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IssuesArchive of Issues2009-3pp.421-434

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B. Kh. Eshmatov, "Nonlinear vibrations and dynamic stability of a viscoelastic circular cylindrical shell with shear strain and inertia of rotation taken into account," Mech. Solids. 44 (3), 421-434 (2009)
Year 2009 Volume 44 Number 3 Pages 421-434
DOI 10.3103/S002565440903011X
Title Nonlinear vibrations and dynamic stability of a viscoelastic circular cylindrical shell with shear strain and inertia of rotation taken into account
Author(s) B. Kh. Eshmatov (Tashkent Institute of Irrigation and Melioration, Kary Niyazova 39, Mirzo-Ulugbekskii r-n, Tashkent, 100000 Uzbekistan, ebkh@mail.ru)
Abstract We consider nonlinear vibration and dynamic stability problems for a viscoelastic circular cylindrical shell according to the refined Timoshenko theory, which takes into account the shear strain and the inertia of rotation, in a geometrically nonlinear setting. The problem data are reduced to systems of nonlinear integro-differential equations with singular relaxation kernels, which can be solved by the Bubnov-Galerkin method combined with a numerical method based on quadrature formulas. We study the numerical convergence of the Bubnov-Galerkin method. We analyze the shell dynamic behavior in a wide range of physical-mechanical and geometric parameters. We demonstrate the influence of the viscoelastic properties of the material on the nonlinear vibrations and dynamic stability of a circular cylindrical shell. We also compare the results obtained according to different theories.
References
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20.  B.Kh. Eshmatov, "Nonlinear Vibrations of Viscoelastic Orthotropic Plates from Composite Materials," in 3rd M.I.T. Conf. Comput. Fluid and Solid Mechancis, Boston, USA (Boston, 2005), p. 93.
21.  B.Kh. Eshmatov, "Dynamic Stability of Viscoelastic Plates under Increasing Compressing Loads," Zh. Prikl. Mekh. Tekhn. Fiz. 47 (2), 165-175 (2006) [J. Appl. Mech. Tech. Phys. (Engl. Transl.) 47 (2), 289-297 (2006)].
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23.  B.Kh. Eshmatov, "Nonlinear Vibrations and Dynamic Stability of Viscoelastic Orthotropic Rectangular Plates," J. Sound Vibr. 300 (3-5), 709-726 (2007).
24.  B.Kh. Eshmatov, "Nonlinear Vibrations of Viscoelastic Cylindrical Shells Taking into Account Shear Deformation and Rotatory Inertia," J. Nonlin. Dyn. 50 (1-2), 353-361 (2007).
25.  B.Kh. Eshmatov and D.A. Khodjaev, "Nonlinear Vibrations and Dynamic Stability of a Viscoelastic Cylindrical Panel with Concentrated Mass," Acta Mech. 190 (1-4), 165-183 (2007).
Received 16 May 2006
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