 | | 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: | | 12854 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8044
|
| In English (Mech. Solids): | | 4810 |
|
| << 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 |
| 1. | E. I. Grigolyuk,
"To Calculations of Stability of Shallow Arches,"
Inzh. Sb.
9, 177-200 (1951). |
| 2. | A. W. Leissa and A. S. Kadi,
"Curvature Effects on Shallow Shell Vibrations,"
J. Sound Vibr.,
16 (2), 173-187 (1971). |
| 3. | A. S. Vol'mir, A. A. Logvinskaya, and V. V. Rogalevich,
"Nonlinear Free Vibrations of Rectangular Plates and Cylindrical Panels,"
in Proc. 8th All-Union Conf. on Theory of Shells and Plates
(Nauka, Moscow, 1973),
pp. 426-431
[in Russian]. |
| 4. | M. Amabili,
"Nonlinear Vibrations of Doubly Curves Shallow Shells,"
Int. J. Nonlin. Mech.
40 (5), 683-710 (2005). |
| 5. | A. W. Leissa,
"The Free Vibration of Rectangular Plates,"
J. Sound Vibr.
31 (3), 257-293 (1973). |
| 6. | L. Zhang and Y. Xiang,
"Vibration of Open Circular Cylindrical Shells with Intermediate Ring Supports,"
Int. J. Solids Struct.
43 (13), 3705-3722 (2006). |
| 7. | V. V. Bolotin (Editor),
Vibrations in Technology. Handbook in 6 Volumes,
Vol. 1: Vibrations of Linear Systems
(Mashinostroenie, Moscow, 1978)
[in Russian]. |
| 8. | A. S. Vol'mir,
Nonlinear Dynamics of Plates and Shells
(Nauka, Moscow, 1972)
[in Russian]. |
| 9. | V. S. Gantkevich,
Natural Vibrations of Plates and Shells
(Naukova Dumka, Kiev, 1964)
[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 |
|
| << Previous article | Volume 48, Issue 2 / 2013 | Next article >> |
|
 If you find a misprint on a webpage, please help us correct it promptly - just highlight and press Ctrl+Enter
|
|
Russian 
English