Chaotic vibrations of spherical and conical axially symmetric shells

Archive of Applied Mechanics

Volumn 74, Issue 5-6, 2005, Pages 338-358

  Krysko, V A ^a   Awrejcewicz, J ^b   Shchekaturova, T V ^a  

^a SARATOV STATE UNIVERSITY   (Russian Federation)

^b LODZ UNIVERSITY OF TECHNOLOGY   (Poland)

Author keywords

Cauchy problem; Chaos; Ritz procedure; Shells

Indexed keywords

BENDING (DEFORMATION); DAMPING; DIFFERENTIAL EQUATIONS; HARMONIC ANALYSIS; LOADS (FORCES); PROBLEM SOLVING; RUNGE KUTTA METHODS; VIBRATIONS (MECHANICAL);

CAUCHY PROBLEM; CONICAL SHELLS; RITZ PROCEDURE; SHELLS;

CHAOS THEORY;

EID: 15544365734     PISSN: 09391533     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00419-004-0356-3     Document Type: Article

References (25)

1. Awrejcewicz, J.; Krysko, V.A.: Nonclassical thermoelastic problems in nonlinear dynamics of shells. Berlin, Springer (2003)
2. Awrejcewicz, J.; Krysko, V.A; Krysko, A.V.: Regular and chaotic behaviour of flexible plates. In: J. Zaraś, K. Kowal-Michalska and J. Rhodes (eds.), Proceedings of the third international conference on thin-walled structures, 5-7, June 2001, Cracow, Poland Elsevier, Amsterdam (2001), 349-356
3. Awrejcewicz, J.; Krysko, V.A; Krysko, A.V.: Spatial-temporal chaos and solitons exhibited by von Kármán model. Int J Bifur Chaos 12(7) (2002) 1405-1513
4. Krysko, V.A; Narkaitis, G.G.; Awrejcewicz, J.: Bifurcations of thin plates transversally and sinusoidally excited. In: H. Grundmann, G. I. Schuëller (eds.), Proceedings of the fourth international conference on structural dynamics EURODYN 2002 Munich, Germany, 2-5 September, (2002) 529-534 (2003)
5. Awrejcewicz, J.; Krysko, V.A.: Nonlinear coupled problems in dynamics of shells. Int J Eng Sci 41(6) (2003) 587-607
6. Awrejcewicz, J.; Krysko, V.A.: Feigenbaum scenario exhibited by thin plate dynamics. Nonlin Dyn 24 (2001) 373-398
7. Krysko, V.A; Sopenko, A.A.; Saliy, E.V.: Complex vibrations of geometrically and physically nonlinear rectangular shallow shells. Izviestia VUZ, Appl Nonl Dyn 1-2 (2002) 92-103 (in Russian)
8. Novozhilov, V.V.: Introduction to nonlinear theory of elasticity. Gostekhizdat, Moscow (1948) (in Russian)
9. Volmir, A.S.: Stability of deformable bodies. Moscow, Nauka (1968), (in Russian)
10. Fedos'ev, V.I.: On one method of solution to stability problems of elastic systems. PMM 27(2) (1963) 265-275 (in Russian)
11. Kantor, B.J.: Nonlinear problems of theory of nonhomogeneous shallow shells. Kiev, Naukova Dumka 1971 (in Russian)
12. Lorenz, E.N.: Deterministic non-periodic flow. Atmos Sci 20(1) (1963) 130-141
13. Curry, J.H.; Herring, J.R.; Loncaric, J.; Orszag, S.A.: Order disorder in two- and three-dimensional Bénárd convection. J Fluid Mech 147(1) (1984) 1-38
14. Collet, P.; Ekcmann, J.-P.: Iterated maps on the interval as dynamical systems. Birkhauser Boston (1980)
15. Tien-Yien, Li; Yorke, J.A.: Period three implies chaos. Am Math Monthly 82 (1975) 985-992
16. Sharkovskii, A.N.: Coexistence of cycles of a continuous map of a line into itself. Ukr Mat Zh 16(1) (1964) 61-71
17. Landau, L.D.: Turbulence. Dokl Acad Nauk SSSR 44(8) (1944) 339-342
18. Krysko, V.A; Krysko, A.V.: Problems of bifurcation and stiff stability loss in nonlinear theory of plates. Mechanics of Shell and Plates in XXI century. Saratov Technical University Press, Saratov 50-67
19. Feigenbaum, M.J.: The universal metric properties of nonlinear transformations. J Stat Phys 21(6) (1979) 669-706
20. Shilnikov, L.P.: Theory of bifurcations and turbulence. Problems of nonlinear and turbulent process in physics (Part 2). Naukova Dumka, Kiev (1985), 118-124
21. Smale, S.: Dynamical systems and turbulence. Lect Notes Math (1962) 615
22. Awrejcewicz, J., Krysko, V.A., Narkaitis, G.G.: Bifurcations of a thin plate-strip excited transversally and axially. Nonlin Dyn 32 (2003) 187-209
23. Bennetin, G., Casartelli, M., Galgani, L., Giorgilli, A., Strelcyn, J.M.: On the reliability of numerical study of stochasticity, I: existence of time averages. Il. Nuovo Cimento 44B(1) (1978) 183-195
24. Bennetin, G., Casartelli, M., Galgani, L., Giorgilli A., Strelcyn, J.M.: On the reliability of numerical studies of stochasticity, II: identification of time averages. Il Nuovo Cimento 50B (1979) 211-232
25. Awrejcewicz, J., Krysko, V.A.: Analysis of complex parametric vibrations of plates and shells using Bubnov-Galerkin approach. Arch Appl Mech 73 (2003) 495-504