 | | 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 |
|
| << Previous article | Volume 44, Issue 3 / 2009 | Next article >> |
| 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 |
| 1. | A.S. Volmir,
Nonlinear Dynamics of Plates and Shells
(Nauka, Moscow, 1972) [in Russian]. |
| 2. | L.H. Donnell,
Beams, Plates, and Shells
(McGraw-Hill, New York, 1976). |
| 3. | S.P. Timoshenko,
Vibration Problems in Engineering
(Nauka, Moscow, 1967) [in Russian]. |
| 4. | R.D. Mindlin,
"Influence of rotatory Inertia and Shear on Flexural Motions of Isotropic, Elastic Plates,"
J. Appl. Mech. 18 (1), 31-38 (1951). |
| 5. | Ya.S. Uflyand,
"Wave Propagation in Transverse Oscillations of Rods and Plates,"
Prikl. Mat. Mekh. 12 (3), 287-300 (1948). |
| 6. | E. Reissner,
"The Effect of Transverse Shear Deformation on the Bending of Elastic Plates,"
J. Appl. Mech. 12 (2), 69-77 (1945). |
| 7. | S.A. Ambartsumyan,
General Theory of Anisotropic Shells
(Nauka, Moscow, 1974) [in Russian]. |
| 8. | A.A. Il'yushin and B.E. Pobedrya,
Foundations of the Mathematical Theory of Thermoviscoelasticity
(Nauka, Moscow, 1970) [in Russian]. |
| 9. | Yu.N. Rabotnov,
Elements of Hereditary Mechanics of Solids
(Nauka, Moscow, 1977) [in Russian]. |
| 10. | A.E. Bogdanovich,
Nonlinear Dynamic Problems for Composite Cylindrical Shells
(Zinatne, Riga, 1987; Chapman and Hall, London, 1993). |
| 11. | J. Awrejcewicz and V.A. Krys'ko,
Nonclassical Thermoelastic Problems in Nonlinear Dynamics of Shells. Applications of the Bubnov-Galerkin and Finite Difference Numerical Methods
(Springer, Berlin, 2003). |
| 12. | K. Shirakawa,
"Effects of Shear Deformation and Rotatory Inertia
on Vibration and Buckling of Cylindrical Shells,"
J. Sound Vibr. 91 (3), 425-437 (1983). |
| 13. | A. Okazaki, A. Tatemichi, and S. Mirza,
"Damping Properties of Two-Layered Cylindrical Shells
with an Unconstrained Viscoelastic Layer,"
J. Sound Vibr. 176 (2), 145-161 (1994). |
| 14. | Cheng Chang-jun and Zhang Neng-hui,
"Dynamical Behavior of Viscoelastic Cylindrical Shells under Axial Pressures,"
Appl. Math. Mech. 22 (1), 1-9 (2001). |
| 15. | V.I. Kozlov and T.V. Karnaukhova,
"Basic Equations for Viscoelastic Laminated Shells
with Distributed Piezoelectric Inclusions Intended to Control Nonstationary Vibrations,"
Int. Appl. Mech. 38 (10), 1253-1260 (2002). |
| 16. | V.D. Potapov,
Stability of Stochastic Elastic and Viscoelastic Systems
(Wiley, Chichester, England, 1999). |
| 17. | M.A. Koltunov,
Creep and Relaxation
(Vysshaya Shkola, Moscow, 1976) [in Russian]. |
| 18. | F.B. Badalov, B.Kh. Eshmatov, and M. Yusupov,
"On Certain Methods of Solving Systems of Integrodifferential Equations Encountered in Viscoelasticity Problems,"
Prikl. Mat. Mekh. 51 (5), 867-871 (1987)
[J. Appl. Math. Mech. (Engl. Transl.) 51 (5), 683-686 (1987)]. |
| 19. | F.B. Badalov and B.Kh. Eshmatov,
"Short Survey and Comparison of Integral Methods of Mathematica Simulation in Problems of Hereditary Mechanics of Solids,"
Elektronnoe Modelirovanie 11 (2), 81-90 (1989) [Electronic Modeling (Engl. Transl.)]. |
| 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)]. |
| 22. | B.Kh. Eshmatov,
"Nonlinear Vibration Analysis of Viscoelastic Plates Based on a Refined Timoshenko Theory,"
J. Int. Appl. Mech. 42 (5), 596-605 (2006). |
| 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 |
| Link to Fulltext |
|
| << Previous article | Volume 44, Issue 3 / 2009 | Next article >> |
|
 If you find a misprint on a webpage, please help us correct it promptly - just highlight and press Ctrl+Enter
|
|
Russian 
English