ISSN 0869-6632 (Print)
ISSN 2542-1905 (Online)

For citation:

Krysko V. A., Sopenko A. A., Salii E. V. Complex vibrations оf geometrically and physically nonlinear shallow shells of rectangular planform. Izvestiya VUZ. Applied Nonlinear Dynamics, 2002, vol. 10, iss. 1, pp. 92-103. DOI: 10.18500/0869-6632-2002-10-1-92-103

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Language: 
Russian
Heading: 
Applied Problems of Nonlinear Oscillation and Wave Theory
Article type: 
Article
UDC: 
539.3
DOI: 
10.18500/0869-6632-2002-10-1-92-103

Complex vibrations оf geometrically and physically nonlinear shallow shells of rectangular planform

Autors: 
Krysko Vadim Anatolievich, Yuri Gagarin State Technical University of Saratov
Sopenko Aleksandr Anatolievich, Yuri Gagarin State Technical University of Saratov
Salii Ekaterina Vyacheslavovna, Yuri Gagarin State Technical University of Saratov
Abstract: 

The paper deals with the problem of dynamic response of geometrically and physically nonlinear shallow shell of rectangular planform to time-dependent transverse loading. Equations of motion were derived from the Hamilton - Ostrogradskii principle. A numerical algorithm of these equations integrating is applied to describe transition processes from periodic to chaotic vibrations for some concrete shell systems. A criterion of the loss of stability is proposed for shells subjected to alternating excitation.

Key words: 
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Reference: 
  1. Volmir AS. Nonlinear Dynamics of Plates and Shells. Moscow: Nauka; 1972. 434 p. (in Russian).
  2. Krysko VA. Nonlinear Statistics and Dynamics of Inhomogeneous Shells. Saratov: Saratov University Publishing; 1976. 216 p. (in Russian).
  3. Palmov VA. Vibrations of Elastoplastic Bodies. Moscow: Nauka; 1976. 328 p. (in Russian).
  4. Agamirov VL. Dynamic Problems of Nonlinear Shell Theory. Moscow: Nauka; 1990. 272 p. (in Russian).
  5. Moon FC. Chaotic Vibrations: An Introduction for Applied Scientists and Engineers. Wiley-VCH; 1987. 309 p.
  6. Anishchenko VS. Complex Oscillations in Simple Systems. Moscow: Nauka; 1990. 312 p. (in Russian).
  7. Bergé P, Pomeau Y, Vidal C. Order within Chaos: Towards a Deterministic Approach to Turbulence. New York: John Wiley & Sons; 1984. 329 p.
  8. Kapitaniak Т. Chaos for Engineers: Theory, Applications, and Control. Berlin - Heidelberg - New York: Springer; 1998. 140 p. DOI: 10.1007/978-3-642-97719-0.
  9. Holms PJ. A nonlinear oscillator with а strange attractor. Phil. Trans. Roy. Soc. London, Ser. А. 1979;292(1394):419-448. DOI: 10.1098/rsta.1979.0068.
  10. Moon FC. Experimental models for strange attractor vibrations in elastic systems. In: New Approaches to Non-Linear Problems in Dynamics (Proc. Conf., Pacific Grove, Calif., 1979). Philadelphia, Pa.: SIAM; 1980. P. 487-495.
  11. Hanagud S, Ashlani Е. Routes to chaos in structural dynamic systems. In: 18th Int. Congr. Theor. and Appl. Mech., Haifa, Aug. 22-28, 1992. Haifa; 1992. P. 70.
  12. Lee J-X, Symonds PS, Borino С. Chaotic responses оf а two-degree-of-freedom elastic-plastic beam model о short pulse loading. Trans. ASME: J. Appl. Mech. 1992;59(4):711-721.
  13. Lepik U. Elastic-plastic vibrations оf а buckled beam. Int. J. Non-Linear Mech. 1999;30(2):129-139. DOI: 10.1016/0020-7462(94)00035-9.
  14. Yagasaki T. Bifurcations and chaos in quasi-periodically forced beam. Theory, simulation and experiment. J. Sound Vibr. 1995;183(1):1-31. DOI: 10.1006/jsvi.1995.0236.
  15. Avreytsevich Y, Krysko VA, Krysko AV. Transition to chaos in dissipative plate structures. In: Materials of the II Belarusian Congress on Theoretical and Applied Mechanics. Minsk; 1999. P. 3 (in Russian).
  16. Krysko VA, Vakhlaeva TV, Krysko AV. Dissipative vibrations of flexible plates and the scenario of their transition to spatio-temporal chaos under harmonic longitudinal influences. In: Nonlinear Dynamics of Mechanical and Biological Systems. Saratov: SSTU; 2000. P. 8-73 (in Russian).
  17. Awrejcewicz J, Krysko VА. Feigenbaum scenario exhibited by thin plate dynamics. Nonlinear Dynamics. 2001;24(4):373-398. DOI: 10.1023/A:1011133223520.
  18. Lepik U. Axisymmetric vibrations of elastic-plastic. cylindrical shells by Galerkin’s method. Int. J. Impact. Eng. 1996;18(5):489-504. DOI: 10.1016/0734-743X(95)00055-F.
  19. Krysko AV, Mitskevich SA, Chebotarevsky YV. Dynamics of cylindrical panels under the action of longitudinal alternating loads (conservative and dissipative systems). In: Nonlinear Dynamics of Mechanical and Biological Systems. Saratov: SSTU; 2000. P. 119 (in Russian).
  20. Krysko VA, Kirichenko AV. On dynamic criteria for loss of stability of flexible flat shells. In: Nonlinear Dynamics of Mechanical and Biological Systems. Saratov: SSTU; 2000. P. 144-152 (in Russian).
  21. Krysko VA, Sopenko AA, Saliy EV. Scenario of transition into chaos of physically and geometrically nonlinear shells under the action of an alternating transverse load. In: Nonlinear Dynamics of Mechanical and Biological Systems. Saratov: SSTU; 2000. P. 108 (in Russian).
  22. Kauderer H. Nichtlineare Mechanik. Berlin: Springer-Verlag; 1958. 766 s. (in German).
  23. Kantor BY. Nonlinear Problems in the Theory of Inhomogeneous Shallow Shells. Kyiv: Naukova Dumka; 1971. 136 p. (in Russian).
  24. Shiau AC, Soong TT, Roth RS. Dynamic buckling оf conical shells with imperfections. АIАА Journal. 1974;12(6):755-760. DOI: 10.2514/3.49346.
Received: 
08.01.2002
Accepted: 
15.02.2002
Available online: 
13.12.2023
Published: 
31.07.2002
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