This article contains derivation of propagation factors and Fourier series for harmonically time varying, traveling electromagnetic fields in a plate and a laminate with rectangular cross sections, isotropic materials and infinite length. Different and quite general fields are taken into account on all boundaries. Choices of boundary conditions and continuity conditions are discussed. Certain combinations of types of boundary conditions make the derivation possible for a laminate. Comparisons are made between results of Fourier series and finite element calculations.
2. De Mey, G., "A method for calculating eddy currents in plates of arbitrary geometry," Archiv fur Elektrotechnik, Vol. 56, No. 3, 137-140, May 1974, [Online], Available: http://dx.doi.org/10.1007/BF01543294.
3. Singh, A., "Analysis of eddy currents in a plate with unequal overhangs," IEEE Transactions on Magnetics, Vol. 12, No. 5, 560-563, September 1976.
4. Mukerji, S. K., M. George, M. B. Ramamurthy, and K. Asaduzzaman, "Eddy currents in solid rectangular cores," Progress In Electromagnetics Research, Vol. 7, 117-131, 2008.
5. Mukerji, S. K., M. George, M. B. Ramamurthy, and K. Asaduzzaman, "Eddy currents in laminated rectangular cores," Progress In Electromagnetics Research, Vol. 83, 435-445, 2008.
6. Mukerji, S. K., D. S. Srivastava, Y. P. Singh, and D. V. Avasthi, "Eddy current phenomena in laminated structures due to travelling electromagnetic fields," Progress In Electromagnetics Research M, Vol. 18, 159-169, 2011.
7. Brander, O., Partiella differential ekvationer-en kurs i fysikens matematiska metoder, del B. Studentlitteratur, 1973.
8. Griffiths, D. J., Introduction to Electrodynamics, 3rd Ed., Pearson, Addison Wesley, 1999.
9. Cheng, D. K., Field and Wave Electromagnetics, 2nd Ed., Addison-Wesley Publishing Company, 1989.
10. Mathworks website, https://www.mathworks.com/, accessed May 30, 2017.
11. Ansys website, http://www.ansys.com/, accessed May 30, 2017.
12. Matweb website, http://matweb.com/search/AdvancedSearch.aspx, accessed February 16, 2017.