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Research Papers

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

[+] Author and Article Information
Fei Qin

College of Mechanical Engineering and Applied Electronics Technology, Beijing University of Technology, Beijing 100022, P.R.C.qfei@bjut.edu.cn

Dongmei Yan

College of Mechanical Engineering and Applied Electronics Technology, Beijing University of Technology, Beijing 100022, P.R.C.

J. Appl. Mech 75(3), 031004 (Mar 05, 2008) (6 pages) doi:10.1115/1.2870266 History: Received April 02, 2007; Revised November 10, 2007; Published March 05, 2008

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.

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Copyright © 2008 by American Society of Mechanical Engineers
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Figures

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Figure 1

Infinite plate subjected to tensile stress p and magnetic field B0

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Figure 2

Infinite plate with a hole subjected to stress p and magnetic field B0

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Figure 3

The rigid magnetic field intensities: (a) Hx− and (b) Hy−

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Figure 4

The perturbed magnetic field intensities: (a) hx− and (b) hy−

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Figure 5

Comparison of intensities along the hole boundary (r=a): (a) Hx− and hx−; (b) Hy− and hy−

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Figure 6

The rigid intensities for various r∕a ratios: (a) Hx− and (b) Hy−

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Figure 7

The perturbed intensities for various r∕a ratios: (a) hx− and (b) hy−

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