Advertisement

Materials Science

, Volume 47, Issue 6, pp 746–756 | Cite as

Torsional oscillations of a finite elastic cylinder containing an outer circular crack

  • V. H. Popov
Article
  • 47 Downloads

We determine the stressed state of a finite cylinder containing an outer circular crack in the process of torsional oscillations. The oscillations are caused by the action of a harmonic torsional moment upon a rigid circular plate attached to one end of the cylinder. The problem is reduced to a Fredholm integral equation of the second kind for the unknown stresses in the plane of the crack.

Keywords

torsional oscillations finite cylinder outer circular crack stress intensity factors 

References

  1. 1.
    Y. Z. Сhen, “Stress intensity factors a finite-length cylinder with a circumferential crack,” Int. J. Press. Vess. Piping, 77, No. 8, 439–444 (2000).CrossRefGoogle Scholar
  2. 2.
    I. S. Jones, and G. Rothwell, “Reference stress intensity factors with application to weight functions for internal circumferential cracks in cylinders,” Eng. Fract. Mech., 68, No. 4, 435–454 (2001).CrossRefGoogle Scholar
  3. 3.
    P. Popov, “Problem of torsion for a finite cylinder with circular crack,” Mashinoznavstvo, No. 9, 15–18 (2005).Google Scholar
  4. 4.
    Han Xue-Li and Wang Duo, “A circular or ring-shaped crack in a nonhomogeneous cylinder under torsion loading,” Int. J. Fract., 68, No. 3, 79–83 (1994).CrossRefGoogle Scholar
  5. 5.
    A. Birinci, T. S. Ozsahin, and R. Erdol, “Axisymmetric circumferential internal crack problem for a long thick-walled cylinder with inner and outer claddings,” Eur. J. Mech. A/Solids, 25, No. 5, 764–777 (2006).CrossRefGoogle Scholar
  6. 6.
    A. Atsumi and Y. Shindo, “Torsional impact response in an infinite cylinder with a circumferential edge crack,” J. Appl. Mech., 49, No. 3, 531–536 (1982).CrossRefGoogle Scholar
  7. 7.
    Y. Shindo and W. Li, “Torsional impact response of a thick-walled cylinder with a circumferential edge crack,” J. Press. Vess. Techn., 112, No. 4, 367–374 (1990).CrossRefGoogle Scholar
  8. 8.
    A. Vaziri and Nayeb-Hashemi, “The effect of crack surface interaction on stress intensity factor in mode III crack growth in round shafts,” Eng. Fract. Mech., 72, No. 4, 617–629 (2005).CrossRefGoogle Scholar
  9. 9.
    H. Bai, A. H. Shah, N. Popplevel, and S. K. Datta, “Scattering of guided waves by circumferential cracks in composite cylinders,” Int. J. Sol. Struct., 39, No. 17, 4583–4603 (2002).CrossRefGoogle Scholar
  10. 10.
    J. M. Bastero and J. M. Martinez-Eshaola, “Singular character of axisymmetric stresses around wedge-shaped notches in cylindrical bodies under torsion: Unit step load,” Theor. Appl. Fract. Mech., 18, No. 3, 247–257 (1993).CrossRefGoogle Scholar
  11. 11.
    A. Dimarogonas and G. Massourors, “Torsional vibration of a shaft with a circumferential crack,” Eng. Fract. Mech., 15, No. 3–4, 439–444 (1981).CrossRefGoogle Scholar
  12. 12.
    O. E. Andreikiv, V. M. Boiko, S. E. Kovchyk, and I. V. Khodun, “Dynamic tension of a cylindrical specimen with circumferential crack,” Mater. Sci., 36, No. 3, 382–391 (2000).CrossRefGoogle Scholar
  13. 13.
    Ya. L. Ivanytskyi, V. M. Boiko, I. V. Khodun, and S. T. Shtayura, “Stress-strain state of a cylinder with an external circular crack under dynamic torsion,” Mater. Sci., 43, No. 2, 203–214 (2007).CrossRefGoogle Scholar
  14. 14.
    G. Ya. Popov, V. V. Reut, and N. D. Vaisfeld, Equations of Mathematical Physics. Method of Integral Transformations [in Ukrainian], Astroprint, Odessa (2005).Google Scholar
  15. 15.
    L. V. Vakhonina and V. G. Popov, “Concentration of stresses near a thin circular absolutely rigid exfoliated inclusion caused by the interaction with torsional waves,” Izv. Ross. Akad. Nauk, Mekh. Tverd. Tela, No. 4, 70–76 (2004).Google Scholar
  16. 16.
    A. P. Prudnikov, Yu. A. Brychkov, and O. I. Marichev, Integrals and Series. Elementary Functions, Moscow, Nauka (1981).Google Scholar
  17. 17.
    W. Kecs and P. P. Teodorescu, Introduction to the Theory of Distributions with Applications to Technique [in Romanian], Tehnica, Bucharest, 1975.Google Scholar
  18. 18.
    L. V. Vakhonina and V. G. Popov, “Interaction of elastic waves with thin rigid circular inclusion in the case of smooth contact,” Teor. Prikl. Mekh., No. 38, 158–166 (2003).Google Scholar

Copyright information

© Springer Science+Business Media, Inc. 2012

Authors and Affiliations

  1. 1.Odessa National Marine AcademyOdessaUkraine

Personalised recommendations