 | | Mechanics of Solids
A Journal of Russian Academy of Sciences | | Founded
in January 1966
Issued 6 times a year
Print ISSN 0025-6544
Online ISSN 1934-7936 |
Archive of Issues
| Total articles in the database: | | 12804 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8044
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| In English (Mech. Solids): | | 4760 |
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| A. G. Bagdoev, A. V. Vardanyan, S. V. Vardanyan, and V. N. Kukudzhanov, "Determining linear vibration frequencies of a ferromagnetic shell," Mech. Solids. 42 (5), 786-795 (2007) |
| Year |
2007 |
Volume |
42 |
Number |
5 |
Pages |
786-795 |
| Title |
Determining linear vibration frequencies of a ferromagnetic shell |
| Author(s) |
A. G. Bagdoev (Institute of Mechanics, National Academy of Sciences of the Republic of Armenia, pr-t Marshla Baghramiana 24B, Erevan, 375019, Republic of Armenia, mechins@sci.am)
A. V. Vardanyan (Institute of Mechanics, National Academy of Sciences of the Republic of Armenia, pr-t Marshla Baghramiana 24B, Erevan, 375019, Republic of Armenia, vardanyan_a@yahoo.com)
S. V. Vardanyan (Institute of Mechanics, National Academy of Sciences of the Republic of Armenia, pr-t Marshla Baghramiana 24B, Erevan, 375019, Republic of Armenia, vardanyan_s@yahoo.com)
V. N. Kukudzhanov (Institute for Problems in Mechanics, Russian Academy of Sciences, pr-t Vernadskogo 101, str. 1, Moscow, 119526, Russia, kukudz@ipmnet.ru) |
| Abstract |
The problems of determining the roots of dispersion equations for free bending vibrations of thin magnetoelastic plates and shells are of both theoretical and practical interest, in particular, in studying vibrations of metallic structures used in controlled thermonuclear reactors. These problems were solved on the basis of the Kirchhoff hypothesis in [1–5]. In [6], an exact spatial approach to determining the vibration frequencies of thin plates was suggested, and it was shown that it completely agrees with the solution obtained according to the Kirchhoff hypothesis. In [7–9], this exact approach was used to solve the problem on vibrations of thin magnetoelastic plates, and it was shown by cumbersome calculations that the solutions obtained according to the exact theory and the Kirchhoff hypothesis differ substantially except in a single case. In [10], the equations of the dynamic theory of elasticity in the axisymmetric problem are given. In [11], the equations for the vibration frequencies of thin ferromagnetic plates with arbitrary conductivity were obtained in the exact statement. In [12], the Kirchhoff hypothesis was used to obtain dispersion relations for a magnetoelastic thin shell. In [5, 13–16], the relations for the Maxwell tensor and the ponderomotive force for magnetics were presented. In [17], the dispersion relations for thin ferromagnetic plates in the transverse field in the spatial statement were studied analytically and numerically.
In the present paper, on the basis of the exact approach, we study free bending vibrations of a thin ferromagnetic cylindrical shell. We obtain the exact dispersion equation in the form of a sixth-order determinant, which can be solved numerically in the case of a magnetoelastic thin shell. The numerical results are presented in tables and compared with the results obtained by the Kirchhoff hypothesis. We show a large number of differences in the results, even for the least frequency. |
| References |
| 1. | S. A. Ambartsumyan, G. E. Bagdasaryan, and M. V. Belubekyan,
Magnetoelasticity of Thin Shells and Plates
(Nauka, Moscow, 1977)
[in Russian]. |
| 2. | S. A. Ambartsumyan and G. E. Bagdasaryan,
Electroconductive Plates and Shells in a Magnetic Field
(Nauka, Moscow, 1996)
[in Russian]. |
| 3. | S. A. Ambartsumyan and M. V. Belubekyan,
Vibrations and Stability of Current-Carrying Plates
(NAN Armenii, Erevan, 1992)
[in Russian]. |
| 4. | A. G. Bagdoev and L. A. Movsisyan,
"Modulations of Thermomagnetoelastic Waves in a Nonlinear Plate,"
Izv. Nats. Akad. Nauk Armenii. Mekhanika
52 (1), 25-30 (1999). |
| 5. | G. E. Bagdasaryan,
Vibrations and Stability of Magnetoelastic Systems
(Erevan State University, Tigran Mets, Erevan)
[in Russian]. |
| 6. | W. Nowacki,
Theory of Elasticity
(PWN, Warsaw, 1970; Mir, Moscow, 1975). |
| 7. | A. G. Bagdoev and S. G. Saakyan,
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Spatial and the Averaged Problems,"
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Mekh. Tverd. Tela,
No. 5, 35-42 (2001)
[Mech. Solids (Engl. Transl.)]. |
| 8. | A. G. Bagdoev and A. A. Vantsyan,
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in Plate in Magnetic Field
for Space and Averaged Problems,"
Int. J. Solids and Struct.
39, 851-859 (2002). |
| 9. | Yu. S. Safaryan,
"Study of Vibrations of Magnetoelastic Plates
in Space and Averaged Approach,"
Inform. Tekhnologii i Upravlenie,
No. 2, 17-19 (2001). |
| 10. | H. Kolsky,
Stress Waves in Solids
(Clarenden Press, Oxford, 1953; Izd. Inostr. Lit., Moscow, 1955). |
| 11. | A. G. Bagdoev and L. S. Kevnakszyan,
"Nonlinear Modulation Waves in
Ferromagnetic Plates for Arbitrary Conductivity,"
Mat. v Vyssh. Shkole,
No. 3, 12-33 (2004). |
| 12. | G. E. Bagdasaryan and M. V. Belubekyan,
"Axisymmetric Vibrations of a
Cylindrical Shell in Magnetic Field,"
Izv. Nats. Akad. Nauk Armenii. Mekhanika
20 (5), 21-27 (1967). |
| 13. | A. I. Akhiezer, V. G. Bar'yakhtar, and S. V. Peletminskii,
Spin Waves
(Nauka, Moscow, 1967; North-Holland, Amsterdam, 1968). |
| 14. | L. D. Landau and E. M. Lifshits,
Electrodynamics of Continua
(Fizmatizd, Moscow, 1959)
[in Russian]. |
| 15. | Kh. A. Rakhmatullin and Yu. S. Shmelev,
Interaction between Media and Fields
(FAN, Tashkent, 1985)
[in Russian]. |
| 16. | I. E. Tamm,
Foundations of the Theory of Electricity
(Nauka, Moscow, 1966)
[in Russian]. |
|
| Received |
19 May 2007 |
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