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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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