International Applied Mechanics

, Volume 50, Issue 2, pp 159–170 | Cite as

Transverse Vibrations of an Elastic Stepped Cylindrical Shell with Cracks


The transverse axisymmetric vibrations of an elastic stepped cylindrical shell with stable cracks in the inside corner of the steps are studied. The effect of the cracks on the vibrations of the shell is evaluated considering local flexibility and the compliance function, which is related to the stress intensity factor of linear fracture mechanics.Amatrix solution for an arbitrary number of cracks is found. The effect of the location and length of cracks on the transverse axisymmetric vibrations of elastic one- and two-step cylindrical shells is evaluated numerically.


cylindrical shell crack transverse axisymmetric vibrations 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    G. G. Vlaikov and A. Ya. Grigorenko, ”Free axisymmetric vibrations of a hollow cylinder with various end conditions,” Prikl. Mekh., 26, No. 5, 109–111 (1990).Google Scholar
  2. 2.
    A. N. Guz, I. S. Chernyshenko, Val. N. Chekhov, Vik. N. Chekhov, and K. I. Shnerenko, Cylindrical Shells Weakened by Holes [in Russian], Naukova Dumka, Kyiv (1974).Google Scholar
  3. 3.
    V. V. Panasyuk, Fundamentals of Fracture Mechanics, Vol. 1 of the 10-volume series Fracture Mechanics and Strength of Materials [in Russian], Naukova Dumka, Kyiv (1988).Google Scholar
  4. 4.
    E. Yu. Bashchuk and V. Yu. Boichuk, “Influence of the inhomogeneity of the principal stress state on the critical loads of a plate with a crack,” Int. Appl. Mech., 49, No. 3, 328–336 (2013).ADSCrossRefGoogle Scholar
  5. 5.
    Y. G. Chondros and S. D. Dimarogonas, “Identification of cracks in welded joints of complex structures,” J. Sound Vibr., 69, No. 4, 531–538 (1980).ADSCrossRefGoogle Scholar
  6. 6.
    A. D. Dimarogonas, “Vibration of cracked structures: a state of the art review,” Eng. Fact. Mech., 55, 831–857 (1996).CrossRefGoogle Scholar
  7. 7.
    M. B. Dovzhik and V. M. Nazarenko, “Fracture of a material compressed along a periodic set of closely spaced cracks,” Int. Appl. Mech., 48, No. 6, 710–718 (2012).ADSCrossRefMathSciNetGoogle Scholar
  8. 8.
    Ya. M. Grigorenko, A. Ya. Grigorenko, and L. I. Zakhariichenko, “Stress–strain analysis of orthotropic closed and open noncircular cylindrical shells,” Int. Appl. Mech., 41, No. 7, 778 –785 (2005).ADSCrossRefGoogle Scholar
  9. 9.
    P. Gudmundson, “Eigenfrequency changes of structures due to cracks, notches or other geometrical changes,” J. Mech. Phys. Solids, 30, No. 5, 339–353 (1982).ADSCrossRefMathSciNetGoogle Scholar
  10. 10.
    M. L. Kikidis and C. A. Papadopoulos, “Slenderness ratio effect on cracked beam,” J. Sound Vibr., 155, No. 1, 1–11 (1992).ADSCrossRefMATHGoogle Scholar
  11. 11.
    Yu. A. Kostandov, P. V. Makarov, M. O. Eremin, I. Yu. Smolin, and I. E. Shipovskii, “Fracture of compressed brittle bodies with a crack,” Int. Appl. Mech., 49, No. 1, 95–101 (2013).ADSCrossRefGoogle Scholar
  12. 12.
    J. Lellep and E. Sakkov, “Buckling of stepped composite columns,” Mech. Comp. Mater., 42, No. 1, 63–72 (2006).CrossRefGoogle Scholar
  13. 13.
    R. Y. Liang, F. K. Choy, and J. Hu, “Detection of cracks in beam structures using measurements of natural frequencies,” J. Franklin Inst., 328, No. 4, 505–518 (1991).ADSCrossRefMATHGoogle Scholar
  14. 14.
    R. Y. Liang, J. Hu, and F. Choy, “Theoretical study of crack-induced eigenfrequency changes on beam structures,” J. Eng. Mech., 118, No. 2, 384–395 (1992).CrossRefGoogle Scholar
  15. 15.
    Y. Murakami, Stress Intensity Factor Handbook, I–II, Pergamon Press, Oxford (1992).Google Scholar
  16. 16.
    B. P. Nandwana and S. K. Marti, “Detection of the location and size of a crack in stepped cantilever beams based on measurements of natural frequencies,” J. Sound Vibr., 203, No. 3, 435–446 (1997).ADSCrossRefGoogle Scholar
  17. 17.
    Y. Narkis and E. Elmanah, “Crack identification in a cantilever beam under uncertain end conditions,” Int. J. Mech. Sci., 38, No. 5, 499–507 (1996).CrossRefMATHGoogle Scholar
  18. 18.
    P. F. Rizos, N. Aspragathos, and A. F. Dimarogonas, “Identification of crack location and magnitude in a cantilever beam from the vibration modes,” J. Sound Vibr., 138, No. 3, 381–388 (1990).ADSCrossRefGoogle Scholar
  19. 19.
    M.-H. Shin and C. Pierre, “Natural modes of Bernoulli–Euler beams with symmetric cracks,” J. Sound Vibr., 138, No. 1, 115–134 (1990).ADSCrossRefGoogle Scholar
  20. 20.
    H. Tada, P. V. Paris, and G. T. Irwin, Stress Analysis of Cracks Handbook, ASME, New York (2000).CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.Institute of MathematicsUniversity of TartuTartuEstonia

Personalised recommendations