Advertisement

Numerical Analysis of Nonstationary Vibrations of Discretely Reinforced Multilayer Shells of Different Geometry

  • V. F. MeishEmail author
  • Yu. A. Meish
  • N. V. Arnauta
Article

The forced vibrations of discretely reinforced multilayer cylindrical, spherical, and conical shells under nonstationary loading are studied. The dynamic behavior of the shells is studied using Timoshenko-type theory of shells and rods. Problem statements are presented and a numerical algorithm of solving problems of this class is elaborated. Numerical examples of dynamic behavior of the shells are presented, and the results obtained are analyzed.

Keywords

shells of revolution Timoshenko-type theory of shells and rods numerical method nonstationary vibrations 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    I. Ya. Amiro, V. A. Zarutskii, and V. G. Palamarchuk, Dynamics of Ribbed Shells [in Russian], Naukova Dumka, Kyiv (1983).zbMATHGoogle Scholar
  2. 2.
    K. G. Golovko, P. Z. Lugovoi, and V. F. Meish, Dynamics of Inhomogeneous Shells under Nonstationary Loads [in Russian], Kievskii Universitet, Kyiv (2012).Google Scholar
  3. 3.
    I. Ya. Amiro, V. A. Zarutskii, V. N. Revutskii, Yu. V. Skosarenko, A. I. Telalov, and S. Yu. Fialko, Vibrations of Ribbed Shells of Revolution [in Russian], Naukova Dumka, Kyiv (1988).Google Scholar
  4. 4.
    G. I. Marchuk, Methods of Computational Mathematics [in Russian], Nauka, Moscow (1977).Google Scholar
  5. 5.
    A. A. Samarskii, Theory of Difference Schemes [in Russian], Nauka, Moscow (1977).zbMATHGoogle Scholar
  6. 6.
    H. Altenbach, “Theories for laminated and sandwich plates: A review,” Mech. of Comp. Mater., 34, No. 3, 243–252 (1998).ADSCrossRefGoogle Scholar
  7. 7.
    V. M. Efimtsov and L. A. Lazarev, “Forced vibrations of plates and cylindrical shells with regular orthogonal system of stiffeners,” J. Sound Vibr., 327, No. 1–2, 41–54 (2009).ADSCrossRefGoogle Scholar
  8. 8.
    P. Z. Lugovoi and V. F. Meish, “Dynamics of inhomogeneous shell systems under nonstationary loading (Survey),” Int. Appl. Mech., 53, No. 5, 481–537 (2017).ADSCrossRefGoogle Scholar
  9. 9.
    V. F. Meish and N. V. Maiborodina, “Stress state of discretely stiffened ellipsoidal shells under a nonstationary normal load,” Int. Appl. Mech., 54, No. 6, 675–686 (2018).ADSMathSciNetCrossRefGoogle Scholar
  10. 10.
    V. F. Meish, Yu. A. Meish, and A. V. Pavlyuk, “Dynamics of a three-layer elliptic cylindrical shell reinforced with discrete rings,” Int. Appl. Mech., 54, No. 2, 172–179 (2018).ADSMathSciNetCrossRefGoogle Scholar
  11. 11.
    A. K. Noor and W. S. Burton, “Assessment of computational models of multilayered composite shells,” Appl. Mech. Rev., 43, No. 4, 67–97 (1990).ADSCrossRefGoogle Scholar
  12. 12.
    N. J. Pagano, “Exact solutions for composite laminates in cylindrical bending,” J. Comp. Mater., 3, 389–411 (1969).Google Scholar
  13. 13.
    N. J. Pagano, “Free edge stress fields in composite laminates,” Int. J. Solids Struct., 14, 401–406 (1978).CrossRefGoogle Scholar
  14. 14.
    M. S. Qatu, “Recent research advances in the dynamic behavior of shells. Part 1: Laminated composite shells,” Appl. Mech. Rev., 55, No. 4, 325–350 (2002).ADSCrossRefGoogle Scholar
  15. 15.
    M. S. Qatu, R. W. Sullivan, and W. Wang, “Recent research advances in the dynamic behavior of composite shells,” Compos. Struct., 93, No. 1, 14–31 (2010).CrossRefGoogle Scholar
  16. 16.
    J. N. Reddy and C. F. Liu, “A higher-order shear deformation theory of laminated elastic shells,” Int. J. Eng. Sci., 23, 669–683 (1985).CrossRefGoogle Scholar
  17. 17.
    J. N. Reddy, “On refined computational models of composite laminates,” Int. J. Numer. Meth. Eng., 27, 361–382 (1989).MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.S. P. Timoshenko Institute of MechanicsNational Academy of Sciences of UkraineKyivUkraine

Personalised recommendations