 | | 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: | | 11223 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8011
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| In English (Mech. Solids): | | 3212 |
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| S. N. Kukudzhanov, "Vibrations and dynamic stability of nearly-cylindrical shells of revolution subjected to normal pressure and meridional loads," Mech. Solids. 41 (2), 36-46 (2006) |
| Year |
2006 |
Volume |
41 |
Number |
2 |
Pages |
36-46 |
| Title |
Vibrations and dynamic stability of nearly-cylindrical shells of revolution subjected to normal pressure and meridional loads |
| Author(s) |
S. N. Kukudzhanov (Tbilisi) |
| Abstract |
Natural vibrations and dynamic stability of nearly cylindrical
shells of revolution subjected to meridional loads uniformly
distributed over the shell edges and to the normal pressure
uniformly distributed over the shell surface are studied. Moderately
long shells with the midsurface generatrix described by a parabola
are considered. On the basis of the shallow shell theory, the
governing equation for the vibration of a pre-stressed shell is
obtained. This equation differs from the known one [1] in an
additional term which can be of the same order of magnitude as all
other terms taken into account. Shells of positive and negative
Gaussian curvatures are considered. The shell edges are assumed to
be simply supported. The main attention is given to the fundamental
vibration frequencies which are most important in practical
applications. Non-dimensional relations and universal curves for
the dependence of the fundamental vibration frequency, vibration
mode shapes, and boundaries of the dynamic instability region on the
pre-stresses, Gaussian curvature, and the amplitude of the shell
shape deflection from a cylinder are obtained. It is shown that in
the pre-stressed case,
the deviation of the shell shape from a
cylinder (commensurable with the wall thickness) can lead to
substantial changes in the fundamental frequencies, vibration mode shapes, and
boundaries of the dynamic instability regions. |
| References |
| 1. | V. M. Darevskii, "Buckling of a nearly-cylindrical shell,"
in Problems of Design of Spatial Structures [in Russian], MISI, Moscow,
pp. 35-45, 1980. |
| 2. | A. S. Vol'mir, Stability of Deformable Systems [in Russian],
Nauka, Moscow, 1967. |
| 3. | V. Z. Vlasov, General Theory of Shells and its Engineering Applications [in Russian],
Gostekhizdat, Moscow, Leningrad, 1995. |
| 4. | P. E. Tovstik, Buckling of Thin Shells. Asymptotic Methods [in Russian],
Nauka, Fizmatlit, Moscow, 1995. |
| 5. | E. I. Grigolyuk and V. V. Kabanov, Buckling of Shells,
Nauka, Moscow, 1978. |
| 6. | S. N. Kukudzhanov, "On the effect of the normal pressure on
the natural frequencies of cylindrical shells," Inzh. Zh. MTT
[Mechanics of Solids], No. 3, pp. 140-144, 1968. |
| 7. | S. N. Kukudzhanov, "On the effect of the normal pressure on the
natural frequencies of nearly-cylindrical shells of revolution,"
Izv. AN. MTT [Mechanics of Solids], No. 6, pp. 121-126, 1996. |
| 8. | Kh. M. Mushtari and A. V. Sachenkov,
"On the buckling of cylindrical and conical shells with circular base under
combined action of axial compression and normal pressure,"
PMM [Applied Mathematics and Mechanics], Vol. 18, No. 6, pp. 667-674, 1954. |
| 9. | M. V. Nikulin, "Effects of the axial loads on the
natural vibration frequencies of a cylindrical shell,"
In: Buckling of Cylindrical Shells [in Russian],
Oborongiz, Moscow, 1959. |
| 10. | M. D. Strutt, Lamé, Mathieu and Related Functions in Physics and
Engineering [Russian translation],
DNTVU, Kharkov, Kiev, 1935. |
| 11. | V. V. Bolotin, Dynamic Stability of Elastic Systems
[in Russian],
Gostekhizdat, Moscow, 1956. |
|
| Received |
13 April 2004 |
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