 | | 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 |
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| In English (Mech. Solids): | | 4760 |
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| N. S. Koreshkova and V. E. Khromatov, "On the Influence of a Transverse Magnetic Field on the Vibration Spectra of Shallow Shells," Mech. Solids. 44 (4), 632-638 (2009) |
| Year |
2009 |
Volume |
44 |
Number |
4 |
Pages |
632-638 |
| DOI |
10.3103/S002565440904013X |
| Title |
On the Influence of a Transverse Magnetic Field on the Vibration Spectra of Shallow Shells |
| Author(s) |
N. S. Koreshkova (Moscow Power Engineering Institute (Technical University), Krasnokazarmennaya 14, Moscow, 111250 Russia)
V. E. Khromatov (Moscow Power Engineering Institute (Technical University), Krasnokazarmennaya 14, Moscow, 111250 Russia, KhromatovVY@mpei.ru) |
| Abstract |
In the design of electric machines, devices, and plasma generator bearing constructions, it is sometimes necessary to study the influence of magnetic fields on the vibration frequency spectra of thin-walled elements. The main equations of magnetoelastic vibrations of plates and shells are given in [1], where the influence of the magnetic field on the fundamental frequencies and vibration shapes is also studied. When studying the higher frequencies and vibration modes of plates and shells, it is very efficient to use Bolotin's asymptotic method [2-4]. A survey of studies of its applications to problems of elastic system vibrations and stability can be found in [5, 6]. Bolotin's asymptotic method was used to obtain estimates for the density of natural frequencies of shallow shell vibrations [3] and to study the influence of the membrane stressed state on the distribution of frequencies of cylindrical and spherical shells vibrations [7, 8]. In a similar way, the influence of the longitudinal magnetic field on the distribution of plate and shell vibration frequencies was studied [9, 10]. It was shown that there is a decrease in the vibration frequencies of cylindrical shells under the action of a longitudinal magnetic field, and the accumulation point of the natural frequencies moves towards the region of lower frequencies [10]. In the present paper, we study the influence of a transverse magnetic field on the distribution of natural frequencies of shallow cylindrical and spherical shells, obtain asymptotic estimates for the density of natural frequencies of shell vibrations, and compare the obtained results with the empirical numerical results. |
| Keywords |
vibrations of shells, magnetoelasticity, eigenfrequency distribution |
| References |
| 1. | S. A. Ambartsumyan, G. E. Bagdasaryan, and M. V. Belubekyan,
Magnetoelasticity of Thin Shells and Plates
(Nauka, Moscow, 1977)
[in Russian]. |
| 2. | V. V. Bolotin,
"The Edge Effect in the Oscillations of Elastic Shells,"
Prikl. Mat. Mekh.
24 (5), 831-842 (1960)
[J. Appl. Math. Mech. (Engl. Transl.)
24 (5), 1257-1272 (1960)]. |
| 3. | V. V. Bolotin,
"On the Density of the Distribution of Natural Frequencies of Thin Elastic Shells,"
Prikl. Mat. Mekh.
27 (2), 362-364 (1963)
[J. Appl. Math. Mech. (Engl. Transl.)
27 (2), 538-543 (1963)]. |
| 4. | V. V. Bolotin (Editor)
Vibrations in Technology.
Handbook in 6 Volumes. Vol. 1.
Vibrations of Linear Systems,
(Mashinostroenie, Moscow, 1999)
[in Russian] |
| 5. | Yu. A. Dubovskikh, V. E. Khromatov, and V. E. Chirkov,
"Asymptotic Analysis of Stability and Postcritical Behavior
of Elastic Panels in a Supersonic Flow,"
Izv. Akad. Nauk. Mekh. Tverd. Tela,
No. 3, 76-88 (1996)
[Mech. Solids (Engl. Transl.)
31 (3), 65-75 (1996)]. |
| 6. | P. Pevzner, T. Weller, and A. Bercovits,
"Further Modification of Bolotin Method
in Vibration Analysis of Rectangular Plates,"
AIAA J.
38 (3), 1725-1729 (2000). |
| 7. | V. E. Khromatov,
"Properties of Spectra of Thin Circular Cylindrical Shells
Oscillating near Momentless Stress State,"
Izv. Akad. Nauk SSSR. Mekh. Tverd. Tela, No. 2, 103-108 (1972)
[Mech. Solids (Engl. Transl.)]. |
| 8. | V. E. Khromatov,
"Density of Frequencies of Natural Oscillations of Thin Spherical Shells in Momentless Stress State,"
Trudy MEI,
No. 101, 148-153 (1972). |
| 9. | N. S. Krasova,
"Studies of the Magnetic Field Influence on the Spectrum of Frequencies of Plasma Generators Plates,"
in Collection of Annotations of the 3rd Kurchatov Youth School
(Moscow, 2005),
p. 42
[in Russian]. |
| 10. | N. S. Krasova, Yu. A. Samogin, and V. E. Khromatov,
"Density of Eigenfrequencies of Oscillations of Circular Cylindrical Shells in the Longitudinal Magnetic Field,"
in Theses of Reports on the 12th International Symposium "Dynamical and Technological Problems of Construction and Continua Mechanics"
(Izd-vo MAI, Moscow, 2006),
p. 195
[in Russian]. |
|
| Received |
05 December 2006 |
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