Skip to main content
SpringerLink
Log in

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

  • Published:
International Applied Mechanics Aims and scope

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  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).

    MATH  Google Scholar 

  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).

    MATH  Google Scholar 

  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).

  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).

  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).

    Article  ADS  MathSciNet  Google Scholar 

  6. R. N. Arnold and G. B. Warburton, “The flexural vibration of thin cylinders,” Proc. Inst. Mech. Engrs., 167A, No. 1, 62–80 (1953).

    Article  Google Scholar 

  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).

    MATH  Google Scholar 

  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).

    Article  MATH  Google Scholar 

  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).

    Article  ADS  Google Scholar 

  10. J. F. Greenspon, “Vibration of thick cylindrical shells,” J. Acoust. Soc. Amer., 31, No. 12, 1682–1683 (1959).

    Article  ADS  Google Scholar 

  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).

    Article  ADS  MATH  Google Scholar 

  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).

    Article  MATH  Google Scholar 

  13. A. W. Leissa, Vibration of Shells, in: NASA SP-228, US Government Printing Office, Washington DC (1973).

    Google Scholar 

  14. S. Markus, The Mechanics of Vibrations of Cylindrical Shells, Elsevier, Amsterdam (1988).

    MATH  Google Scholar 

  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).

    Article  ADS  Google Scholar 

  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.

  17. J. A. Stricklin, “Nonlinear dynamic analysis of shells of revolution by matrix displacement method,” AIAA J., 9, No. 4, 629–636 (1971).

    Article  ADS  MATH  Google Scholar 

  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).

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, 3 Nesterova St., Kyiv, Ukraine, 03057

    A. Ya. Grigorenko

  2. Sukhomlynskyi Mykolaiv National University, 24 Nikol’skaya St., Nikolaev, Ukraine, 54000

    M. Yu. Borisenko, E. V. Boichuk & A. P. Prigoda

Authors
  1. A. Ya. Grigorenko
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. M. Yu. Borisenko
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. E. V. Boichuk
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. A. P. Prigoda
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to A. Ya. Grigorenko.

Additional information

Translated from Prikladnaya Mekhanika, Vol. 54, No. 1, pp. 90–100, January–February, 2017.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Grigorenko, A.Y., Borisenko, M.Y., Boichuk, E.V. et al. Numerical Determination of Natural Frequencies and Modes of the Vibrations of a Thick-Walled Cylindrical Shell. Int Appl Mech 54, 75–84 (2018). https://doi.org/10.1007/s10778-018-0861-7

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10778-018-0861-7

Keywords

Search

Navigation