Vibrations and stability of a ferromagnetic cylindrical shell in a magnetic field

Аuthors

Khromatov V. E.^*, Golubeva T. N.^**

Moscow Power Engineering Institute (National Research University), 14, Krasnokazarmennaja St., Moscow, 111250, Russia

*e-mail: KhromatovVY@mpei.ru
**e-mail: komissarovatn@mail.ru

Abstract

Purpose
Vibrations of closed ferromagnetic cylindrical shells in magnetic fields produced by direct currents flowing along shells axes of rotation were investigated. Design/methodology/approach
Using the basic assumptions of the classical theory of cylindrical shells and the theory of magnetoelasticity the natural frequencies of the magnetically soft ferromagnetic cylindrical shell in the magnetic field were computed. The effect of the magnetic field to shells natural frequencies was investigated numerically on the basis of Mathcad software.
Findings
The main results of investigations of the effect of magnetic fields to natural frequencies of diamagnetic, paramagnetic and ferromagnetic thin plates and shells are reviewed. The governing equations of vibrations ofcylindrical shells in azimuthal magnetic fields of the direct axial current are derived. The main relationships for natural frequencies of circular cylindrical shells in magnetic fields and the ratio of external magnetic field resulting to static stability loss of the shell are obtained. It is shown that magnetic fields decrease ferromagnetic and nonmagnetic shells natural frequencies.
Practical implications
Structural design of aircrafts requires the information about natural frequencies needed to tune out from resonance and to estimate the influence of magnetic fields on the vibration and stability of cylindrical shells.
Originality/value
On the basis of mathematical models of magnetoelastic vibrations of thin-walled structural elements and Borland Delphi 7.0 software, universal software for the computation of natural frequencies of plates and shells in magnetic fields was constructed

Keywords:

ferromagnetic cylindrical shell, azimuthal magnetic field, natural frequency

References

1. Panovko Ya.G., Gubanova I.I. Ustoichivost ikolebaniya uprugikh sistem. Sovremennye kontseptsii, paradoksy ioshibki (Stability and vibrations ofelastic systems. Modern concepts, paradoxes and errors), Moscow, KomKniga, 2006, 352p.
2. Mun F.S., Pao I-sin Prikladnaya Mekhanika, 1969, no.1, pp. 59-65.
3. Ambartsumyan S.A., Bagdasaryan G.E., Belubekyan M.V. Magnitouprugost tonkikh obolochek iplastin (Magnetoelasticity thin shells and plates), Moscow, Nauka, 1977, 272p.
4. Ambartsumyan S.A., Bagdasaryan G.E.Elektropro- vodyashchie plastinki iobolochki vmagnitnom pole (Conductive plates and shells inamagnetic field), Moscow, Fizmatlit, 1996, 286p.
5. Bagdasaryan G.E. Kolebaniya ustoichivost magnitouprugikh system (Vibrations and stability ofmagnetoelastic systems), Erevan, Tigran Mets, 1999, 436p.
6. Bagdasaryan G.E. Problemy mashinostroeniya, 1986, no.25, pp. 63-68.
7. Bolotin V.V. Vibratsii vtekhnike (Vibrations inthe engineering), Moscow, Mashinostroenie, 1999, vol.1, 506p.
8. Krasova N.S., Samogin Yu.A., Khromatov V.E. Materialy XII mezhdunarodnogo simpoziuma Dinamicheskie itekhnologicheskie problemy mekhaniki konstruktsii isploshnykh sredim. A.G. Gorshkova, Moscow, 2006, p.195.
9. Krasova N.S., Samogin Yu.N., Khromatov V.E. Materialy XIII mezhdunarodnogo simpoziuma Dinamicheskie itekhnologicheskie problemy mekhaniki Applied mathematics, physics, mechanics konstruktsii isploshnykh sredim. A.G. Gorshkova, Moscow, 2007, p.151.
10. Komissarova T.N., Koreshkova N.S. Materialy XIV mezhdunarodnogo simpoziuma Dinamicheskie itekhnologicheskie problemy mekhaniki konstruktsii isploshnykh sredim. A.G. Gorshkova, Moscow, 2008, pp. 121-122.
11. Khromatov V.E. Koreshkova N.S. Vestnik MEI, 2008, no.1, pp. 71-75.
12. Koreshkova N.S., Khromatov V.E. Izvestiya Rossiiskoi akademii nauk. Mekhanika verdogo tela, 2009, no.4, pp. 165-171.
13. Khromatov V.E., Koreshkova N.S., Samogin Yu.N. Materialy XVmezhdunarodnogo simpoziuma Dinamicheskie itekhnologicheskie problemy mekhaniki konstruktsii isploshnykh sredim. A.G. Gorshkova, Moscow, 2009, pp. 159-160.
14. Golubeva T.N., Gecha V.Ya., Khromatov V.E. Materialy XVI mezhdunarodnogo simpoziuma Dinamicheskie itekhnologicheskie problemy mekhaniki konstruktsii isploshnykh sredim. A.G. Gorshkova, Moscow, 2010, pp. 52-53.
15. Golubeva T.N., Khromatov V.E. Materialy XVII mezhdunarodnogo simpoziuma Dinamicheskie itekhnologicheskie problemy mekhaniki konstruktsii isploshnykh sredim. A.G.Gorshkova, Moscow, 2011, pp. 58-59.
16. Golubeva T.N., Khromatov V.E. Materialy XVIII mezhdunarodnogo simpoziuma Dinamicheskie itekhnologicheskie problemy mekhaniki konstruktsii isploshnykh sredim. A.G. Gorshkova, Moscow, 2012, pp. 45-46.
17. Golubeva T.N., Khromatov V.E. Materialy XIX mezhdunarodnogo simpoziuma Dinamicheskie itekhnologicheskie problemy mekhaniki konstruktsii isploshnykh sredim. A.G. Gorshkova, Moscow, 2013, pp. 67-68.
18. Khromatov V.E., Shchugorev V.N., Novikova O.V. Materialy XIX mezhdunarodnogo simpoziuma Dinamicheskie itekhnologicheskie problemy mekhaniki konstruktsii isploshnykh sredim. A.G. Gorshkova, Moscow, 2013, pp. 196-200.
19. Golubeva T.N., Khromatov V.E. Elektronnyi zhurnal Novoe vRossiiskoi elektroenergetike, 2012, no.3, availableat: http://www.energo-press.info/nre/body/ arch/2012/ann2011/3/2.php
20. Golubeva T.N., Korobkov Yu.S., Khromatov V.E. Elektrotekhnika, 2013, no.3, pp. 44-49.
21. Golubeva T.N. Spravochnik. Inzhenernyi zhurnal, 2013, no.5, pp. 20-24.