonic mechanical force, and (ii) a harmonic magnetic field force. Analytical descriptions of the two-dimensional equations and associate conditions of dynamic instability are presented. On the basis of the formulated problems, specific issues related to the dynamic instability of electroconductive cylindrical shells in a magnetic field are offered. The study illustrated the effect of magnetoelastic interaction. Specifically it is shown that there exist a minimum value of the given magnetic field intensity, above which the parametric resonance due to external harmonic force is eliminated; furthermore, in a presence of time-harmonic magnetic field the parametric resonance with a resonance frequency can be generated not only near the first frequency of the external magnetic field (which is equal to the natural frequency of vibrations), but near the double frequency of natural vibrations. When the forced vibrations of conductive shells caused by external forces of non-electromagnetic origin is considered, including the effect of a time-harmonic magnetic field, resonance can occur in the presence of a non-stationary harmonic magnetic field. Results reveal that the rapid increase of the amplitude of vibrations occurs when the frequency of the external magnetic field is in close proximity to the first natural frequency of the magnetoelastic vibrations of the plate, as well as when the frequency of the magnetic field, is equal to half of the shell natural frequency.