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Dynamic and quasi-static behaviors of magneto-thermo-elastic stresses in a conducting infinite plate subjected to an arbitrary variation of magnetic field. (English) Zbl 1117.74018

Summary: We investigate dynamic and quasi-static behaviors of magneto-thermo-elastic stresses in a conducting infinite plate subjected to an arbitrary variation of the magnetic field. It is assumed that the 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, we derive analytically solutions for magnetic field, eddy current, temperature change and both dynamic solutions and quasi-static ones for stresses and deformations in the infinite plate. The solutions for stresses are determined to be sums of thermal stress caused by eddy current loss and magnetic stress caused by Lorentz force. When the arbitrary function is given by sine function, the dynamic and quasi-static behavior of stresses is examined by numerical calculations.

MSC:

74F15 Electromagnetic effects in solid mechanics
74F05 Thermal effects in solid mechanics
74K20 Plates
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