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

In the present paper, dynamic and quasi-static behaviors of magneto-thermo-elastic stresses in a conducting hollow circular cylinder subjected to an arbitrary variation of magnetic field are investigated. It is assumed that a magnetic field defined by an arbitrary function of time acts on the outer surface in the direction parallel to its surface. Fundamental equations of plane axisymmetrical 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 are analytically derived in the forms including the arbitrary function. 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.