исследование магнитного поля трехмерных ферромагнитных

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ISSN 1607-7970.
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1.
.
. – .:
, 1986. – 216 .
Krasnov I.P. Calculation methods for ship magnetism and electrical engineering. – Leningrad: Sudostroenie,
1986. – 216 p. (Rus.)
2.
.
/
/
; 11 (1127) –
: 1999. – 28 .
Liubimov V.V. Artificial and natural electromagnetic fields in human environment and devices for its detection
and fixation / Preprint / IZMIRAN; 11 (1127). – Troitsk: 1999. – 28 p. (Rus.)
3.
.,
.,
.,
.
«
»
//
. – 1978. – 2. – . 74–76.
Nakhilnitskaia Z.N., Mastriukova V.M, Andrianova L.A., Borodkina A.T. Reaction of organism to zero magnetic field exposure // Kosmicheskaia biologiia i meditsina. – 1978. – 2. – P. 74–76. (Rus.)
4.
.
.–
:
, 1969. – 345 .
Nesterenko A.D. Introduction to Theoretical Electrical Engineering. – Kiev: Naukova dumka, 1969. – 345 p. (Rus).
5.
.
. – .:
, 1984. – 150 .
Patankar S. Numerical methods for solving heat transfer and fluid flow problems. – Moskva: Energoatomizdat,
1984. – 150 p. (Rus.)
6.
.
//
2.
.«
». M.: 1999. – . 135–136.
Pokhodzei L.V. Hypogeomagnetic conditions as a risk factor for human health // Trudy II Mezhdunar. konf.
"Electromagnitnye polia i zdorovie cheloveka". – Moskva: 1999. – P. 135 136. (Rus.)
7.
.
//
. – 2005. – .75. – 6. – . 85–92.
Rezinkina M.M. Growth of dendrite branches in polyethylene insulation under a high voltage versus the branch
conductivity // Zhurnal Tekhnicheskoi Fisiki. – 2005. – Vol.75.
6. – P. 85 92. (Rus.)
8.
.
//
. – 2009. – .79. – 8. – . 8–17.
22
ISSN 1607-7970.
.
. 2011.
1
Rezinkina M.M. Numerical calculation of the magnetic field and magnetic moment of ferromagnetic bodies
with a complex spatial configuration // Zhurnal Tekhnicheskoi Fisiki. – 2009. – Vol.79.
8. – P. 8 17. (Rus).
9.
.
. – .:
, 1989. – 504 .
Tamm I.E. Fundamentals of electricity. – Moskva: Nauka, 1989. – 504 p. (Rus.)
10.
.–
2.2.4.1191-03 «
». – .: 2003. – 19 .
Physical factors of the production environment Sanitary-epidemiological rules and norms. – SanPiN
2.2.4.1191-03 "Electromagnetic fields in production environment". – M.: 2003. – 19 p. (Rus.)
11.
.,
.
.–
:
, 2008. – 248 .
Shcherba A.A., Rezinkina M.M. Modelling and analysis of electrical fields of power objects. – Kyiv: Naukova
dumka, 2008. – 248 p. (Rus.)
12.
.,
.
.–
:
, 2009. – 191 .
Shcherba A.A., Rezinkina M.M. Electromagnetic fields and their influence on the objects. Kyiv: Naukova
dumka, 2009. – 191 p. (Rus.)
13.
.
. – .– .:
, 1941. – 283 .
Yanovskii B.M. Terrestrial magnetism. Moskva–Leningrad: Glavsevmorputi, 1941. – 283 p. (Rus.)
14. Conley C.C. A review of the biological effects of very low magnetic fields // Report NASA TN D-5902.
– National Aeronautics and Space Administration, Washington, D. C. 20546. – 1970. – 25 p.
15. Paluszek M., Thomas S., Mueller J., Bhatta P. Spacecraft attitude and orbit control. – Princeton: Princeton
Satellite Systems, 2007. – 476 p.
16. Salinas E., Rezinkina M., Atalaya J. Some 2D–3D aspects of shielding of longitudinal sources of extremely
low frequency magnetic fields // Environmentalist. – 2009. – Vol. 29. – 2. – P. 141–146.
17. Salinas E., Rezinkina M. Choice of parameters for passive shielding of power-frequency magnetic fields //
Environmentalist. – 2009. – Vol. 29. – 2. – P. 135–140.
18. Taflove A., Hagness S. Computational electrodynamics: the finite difference time domain method. – Boston-London: Artech House, 2000. – 852 p.
19. Xuebin W., Bing L.I., Muling X.U. et al. Long-term memory was impaired in one-trial passive avoidance
task of day-old chicks hatching from hypomagnetic field space // China Sci. Bull. – 2003. – Vol. 48. – P. 2454–2457.
20. Zhang B., Lu H., Xi W. et al. Exposure to hypomagnetic field space for multiple generations causes amnesia in Drosophila melanogaster // Neuroscience Letters. – 2004. – Vol. 371. – 2–3. – P. 190–195.
21. Zhang X., Li J-F., Wu Q-J., Li B., Jiang J-C. Effects of hypomagnetic field in noradrenergic activities in
the brainstem of golden hamster // Bioelectromagnetics. – 2007. – Vol. 28. – P. 155–158.
621.317.42
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M.M.Rezynk na1, L.E.Lobzhanidze2
Scientific and Technical Center of Magnetism of Technical Objects of National Academy of Science of Ukraine,
Industrialna, 19, a/s 72, Kharkiv, 61106, Ukraine
Analysis of magnetic field of three-dimensional ferrous objects
Methodology of numerical calculations of magnetic field and magnetic moment of ferromagnetic objects with complicated space
form has been described with the help of the method of final volume and absorbing boundary conditions. Calculations of magnetic
field and magnetic moment in the row of ferromagnetic objects have been performed with developed methodology. Dependence of
magnetic moments of ferromagnetic constructions on their geometric shape has been analysed. References 21, figures 5.
Key words: magnetic field, ferromagnetic object, method of final volume, absorbing boundary conditions.
1, 2
16.04.2010
Received 16.04.2010
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