 | | 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
|
| In English (Mech. Solids): | | 4760 |
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| << Previous article | Volume 48, Issue 2 / 2013 | Next article >> |
| K.V. Avramov and I.D. Breslavskii, "Vibrations of Shallow Shells Rectangular in the Horizontal Projection with Two Freely Supported Opposite Edges," Mech. Solids. 48 (2), 186-193 (2013) |
| Year |
2013 |
Volume |
48 |
Number |
2 |
Pages |
186-193 |
| DOI |
10.3103/S0025654413020106 |
| Title |
Vibrations of Shallow Shells Rectangular in the Horizontal Projection with Two Freely Supported Opposite Edges |
| Author(s) |
K.V. Avramov (Podgorny Institute for Problems in Mechanical Engineering, National Academy of Sciences of Ukraine, Dm. Pozharskogo 2/10, Kharkiv, 61046 Ukraine, kvavr@kharkov.ua)
I.D. Breslavskii (National Technical University "Kharkiv Polytechnic Institute," Frunze 21, Kharkiv, 61002 Ukraine, id.breslavsky@gmail.com) |
| Abstract |
The exact mode shapes of linear vibrations of a shallow shell rectangular in the horizontal projection with two freely supported opposite edges are obtained. These shapes are used to construct a discrete model of vibrations of a shallow shell in geometrically nonlinear deformation. The harmonic balance method is used to study the free and forced nonlinear vibrations under internal resonance. The Lyapunov stability of the obtained periodic vibrations is analyzed. |
| Keywords |
shallow shell, nonlinear vibrations, internal resonance, stability of motion |
| References |
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| 2. | A. W. Leissa and A. S. Kadi,
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| 3. | A. S. Vol'mir, A. A. Logvinskaya, and V. V. Rogalevich,
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[in Russian]. |
| 4. | M. Amabili,
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[in Russian]. |
| 9. | V. S. Gantkevich,
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[in Russian]. |
| 10. | M. Amabili,
Nonlinear Vibrations and Stability of Shells and Plates
(Cambridge Univ. Press, Cambridge, 2008)
[in Russian]. |
| 11. | K. Avramov, Yu. Mikhlin, and E. Kurilov,
"Asymptotical Analysis of Nonlinear Dynamics of Simply Supported Cylindrical Shells,"
Nonlin. Dyn.
47 (4), 331-352 (2007). |
| 12. | I. Breslavskii, K. V. Avramov, Yu. Mikhlin, and R. Kochurov,
"Nonlinear Modes of Snap-Through Motions of a Shallow Arch,"
J. Sound Vibr.
311 (1-2), 297-313 (2008). |
| 13. | V. S. Anishchenko,
Complex Vibrations in Simple Systems
(Nauka, Moscow, 1990)
[in Russian]. |
| 14. | V. A. Yakubovich and V. M. Starzhinskii,
Linear Differential Equations with Periodic Coefficients and Their Applications
(Nauka, Moscow, 1972)
[in Russian]. |
|
| Received |
26 April 2010 |
| Link to Fulltext |
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