International Applied Mechanics

, Volume 54, Issue 1, pp 75–84 | Cite as

Numerical Determination of Natural Frequencies and Modes of the Vibrations of a Thick-Walled Cylindrical Shell

  • A. Ya. Grigorenko
  • M. Yu. Borisenko
  • E. V. Boichuk
  • A. P. Prigoda

The dynamic characteristics of a thick-walled cylindrical shell are determined numerically using the finite-element method implemented with licensed FEMAR software. The natural frequencies and modes are compared with those obtained earlier experimentally by the method of stroboscopic holographic interferometry. Frequency coefficients demonstrating how the natural frequency depends on the physical and mechanical parameters of the material are determined.


natural frequencies vibration modes thick-walled cylindrical shell finite-element method stroboscopic holographic interferometry 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    V. D. Budak, O. Ya. Grigorenko, M. Yu. Borisenko, and O. V. Boychuk, “Free vibrations of an elliptic shell of variable thickness,” Visn. T. Shevchenko Kyiv. Nat. Univ., Ser. Math., Mech., 32, No. 2, 32–37 (2014).zbMATHGoogle Scholar
  2. 2.
    V. D. Budak, O. Ya. Grigorenko, M. Yu. Borisenko, and O. V. Boychuk, “Effect of eccentricity of an elliptic shell on distribution of its dynamic characteristics,” Visn. T. Shevchenko Kyiv. Nat. Univ., Ser. Fiz.- Math. Sci., 2, 23–28 (2015).zbMATHGoogle Scholar
  3. 3.
    V. D. Budak, O. Ya. Grigorenko, M. Yu. Borisenko, and O. V. Boychuk, “Free vibrations of cylindrical shells with circular and noncircular cross-section under various boundary conditions,” Visn. Zaporizh. Nat. Univ., Ser. Fiz.- Math. Sci., No. 2, 20–28 (2015).Google Scholar
  4. 4.
    V. D. Budak, O. Ya. Grigorenko, M. Yu. Borisenko, O. P. Prigoda, and O. V. Boychuk, “Determination of natural frequencies of a thin-walled shell of noncircular cross-section with the stroboscopic holographic interferometry method,” Probl. Vychisl. Mekh. Prochn. Struct., No. 24, 18–25 (2015).Google Scholar
  5. 5.
    A. Ya. Grigorenko and T. L. Efimova, “Using spline-approximation to solve problems of axisymmetric free vibration of thick-walled orthotropic cylinders,” Int. Appl. Mech., 44, No. 10, 1137–1147 (2008).ADSMathSciNetCrossRefGoogle Scholar
  6. 6.
    R. N. Arnold and G. B. Warburton, “The flexural vibration of thin cylinders,” Proc. Inst. Mech. Engrs., 167A, No. 1, 62–80 (1953).CrossRefGoogle Scholar
  7. 7.
    M. L. Baron and H. H. Bleich, “Tables for frequencies and modes of free vibration of infinitely long thin cylindrical shells,” J. Appl. Mech., 21, No. 2, 178–188 (1954).zbMATHGoogle Scholar
  8. 8.
    V. D. Budak, A. Ya. Grigorenko, M. Yu. Borisenko, and E. V. Boychuk, “Determination of eigenfrequencies of an elliptic shell with constant thickness by the finite-element method,” J. of Math. Sci., 212, No. 2, 182–192 (2016).CrossRefzbMATHGoogle Scholar
  9. 9.
    V. D. Budak, A. Ya. Grigorenko, V. V. Khorishko, and M. Yu. Borisenko, “Holographic interferometry study of the free vibrations of cylindrical shells of constant and variable thickness,” Int. Appl. Mech., 50, No. 1, 68–74 (2014).ADSCrossRefGoogle Scholar
  10. 10.
    J. F. Greenspon, “Vibration of thick cylindrical shells,” J. Acoust. Soc. Amer., 31, No. 12, 1682–1683 (1959).ADSCrossRefGoogle Scholar
  11. 11.
    Ya. M. Grigorenko and L. S. Rozhok, “Solving the stress problem for hollow cylinders with corrugated elliptical cross-section,” Int. Appl. Mech., 40, No. 2, 169–175 (2004).ADSCrossRefzbMATHGoogle Scholar
  12. 12.
    A. Grigorenko, Yu. Zolotoi, A. Prigoda, I. Zhuk, V. Khorishko, and A. Ovcharenko, “Experimental investigation of natural vibrations of a thick-walled cylindrical shell by the method of holographic interferometry,” J. Math. Sci., 194, No. 3, 239–244 (2013).CrossRefzbMATHGoogle Scholar
  13. 13.
    A. W. Leissa, Vibration of Shells, in: NASA SP-228, US Government Printing Office, Washington DC (1973).Google Scholar
  14. 14.
    S. Markus, The Mechanics of Vibrations of Cylindrical Shells, Elsevier, Amsterdam (1988).zbMATHGoogle Scholar
  15. 15.
    T. Mazch et al., “Natural modes and frequencies of a thin clamped-free steel cylindrical storage tank partially filled with water: FEM and measurement,” J. Sound Vibr., 193, No. 3, 669–690 (1996).ADSCrossRefGoogle Scholar
  16. 16.
    F. Pellicano, “Linear and nonlinear vibration of shells,” in: Proc. 2nd Int. Conf. on Nonlinear Normal Modes and Localization in Vibration Systems, Samos, June 19–23 (2006), pp. 1–12.Google Scholar
  17. 17.
    J. A. Stricklin, “Nonlinear dynamic analysis of shells of revolution by matrix displacement method,” AIAA J., 9, No. 4, 629–636 (1971).ADSCrossRefzbMATHGoogle Scholar
  18. 18.
    Y. Y. Yu, “Free vibration of thin cylindrical shells having finite length with freely supported and clamped edges,” J. Appl. Mech., 22, No. 4, 547–552 (1955).zbMATHGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  • A. Ya. Grigorenko
    • 1
  • M. Yu. Borisenko
    • 2
  • E. V. Boichuk
    • 2
  • A. P. Prigoda
    • 2
  1. 1.S. P. Timoshenko Institute of MechanicsNational Academy of Sciences of UkraineKyivUkraine
  2. 2.Sukhomlynskyi Mykolaiv National UniversityNikolaevUkraine

Personalised recommendations