 | | 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: | | 11223 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8011
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| In English (Mech. Solids): | | 3212 |
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| V.A. Krys'ko, I.V. Papkova, and V.V. Soldatov, "Analysis of Nonlinear Chaotic Vibrations of Shallow Shells of Revolution by Using the Wavelet Transform," Mech. Solids. 45 (1), 85-93 (2010) |
| Year |
2010 |
Volume |
45 |
Number |
1 |
Pages |
85-93 |
| DOI |
10.3103/S0025654410010127 |
| Title |
Analysis of Nonlinear Chaotic Vibrations of Shallow Shells of Revolution by Using the Wavelet Transform |
| Author(s) |
V.A. Krys'ko (Saratov State Technical University, Politekhnicheskaya 77, Saratov, 410054 Russia, tak@san.ru)
I.V. Papkova (Saratov State Technical University, Politekhnicheskaya 77, Saratov, 410054 Russia, IKravzova@mail.ru)
V.V. Soldatov (Saratov State Technical University, Politekhnicheskaya 77, Saratov, 410054 Russia, v_soldatow@mail.ru) |
| Abstract |
In the present paper, we study complex vibrations of flexible axisymmetric shallow shells under the action of transverse sing-alternating pressure. In addition to the traditional methods of nonlinear dynamics, we for the first time use the wavelet transform to analyze the transition from harmonic to chaotic vibrations. We analyze the use of Gauss-type wavelets (the order of derivatives varies from m=1 to m=8) and also the use of the Morlet wavelet (both real and complex). We conclude that the use of the complex Morlet wavelet is preferable to that of the Gaussian wavelets: the more zero moments a wavelet has, the better it describes the complex vibrations of flexible shallow shells. |
| Keywords |
wavelet analysis, Morlet wavelet, flexible axisymmetric shallow shell, nonlinear vibrations, nonlinear dynamics |
| References |
| 1. | J. Awrejcewicz, V. A. Krys'ko, and A. F. Vakakis,
Nonlinear Dynamics of Continuous Elastic Systems
(Springer, Berlin, 2004). |
| 2. | J. Awrejcewicz and V. A. Krys'ko,
Nonclassical Thermoelastic Problems in Nonlinear Dynamics of Shells
(Springer, Berlin, 2003). |
| 3. | J. Awrejcewicz, V. A. Krys'ko, and A. V. Krys'ko,
Thermo-Dynamics of Plates and Shells
(Springer, Berlin, 2007). |
| 4. | J. Awrejcewicz and V. A. Krys'ko,
Chaos in Structural Mechanics
(Springer, Berlin, 2008). |
| 5. | V. A. Krys'ko, J. Awrejcewicz, E. S. Kusnetsova, and A. V. Krys'ko,
"Chaotic Vibrations of Closed Cylindrical Shells in a Temperature Field,"
Int. J. Bif. Chaos
18 (5), 1551-1529 (2008). |
| 6. | V. A. Krys'ko, J. Awrejcewicz, E. S. Kusnetsova, and A. V. Krys'ko,
"Chaotic Vibrations of Closed Cylindrical Shells in a Temperature Field,"
Shock Vibr. Part 2,
15 (3-4), 335-343 (2008). |
| 7. | J. Awrejcewicz and V. A. Krys'ko,
Introduction to Asymptotic Methods
(Chapman and Hall, London, 2006). |
| 8. | V. A. Krys'ko and I. V. Kravtsova,
"Control of Chaotic Vibrations in Flexible Spherical Shells,"
Izv. Akad. Nauk. Mekh. Tverd. Tela,
No. 1, 161-172 (2006)
[Mech. Solids (Engl. Transl.)
41 (1), 124-134 (2006)]. |
| 9. | V. A. Krys'ko and T. V. Shchekaturova,
"Chaotic Vibrations of Cone Shells,"
Izv. Akad. Nauk. Mekh. Tverd. Tela,
No. 5, 153-163 (2004)
[Mech. Solids (Engl. Transl.)
39 (5), 124-133 (2004)]. |
| 10. | A. Grossmann and S. Morlet,
"Decomposition of Hardy Functions into Square Integrable Wavelets of Constant Shape,"
SIAM J. Math. Anal.
15 (4), 723-736 (1984). |
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"Nonlinear Physics. Stochastic and Structures,"
in Physics of 20th Century. Development and Perspectives
(Nauka, Moscow, 1984),
pp. 219-280
[in Russian]. |
| 13. | R. Van Buskirk and C. Jeffries,
"Observations of Chaotic Dynamics of Coupled Nonlinear Oscillators,"
Phys. Rev. A
31 (5), 3332-3357 (1985). |
| 14. | N. V. Valishvili,
Computer Methods for Calculations of Shells of Revolution
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[in Russian]. |
| 15. | M. J. Feigenbaum,
"Quantitative Universality for a Class of Nonlinear Transformations,"
J. Stat. Phys.
19 (1), 25-52 (1978). |
|
| Received |
15 July 2008 |
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