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The transient eddy current field is analytically modeled by applying inverse Laplace transform to pulsed eddy current testing. The closed-form solution to transient eddy current field in a complex domain is obtained by using the truncated region eigenfunction expansion (TREE) method and the theory of reflection and transmission of electromagnetic waves. After extensive algebraic transform, the poles of the developed model and corresponding residues are able to be calculated. As a result, partial fraction expansion can be used to split up the complicated complex-domain model into the forms that are listed in the Laplace Transform table. Therefore, it is easy to derive the time-domain solutions to transient eddy current field with step and exponential current excitations respectively. The derived time-domain model not only has some advantages in the sense of implementation and efficiency, but also removes the Gibbs phenomenon. Finally, the inverse Fourier transform of induced voltage in the probe is performed and the good agreement demonstrates the validity of the established model.
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Keywords:
- pulsed eddy current testing /
- transient eddy current field /
- analytical time-domain model /
- inverse Laplace transform
[1] Tian G Y, Li Y, Mandache C 2009 IEEE Trans. Magn. 45 184
[2] Abidin I Z, Mandache C, Tian G Y, Morozov M 2009 NDT&E Int. 42 599
[3] Yu A L 2008 Chin. Phys. B 17 878
[4] Shi Q F, Gou M J, Yang X, Zhang Y 2010 Acta Phys. Sin. 59 3905 (in Chinese) [史庆藩、 苟铭江、 杨 曦、 张 宇 2010 59 3905]
[5] Fan M B, Huang P J, Ye B, Hou D B, Zhang G X, Zhou Z K 2009 NDT and E Int. 42 376
[6] Li Y, Tian G Y, Simm A. 2008. NDT and E Int. 41 477
[7] Tai C C, Rose J R, Moulder JC 1996. Rev. Sci. Instrum. 67 3965
[8] Bowler J R, Johnson M 1997 IEEE Trans. Magn. 33 2258
[9] Haan V O, Jong P A 2004 IEEE Trans. Magn. 40 371
[10] Fu F, Bowler J R 2008 IEEE Trans. Magn. 42 2029
[11] Xie L, Lei Y Z 2006 Acta Phys. Sin. 55 4397 (in Chinese) [谢 莉、 雷银照 2006 55 4397]
[12] Theodoulidis T P 2008 IEEE Trans. Magn. 42 1894
[13] Dodd C D, Deeds WE 1968 J. Appl. Phys. 39 2829
[14] Fan M B, Huang P J, Ye B, Hou D B, Zhang G X, Zhou Z K 2009 Acta Phys. Sin. 58 5950 (in Chinese) [范孟豹、 黄平捷、 叶 波、 侯迪波、 张光新、 周泽魁 2009 58 5950]
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[1] Tian G Y, Li Y, Mandache C 2009 IEEE Trans. Magn. 45 184
[2] Abidin I Z, Mandache C, Tian G Y, Morozov M 2009 NDT&E Int. 42 599
[3] Yu A L 2008 Chin. Phys. B 17 878
[4] Shi Q F, Gou M J, Yang X, Zhang Y 2010 Acta Phys. Sin. 59 3905 (in Chinese) [史庆藩、 苟铭江、 杨 曦、 张 宇 2010 59 3905]
[5] Fan M B, Huang P J, Ye B, Hou D B, Zhang G X, Zhou Z K 2009 NDT and E Int. 42 376
[6] Li Y, Tian G Y, Simm A. 2008. NDT and E Int. 41 477
[7] Tai C C, Rose J R, Moulder JC 1996. Rev. Sci. Instrum. 67 3965
[8] Bowler J R, Johnson M 1997 IEEE Trans. Magn. 33 2258
[9] Haan V O, Jong P A 2004 IEEE Trans. Magn. 40 371
[10] Fu F, Bowler J R 2008 IEEE Trans. Magn. 42 2029
[11] Xie L, Lei Y Z 2006 Acta Phys. Sin. 55 4397 (in Chinese) [谢 莉、 雷银照 2006 55 4397]
[12] Theodoulidis T P 2008 IEEE Trans. Magn. 42 1894
[13] Dodd C D, Deeds WE 1968 J. Appl. Phys. 39 2829
[14] Fan M B, Huang P J, Ye B, Hou D B, Zhang G X, Zhou Z K 2009 Acta Phys. Sin. 58 5950 (in Chinese) [范孟豹、 黄平捷、 叶 波、 侯迪波、 张光新、 周泽魁 2009 58 5950]
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