 | | 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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| S. N. Kukudzhanov, "Effect of meridional loads on the natural vibrations and dynamic stability of a nearly-cylindrical shell of revolution," Mech. Solids. 40 (1), 132-141 (2005) |
| Year |
2005 |
Volume |
40 |
Number |
1 |
Pages |
132-141 |
| Title |
Effect of meridional loads on the natural vibrations and dynamic stability of a nearly-cylindrical shell of revolution |
| Author(s) |
S. N. Kukudzhanov (Tbilisi) |
| Abstract |
Effects of meridional edge loads (compressive and tensile) on the
vibration modes, lowest natural vibration frequencies and dynamic
stability of a nearly cylindrical shell of revolution are studied.
Moderately long shells are considered with the midsurface generating
curve described by a parabola. On the basis of the shallow shell
theory, the governing equation of the vibration modes 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. Non-dimensional formulas and universal
curves for the dependence of the lowest vibration frequency, vibration
mode and boundaries of the dynamic instability region on the initial
loads and the amplitude of shell shape deflection from a
cylinder. It is shown that once the initial loads are present, the
shell shape deviation from a cylinder (by values of the order of its
wall thickness) can lead to substantial variation in the lowest
frequencies, vibration modes and boundaries of the dynamic instability
region. |
| References |
| 1. | V. M. Darevskii, "Buckling 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. 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, Moscow, 1995. |
| 5. | 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. |
| 6. | 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. |
| 7. | 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. |
| 8. | S. S. Kann, "Buckling of axially compressed shells of revolutions
with curvilinear generating curves," Prikl. Mekhanika, Vol. 2, No. 1,
pp. 59-68, 1966. |
| 9. | M. D. Strutt, Lamé, Mathieu and Related Functions in Physics and
Engineering [Russian translation],
DNTVU, Kharkov, Kiev, 1935. |
| 10. | V. V. Bolotin, Dynamic Stability of Elastic Systems
[in Russian],
Gostekhizdat, Moscow, 1956. |
|
| Received |
13 March 2003 |
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