 | | 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: | | 12882 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8071
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| In English (Mech. Solids): | | 4811 |
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| << Previous article | Volume 38, Issue 6 / 2003 | Next article >> |
| S. N. Kukudzhanov, "On the influence of the boundary conditions on natural vibrations of prestressed nearly cylindrical shells of revolution," Mech. Solids. 38 (6), 102-110 (2003) |
| Year |
2003 |
Volume |
38 |
Number |
6 |
Pages |
102-110 |
| Title |
On the influence of the boundary conditions on natural vibrations of prestressed nearly cylindrical shells of revolution |
| Author(s) |
S. N. Kukudzhanov (Tbilisi) |
| Abstract |
The influence of the boundary conditions on the waveform and lower natural frequencies of nearly cylindrical shells of revolution is studied. The shell is assumed to be subjected to preliminary action of normal pressure. We consider shells of medium length and assume that the shape of the generatrix of the midsurface of the shell is described by a sufficiently smooth function that does not change in sign. We analyze and simplify the governing equations and boundary conditions. If the generatrix of the shell midsurface is a parabola, the reduced equation differs from the familiar equation [1] in an additional term, the order of magnitude of which may coincide with that of other terms. Shells of both positive and negative Gaussian curvature are considered. We investigate the cases where either both edges of the shell are clamped or one of the edges is simply supported, whereas the other one is clamped. Analytical relations and curves are presented that characterize the fundamental frequency and waveform as depending on the type of the boundary conditions, preliminary stress, and the maximum deviation of the shape of the shell from a cylinder. (The last quantity is assumed to coincide with the thickness of the shell in order of magnitude.) It is shown that the degree of influence of the boundary conditions is different for shells of positive and negative Gaussian curvature and depends on the maximum deviation of the shell from a cylindrical shape and the preliminary stress. |
| References |
| 1. | V. M. Darevskii, "Stability of a nearly cylindrical shell,"
in Problems of Design of Spatial Structures [in Russian], pp. 35-45,
MISI, Moscow, 1980. |
| 2. | A. S. Vol'mir, Stability of Deformable Systems [in Russian], Nauka, Moscow, 1967. |
| 3. | V. V. Novozhilov, Theory of Thin Shells [in Russian],
Sudpromgiz, Leningrad, 1962. |
| 4. | V. Z. Vlasov, General Theory of Shells and its Applications in Engineering [in Russian],
Gostekhizdat, Moscow, 1949. |
| 5. | A. L. Goldenveizer, V. B. Lidskii, and P. E. Tovstik,
Natural Vibrations of Thin Elastic Shells
[in Russian], Nauka, Moscow, 1979. |
| 6. | P. E. Tovstik, Stability of Thin Shells
[in Russian], Nauka, Moscow, 1995. |
| 7. | S. N. Kukudzhanov,
"Influence of the normal pressure on the natural vibration frequencies of nearly cylindrical shells of revolution,"
Izv. AN. MTT [Mechanics of Solids], No. 6, pp. 121-126, 1996. |
|
| Received |
08 November 2000 |
| << Previous article | Volume 38, Issue 6 / 2003 | Next article >> |
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