Thermomagnetoelastic Stability of Ferromagnetic Cylindrical Shell Carrying Constant Electric Current

Abstract

The modeling and study of the instability behavior of a magnetically active ferromagnetic cylindrical shell exposed to thermal and magnetic fields with a constant electric current is considered in this paper. It is assumed that the internal surface area of the shell is covered by the thin conductive cylindrical strip. The thickness of this metallic strip is small as compared to the total thickness of the shell and therefore its contribution to the elastic properties of the overall cylindrical shell can be considered negligible. The thermal and magnetic fields of the undisturbed state of the shell are determined assuming that the edges of the shell are thermo-isolated. Undisturbed state coincides with the equilibrium which was generated under the action of thermal field (in equilibrium the forces of magnetic origin are equal to zero). It is also assumed that the thermal exchanges shell-to-strip and shell-to-external media follow Newton-Rickman's law. Using the theory of thermo-magneto-elasticity of undisturbed state in conjunction with the predetermined thermal and magnetic fields the stresses of the undisturbed state are determined under the assumption that the deflection along the generators of the shell equals to zero. The solutions of the homogeneous boundary value problems are carried out and the buckling analysis of the shell is investigated. In particular, a close-form solution for the critical value of electric current for which the shell becomes statically unstable is presented.