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IssuesArchive of Issues2008-5pp.815-826

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S. N. Kukudzhanov, "Dynamic stability of nearly cylindrical orthotropic shells of revolution subjected to meridional forces," Mech. Solids. 43 (5), 815-826 (2008)
Year 2008 Volume 43 Number 5 Pages 815-826
DOI 10.3103/S0025654408050178
Title Dynamic stability of nearly cylindrical orthotropic shells of revolution subjected to meridional forces
Author(s) S. N. Kukudzhanov (Razmadze Mathematical Institute, Georgian Academy of Sciences, M. Aleksidze 1, Tbilisi, 0193, Georgia, sergo@rmi.acnet.ge)
Abstract We study the natural vibrations and the dynamic stability of nearly cylindrical orthotropic shells of revolution subjected to meridional forces uniformly distributed over the shell ends. We consider shells of medium length for which the shape of the midsurface generatrix is described by a parabolic function. Using the theory of shallow shells, we obtain the resolving equation for the vibrations of the corresponding prestressed shell. In the isotropic case, this equation differs from the well-known equation [1] by an additional term, which can be of the same order as the other terms taken into account. We consider shells of both positive and negative Gaussian curvature. We assumed that the shell ends are freely supported. The formulas and universal curves describing the dependence of the minimum frequency, the wave generation shape, and the dynamic instability domain boundaries on the orthotropy parameters, the preliminary stress, the Gaussian curvature, and the amplitude of the shell deviation from the cylinder are given in dimensionless form. We find that in the case of prestresses the orthotropy parameters and the shell deviation from the cylinder (of the order of thickness) can significantly change the least frequencies, the wave generation shape, and the dynamic instability domain boundaries of the corresponding prestressed orthotropic cylindrical shell.

In this case, we note that for convex shells under preliminary compression the influence of the elastic parameter in the axial direction is stronger than the influence of the elastic parameter in the circular direction, while the situation is opposite in the case of concave shells. In the case of preliminary extension, the leading role of any orthotropy parameter can vary depending on the value of the preliminary stress and the Gaussian curvature.
Received 15 June 2005
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