Dynamic and quasi-static behaviors of magneto-thermo-elastic stresses in a conducting infinite plate subjected to an arbitrary variation of magnetic field

Abstract

In the present paper, dynamic and quasi-static behaviors of magneto-thermo-elastic stresses in a conducting infinite plate subjected to an arbitrary variation of the magnetic field are investigated. It is assumed that a magnetic field defined by an arbitrary function of time acts on both side surfaces of the infinite plate in the direction parallel to its surfaces. Fundamental equations of one-dimensional electromagnetic, temperature and elastic fields are formulated. Then, solutions of magnetic field, eddy current, temperature change and both dynamic solutions and quasi-static ones of stresses and deformations in the infinite plate are derived analytically. The solutions of stresses are determined to be sums of thermal stress caused by eddy current loss and magnetic stress caused by Lorentz force. For the case that the arbitrary function is given by the sine function, the dynamic and quasi-static behaviors of the stresses are examined by numerical calculations.