Advertisement

Chaotic Dynamics of Closed Cylindrical Shells Under Local Transversal Load and Temperature Field (First-Order Kirchhoff–Love Approximation Model)

  • Vadim A. Krysko
  • Jan AwrejcewiczEmail author
  • Maxim V. Zhigalov
  • Valeriy F. Kirichenko
  • Anton V. Krysko
Chapter
Part of the Advances in Mechanics and Mathematics book series (AMMA, volume 42)

Abstract

This chapter is devoted to the study of chaotic vibrations of closed cylindrical shells subject to a local transversal load and temperature field employing the first-order Kirchhoff–Love approximations.

References

  1. 1.
    Karmishin, A. V., Mechenkov, V. I., & Frolov, A. N. (1975). Statics and dynamics of thin walled shell structures. Moscow (in Russian): Mashinostroenie.Google Scholar
  2. 2.
    Andreev, L. V., Obodan, N. I., & Lebedev, A. G. (1988). Stability of shells under non-axisymmetric deformation. Moscow (in Russian): Nauka.Google Scholar
  3. 3.
    Krysko, A. V., Awrejcewicz, J., & Saveleva, N. E. (2008). Stability, bifurcation and chaos of closed flexible cylindrical shells. International Journal of Mechanical Sciences, 50(2), 247–274.CrossRefGoogle Scholar
  4. 4.
    Awrejcewicz, J., Krysko, V. A., & Saveleva, N. E. (2007). Routes to chaos exhibited by closed flexible cylindrical shells. Journal of Computational and Nonlinear Dynamics, 2(1), 1–9.CrossRefGoogle Scholar
  5. 5.
    Krysko, V. A., Awrejcewicz, J., Saveleva, N. E., & Krysko, A. V. (2006). Dynamics of flexible shells and Sharkovskiy’s periodicity. Differential Equations and Nonlinear Mechanics, 2006, 59709.MathSciNetCrossRefGoogle Scholar
  6. 6.
    Landau, L.D. (1965). On the problem of turbulence. In: Collected Papers of L.D. Landau (pp. 387–391). New York: Elsevier.Google Scholar
  7. 7.
    Krysko, V. A. (1976). Nonlinear statics and dynamics of inhomogeneous membranes. Saratov: Publishing House Saratov University Press.Google Scholar
  8. 8.
    Krysko, A. V., Awrejcewicz, J., Kuznetsova, E. S., & Krysko, V. A. (2008). Chaotic vibrations of closed cylindrical shells in a temperature field. Shock and Vibration, 15(3–4), 335–343.CrossRefGoogle Scholar
  9. 9.
    Awrejcewicz, J., Krysko, V. A., Kutepov, I. E., Zagniboroda, N. A., Dobriyan, V., Papkova, I. V., et al. (2015). Chaotic vibrations of flexible curvilinear beams in temperature and electric fields. International Journal of Non-Linear Mechanics, 76, 29–41.CrossRefGoogle Scholar
  10. 10.
    Krysko, V. A., Awrejcewicz, J., Papkova, I. V., Kutepov, I. E., Zagniboroda, N. A., Serebryakov, A. V., et al. (2013). Chaotic dynamics of flexible beams with piezoelectric and temperature phenomena. Physics Letters A, 377, 2058–2061.MathSciNetCrossRefGoogle Scholar
  11. 11.
    Krysko, V.A., Awrejcewicz, J., Papkova, I.V., Baiburin, V.B., & Yakovleva, T.V. (2014). Non-linear phenomena exhibited by flexible cylindrical and sector shells. In: J. Awrejcewicz (Ed.) Applied Non-Linear Dynamical Systems, pp. 23–35.Google Scholar
  12. 12.
    Awrejcewicz, J., Krysko, A.V., Krysko, V.A., Krylova, E.Y., Mitskievich, S.A., Papkova, I.V., et al. (2014). Turbulent phenomena in flexible plates and shells. In: J. Awrejcewicz (Ed.) Applied Non-Linear Dynamical Systems, pp. 49–76.Google Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Vadim A. Krysko
    • 1
  • Jan Awrejcewicz
    • 2
    Email author
  • Maxim V. Zhigalov
    • 1
  • Valeriy F. Kirichenko
    • 1
  • Anton V. Krysko
    • 3
  1. 1.Department of Mathematics and ModelingSaratov State Technical UniversitySaratovRussia
  2. 2.Department of Automation, Biomechanics and MechatronicsLodz University of TechnologyLodzPoland
  3. 3.Department of Applied Mathematics and Systems AnalysisSaratov State Technical UniversitySaratovRussia

Personalised recommendations