 | | 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
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| In English (Mech. Solids): | | 4760 |
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| S. P. Kuntsevich and G. I. Mikhasev, "Local parametric vibrations of a noncircular conical shell subjected to nonuniform pulsating pressure," Mech. Solids. 37 (3), 134-139 (2002) |
| Year |
2002 |
Volume |
37 |
Number |
3 |
Pages |
134-139 |
| Title |
Local parametric vibrations of a noncircular conical shell subjected to nonuniform pulsating pressure |
| Author(s) |
S. P. Kuntsevich (Vitebsk)
G. I. Mikhasev (Vitebsk) |
| Abstract |
The problem of parametric instability is studied for a thin conical shell
subjected to nonuniform pulsating pressure. The edges of the shell (not
necessary planar curves) are simply supported. The excitation frequency is
assumed to be close to the twice the fundamental natural frequency of the
shell. By using the WKB method combined with the method of multiple time
scales we construct solutions of the governing equations as functions
decreasing away from a certain "most weak" generatrix and slowly
increasing in time in the case of parametric resonance. Taking into account
the viscous friction, we find the boundaries of the principal domain of
local parametric instability. |
| References |
| 1. | V. V. Bolotin, Dynamic Stability of Elastic Systems [in Russian],
Gostekhizdat, Moscow, 1956. |
| 2. | A. N. Markov, "Dynamic stability of anisotropic cylindrical
shells," PMM [Applied Mathematics and Mechanics], Vol. 13, No. 2,
pp. 145-150, 1949. |
| 3. | O. D. Oniashvili, "On the dynamic stability of shallow shells,"
Soobshch. AN GSSR, Vol. 11, No. 3, pp. 169-175, 1950. |
| 4. | J. C. Yao, "Dynamic stability of cylindrical shells under static
and periodic axial and radial loads," AIAA Journal, Vol. 1, No. 4,
pp. 985-990, 1963. |
| 5. | A. Vijayaraghavan and R. M. Evan-Iwanowski, "Parametric instability
of circular cylindrical shell," Trans. ASME, Ser. E, J. Appl. Mech.,
Vol. 34, No. 4, pp. 985-990, 1967. |
| 6. | G. M. Sal'nikov, "Dynamic stability of cylindrical and conical
shells of circular and noncircular cross-section subjected to different
boundary conditions," in Studies on the Theory of Plates and Shells.
Volume 5 [in Russian], pp. 469-479, Izd-vo Kazan. Un-ta, Kazan, 1967. |
| 7. | A. Kornecki, "Dynamic stability of truncated conical shells under
pulsating pressure," Israel J. Technol., Vol. 4, No. 1-2, pp. 110-120,
1966. |
| 8. | A. L. Goldenveizer, V. B. Lidskii, and P. E. Tovstik, Free
Vibrations of Thin Elastic Shells [in Russian], Nauka, Moscow, 1979. |
| 9. | P. E. Tovstik, Stability of Thin Shells: Asymptotic Methods [in
Russian], Nauka, Fizmatgiz, Moscow, 1995. |
| 10. | V. V. Novozhilov, Theory of Thin Shells [in Russian], Sudpromgiz,
Leningrad, 1962. |
| 11. | G. I. Mikhasev, "Free and parametric vibrations of cylindrical
shells under static and periodic axial loads," Technische Mechanik,
Bd. 17, H. 3, S. 209-216, 1997. |
| 12. | P. E. Tovstik, "On the definition of the lowest frequency of a
conical shell of revolution," in Studies on the Elasticity and Plasticity
[in Russian], pp. 109-116, Izd-vo LGU, Leningrad, 1967. |
| 13. | G. I. Mikhasev and S. P. Kuntsevich, "Thermoelastic vibrations of
noncircular cylindrical shells in nonstationary temperature field,"
Technische Mechanik, Bd. 17, H. 2, S. 113-120, 1997. |
| 14. | S. P. Kuntsevich and G. I. Mikhasev, "Parametric vibrations of
viscoelastic cylindrical shells under static and periodic axial loads,"
Technische Mechanik, Bd. 19, H. 3, S. 187-195, 1999. |
|
| Received |
10 January 2000 |
| << Previous article | Volume 37, Issue 3 / 2002 | Next article >> |
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