{"title":"Impedance of an Encircling Coil due to a Cylindrical Tube with Varying Properties","authors":"Valentina Koliskina","volume":52,"journal":"International Journal of Mathematical and Computational Sciences","pagesStart":575,"pagesEnd":579,"ISSN":"1307-6892","URL":"https:\/\/publications.waset.org\/pdf\/11145","abstract":"Change in impedance of an encircling coil is obtained\r\nin the present paper for the case where the electric conductivity and\r\nmagnetic permeability of a metal cylindrical tube depend on the\r\nradial coordinate. The system of equations for the vector potential is\r\nsolved by means of the Fourier cosine transform. The solution is\r\nexpressed in terms of improper integral containing modified Bessel\r\nfunctions of complex order.","references":"[1] N. Burais, and A. Nicolas, \"Electromagnetic field analysis in remote\r\nfield eddy current testing systems\", IEEE Trans. Magn., vol. 25, pp.\r\n3010-3012, 1989.\r\n[2] C. Reboud, D. Pr\u00e9mel, D. Lesselier, and B. Bisiaux, \"Recent advances\r\nin simulation of eddy current testing of tubes and experimental\r\nvalidations\", Review of Quantitative Nondestructive Evaluation, vol.\r\n26, pp. 241-248, 2007\r\n[3] V. Monebhurrun, B. Duch\u251c\u00acne, and D. Lesselier, \"Three-dimensional\r\ninversion of eddy current data for nondestructive evaluation of steam\r\ngenerator tubes\", Inverse Problems, vol. 14, pp. 707-724, 1998.\r\n[4] J.F.P.J. Abascal, M. Lambert, D. Lesselier, and O. Dorn, \"3D eddy\r\ncurrent imaging of metal tubes by gradient-based, controlled evolution\r\nof level sets\", IEEE Trans. Magn., vol. 44, pp. 4721-4729, 2008.\r\n[5] C.V. Dodd, and W.E. Deeds, \"Analytical solutions to eddy-current\r\nprobe-coil problems\", J. Appl. Phys., vol. 39, pp. 2829-2838, 1968.\r\n[6] C.V. Dodd, W.E. Deeds, and J.W. Luquire, \"Integral solutions to some\r\neddy current problems\", Int. J. Nondestructive Testing, vol. 1, pp. 29-\r\n107, 1969.\r\n[7] C.V. Dodd, C.C. Cheng, and W.E. Deeds, \"Induction coils coaxial with\r\nan arbitrary number of cylindrical conductors\", J. Appl. Phys., vol. 45,\r\npp. 638-647, 1974.\r\n[8] J.R. Bowler, and T.P. Theodoulidis, \"Eddy currents induced in a\r\nconducting rod of finite length by a coaxial encircling coil\", J. Phys.\r\nD: Appl. Phys., vol. 38, pp. 2861-2868, 2005.\r\n[9] C.-C. Tai, H.-C. Yang, and Y.-H. Liu, \"Modeling the surface condition\r\nof ferromagnetic metal by the swept-frequency eddy current method\",\r\nIEEE Trans. Magn., vol. 38, pp. 205-210, 2002.\r\n[10] C.-C. Tai, \"Characterization of coatings on magnetic metal using the\r\nswept-currency eddy current method\", Rev. Sci. Instr., vol. 71, pp.\r\n3161-3167, 2000.\r\n[11] M.Ya. Antimirov, A.A. Kolyshkin, and R. Vaillancourt, Mathematical\r\nmodels for eddy current testing. Montreal: CRM, 1997.\r\n[12] A.D. Polyanin, and V.F. Zaitsev, Handbook of exact solutions for\r\nordinary differential equations . Florida: Chapman&Hall\/CRC, 2003.","publisher":"World Academy of Science, Engineering and Technology","index":"Open Science Index 52, 2011"}