Analytical Solution of the Perturbed Magnetic Fields of Plates Under Tensile Stress

Abstract

Development of magnetism based nondestructive testing technology and the Microelectronic mechanical system require accurate computation of perturbed magnetic fields generated by mechanical stress. In this paper, based on the linearized magnetoelastic theory, the governing equations and continuity conditions to determine the perturbed magnetic fields were formulated for the case of weak external magnetic fields such as the earth’s magnetic field. Under those weak magnetic fields, the effect of the magnetic fields on mechanical deformation was neglected. As a result, the interaction between the deformation and the magnetic field was simplified. The effect of deformation on the perturbed magnetic field was taken into account by introducing the displacement gradient into the boundary conditions that the perturbed field should satisfy. As examples, analytic solutions of the perturbed magnetic field of infinite plates with and without a round hole, which are subjected to tensile stresses and weak external magnetic fields, were obtained by the approach presented. The results show that the perturbed magnetic fields induced by stress are three orders less in magnitude of intensity than that of magnetic fields without stress, and some prominent local features such as that has more peaks and decays more rapidly in the radial direction than the case of stress free that are predicted by the solutions.