Table of Contents Author Guidelines Submit a Manuscript
Mathematical Problems in Engineering
Volume 2006, Article ID 35672, 25 pages
http://dx.doi.org/10.1155/MPE/2006/35672

Dynamics and statics of flexible axially symmetric shallow shells

1Department of Automatics and Biomechanics, Technical University of Lodz, 1/15 Stefanowskiego Street, Lodz 90924, Poland
2Department of Mathematics, Saratov State University, Saratov 410054, Russia

Received 24 June 2005; Accepted 12 July 2005

Copyright © 2006 J. Awrejcewicz et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. J. Awrejcewicz and V. A. Krysko, “Feigenbaum scenario exhibited by thin plate dynamics,” Nonlinear Dynamics, vol. 24, no. 4, pp. 373–398, 2001. View at Google Scholar · View at Zentralblatt MATH
  2. J. Awrejcewicz and A. V. Krysko, “Analysis of complex parametric vibrations of plates and shells using Bubnov-Galerkin approach,” Archive of Applied Mechanics, vol. 73, no. 7, pp. 495–504, 2003. View at Publisher · View at Google Scholar
  3. J. Awrejcewicz and V. A. Krysko, Nonclassical Thermoelastic Problems in Nonlinear Dynamics of Shells. Applications of the Bubnov-Galerkin and Finite Difference Numerical Methods, Scientific Computation, Springer, Berlin, 2003. View at Zentralblatt MATH · View at MathSciNet
  4. J. Awrejcewicz and V. A. Krysko, “Nonlinear coupled problems in dynamics of shells,” International Journal of Engineering Science, vol. 41, no. 6, pp. 587–607, 2003. View at Google Scholar · View at MathSciNet
  5. J. Awrejcewicz, V. A. Krysko, and A. V. Krysko, “Spatial-temporal chaos and solitons exhibited by von Kármán model,” International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, vol. 12, no. 7, pp. 1465–1513, 2002. View at Google Scholar
  6. J. Awrejcewicz, V. A. Krysko, and A. V. Krysko, “Complex parametric vibrations of flexible rectangular plates,” Meccanica. International Journal of the Italian Association of Theoretical and Applied Mechanics, vol. 39, no. 3, pp. 221–244, 2004. View at Google Scholar · View at MathSciNet
  7. J. Awrejcewicz, V. A. Krysko, and G. G. Narkaitis, “Bifurcations of a thin plate-strip excited transversally and axially,” Nonlinear Dynamics, vol. 32, pp. 187–209, 2003. View at Google Scholar
  8. J. Awrejcewicz, V. A. Krysko, and A. F. Vakakis, Nonlinear Dynamics of Continuous Elastic Systems, Springer, Berlin, 2004. View at Zentralblatt MATH · View at MathSciNet
  9. V. F. Fedos'ev, “Application of the step method to analyse stability of compressed rod,” Prikladnaya Matematika i Mekhanika, vol. 27, no. 5, pp. 833–841, 1963 (Russian). View at Google Scholar
  10. V. F. Fedos'ev, “On the method of solutions of stability of deformable bodies,” Prikladnaya Matematika i Mekhanika, vol. 27, no. 2, pp. 265–275, 1963 (Russian). View at Google Scholar
  11. M. J. Feigenbaum, “The universal metric properties of nonlinear transformations,” Journal of Statistical Physics, vol. 21, no. 6, pp. 669–706, 1979. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  12. A. Hübler and E. Lüscher, “Resonant stimulation and control of nonlinear oscillators,” Naturwissenschaften, vol. 76, no. 2, pp. 67–69, 1989. View at Google Scholar
  13. E. A. Jackson, “The entrainment and migration controls of multiple-attractor systems,” Physics Letters. A, vol. 151, no. 9, pp. 478–484, 1990. View at Google Scholar · View at MathSciNet
  14. E. A. Jackson, “On the control of complex dynamic systems,” Physica D. Nonlinear Phenomena, vol. 50, no. 3, pp. 341–366, 1991. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  15. V. A. Krysko, J. Awrejcewicz, and V. M. Bruk, “On the solution of a coupled thermo-mechanical problem for non-homogeneous {T}imoshenko-type shells,” Journal of Mathematical Analysis and Applications, vol. 273, no. 2, pp. 409–416, 2002. View at Google Scholar · View at MathSciNet
  16. V. A. Krysko and I. V. Kravtsova, “Stochastic vibrations of flexible flat axisymmetric shells exposed inhomogeneous loading,” in Proceedings of 7th International Conference on Dynamics of System—Theory and Applications (Łódź, 2003), pp. 189–197, 2003.
  17. V. A. Krysko and I. V. Kravtsova, “Stochastic vibrations of flexible axially symmetric supported along contour spherical shells,” Izviestia VUZ, Maschinostroyeniye, vol. 1, pp. 3–13, 2004 (Russian). View at Google Scholar
  18. V. A. Krysko and T. V. Shchekaturova, “Chaotic vibrations of shallow shells,” Izviesta AN Mekhanika Tviordoga Tela, vol. 4, pp. 140–150, 2004 (Russian). View at Google Scholar
  19. L. D. Landau, “On the problem of a turbulence,” Doklady Akademii Nauk, vol. 44, no. 8, pp. 339–342, 1944 (Russian). View at Google Scholar
  20. B. B. Mandelbrot, The Fractal Geometry of Nature, Schriftenreihe für den Referenten, W. H. Freeman, California, 1982. View at Zentralblatt MATH · View at MathSciNet
  21. P. Manneville and Y. Pomeau, “Different ways to turbulence in dissipative dynamical systems,” Physica D. Nonlinear Phenomena, vol. 1, no. 2, pp. 219–226, 1980. View at Google Scholar · View at MathSciNet
  22. E. Ott, C. Grebogi, and J. A. Yorke, “Controlling chaos,” Physical Review Letters, vol. 64, no. 11, pp. 1196–1199, 1990. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  23. V. Petrov, V. Gaspar, J. Massere, and K. Showalter, “Controlling chaos in the Belousov-Zhabotinsky reaction,” Nature, vol. 361, no. 6409, pp. 240–243, 1993. View at Google Scholar
  24. D. Ruelle and F. Takens, “On the nature of turbulence,” Communications in Mathematical Physics, vol. 20, pp. 167–192, 1971. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  25. S. J. Schiff, K. Jerger, D. H. Duong, T. Chang, M. L. Spano, and W. L. Ditto, “Controlling chaos in the brain,” Nature, vol. 370, no. 6491, pp. 615–620, 1994. View at Google Scholar
  26. T. Shinbrot, C. Grebogi, J. A. Yorke, and E. Ott, “Using small perturbations to control chaos,” Nature, vol. 363, no. 6428, pp. 411–417, 1993. View at Google Scholar
  27. J. Singer, Y.-Z. Wang, and H. H. Bau, “Controlling a chaotic system,” Physical Review Letters, vol. 66, no. 9, pp. 1123–1125, 1991. View at Google Scholar
  28. S. Smale, “Dynamical systems and turbulence,” in Turbulence Seminar (Univ. Calif., Berkeley, Calif., 1976/1977), vol. 615 of Lecture Notes in Math., pp. 48–70, Springer, Berlin, 1977. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  29. N. V. Valishvili, Methods of Computation of Rotational Shells, Mashinostroyeniye, Moscow, 1976.