The stress intensity factors (SIF) for a plane circular crack in a finite cylinder undergoing torsional vibrations are determined. The vibrations are generated by a rigid circular plate attached to one end of the cylinder and subjected to a harmonic moment. The boundary-value problem is reduced to the Fredholm equation of the second kind. This equation is solved numerically, and the solution is used to derive a highly accurate approximate formula to calculate the SIFs. The calculated results are plotted and analyzed
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
L. V. Vakhonina and V. G. Popov, “Stress concentration around a circular thin perfectly rigid inclusion interacting with a torsional wave,” Izv. RAN, Mekh. Tverd. Tela, No. 4, 70–76 (2004).
L. V. Vakhonina and V. G. Popov, “Interaction of elastic waves with a circular thin rigid inclusion in the case of smooth contact,” Teor. Prikl. Mekh., 38, 158–166 (2003).
I. S. Gradshteyn and I. M. Ryzhik. Tables of Integrals, Sums, Series and Products, Academic Press, New York (1980).
A. N. Guz and V. V. Zozulya, Brittle Fracture of Materials under Dynamic Loading [in Russian], Naukova Dumka, Kyiv (1993).
W. Kecs and P. P. Teodorescu, Introduction to the Theory of Distributions in Engineering [in Romanian], Editura Tehnica, Bucharest (1975).
A. V. Men’shikov and I. A. Guz, “Friction in harmonic loading of a circular crack,” Dop. NAN Ukrainy, No. 1, 77–82 (2007).
G. Ya. Popov, “On a method of solving mechanics problems for domain with slits or thin inclusions,” J. Appl. Mat. Mech., 42, No. 1, 125–139 (1978).
G. Ya. Popov, S. A. Abdymanapov, and V. V. Efimov, Green Functions and Matrices of One-Dimensional Boundary-Value Problems [in Russian], Rauan, Almaty (1999).
G. Ya. Popov, V. V. Reut, and N. D. Vaisfel’d, Equations of Mathematical Physics. Integral Transform Method [in Ukrainian], Astroprint, Odessa (2005).
T. Akiyawa, T. Hara, and T. Shibua, “Torsion of an infinite cylinder with multiple parallel circular cracks,” Theor. Appl. Mech., 50, 137–143 (2001).
D.-S. Lee, “Penny shaped crack in a long circular cylinder subjected to a uniform shearing stress,“ Europ. J. Mech., 20(2), 227–239 (2001).
F. Narita, Y. Shindo, and S. Lin, “Impact response of a piezoelectric ceramic cylinder with a penny-shaped crack,” Theor. Appl. Mech., 52, 153–162 (2003).
A. N. Guz, V. V. Zozulya, and A. V. Men’shikov, “Three-dimensional dynamic contact problem for an elliptic crack interacting with a normally incident harmonic compression-expansion wave,” Int. Appl. Mech., 39, No. 12, 1425–1428 (2003).
A. N. Guz, V. V. Zozulya, and A. V. Men’shikov, “General spatial dynamic problem for an elliptic crack under the action of a normal shear wave, with consideration for the contact interaction of the crack faces,” Int. Appl. Mech., 40, No. 2, 156–159 (2004).
A. N. Guz, V. V. Zozulya, and A. V. Men’shikov, “Surface contact of elliptical crack under normally incident tension–compression wave,” Theor. Appl. Fract. Mech., 40, No. 3, 285–291 (2008).
G.-Y. Huang, Y.-S. Wang, and S.-W. Yu, “Stress concentration at a penny-shaped crack in a nonhomogeneous medium under torsion,” Acta Mech., December, 180, No. 1–4, 107–115 (2005).
Z. H. Jia, D. I. Shippy, and F. I. Rizzo, “Three-dimensional crack analysis using singular boundary element,” Int. J. Numer. Meth. Eng., 28(10), 2257–2273 (2005).
M. O. Kaman and R. G. Mehmet, “Cracked semi-infinite cylinder and finite cylinder problems,” Int. J. Eng. Sci., 44(20), 1534–1555 (2006).
P. A. Martin and G. R. Wickham, “Diffraction of elastic waves by a penny-shaped crack: Analytical and numerical results,” Proc. Royal Soc. London, Ser. A, Math. Phys. Sci., 390, No. 1798, 91–129 (1983).
B. M. Singh, J. B. Haddow, J. Vibik, and T. B. Moodie, “Dynamic stress intensity factors for penny-shaped crack in twisted plate,” J. Appl. Mech., 47, 963–965 (1980).
K. N. Srivastava, R. M. Palaiya, and O. P. Cupta, “Interection of elastic waves with a penny-shaped crack in an infinitely long cylinder,” J. Elast., 12, No. 1, 143–152 (1982).
W. Aishi, “A note on the crack-plane stress field method for analyzing SIFs and ITS to a concentric penny-shaped crack in a circular cylinder opened up by constant pressure,” Int. J. Fract., 66, 73–76 (1994).
Author information
Authors and Affiliations
Corresponding author
Additional information
Translated from Prikladnaya Mekhanika, Vol. 48, No. 4, pp. 86–93, July–August 2012.
Rights and permissions
About this article
Cite this article
Popov, V.G. Stress state of a finite elastic cylinder with a circular crack undergoing torsional vibrations. Int Appl Mech 48, 430–437 (2012). https://doi.org/10.1007/s10778-012-0530-1
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10778-012-0530-1