Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



Normal compression waves scattering at a flat annular crack in an infinite elastic solid

Author: Yasuhide Shindo
Journal: Quart. Appl. Math. 39 (1981), 305-315
MSC: Primary 73D99; Secondary 73M05
DOI: https://doi.org/10.1090/qam/636237
MathSciNet review: 636237
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Abstract: The Hankel transform is used to obtain a complete solution for the dynamic stresses and displacements around a flat annular surface of a crack embedded in an infinite elastic solid, which is excited by normal compression waves. The singular stresses near the crack tips are obtained in closed elementary forms, while the magnitude of these stresses, governed by the dynamic stress-intensity factors, is calculated numerically from a singular integral equation of the first kind. The variations of the dynamic stress-intensity factors with the normalized frequency for the ratio of the inner radius to the outer one and Poisson's ratio are shown graphically.

References [Enhancements On Off] (What's this?)

  • [1] G. C. Sih, Elastodynamic crack problems, Noordhoff International Publishing, Leyden, 1977
  • [2] G. C. Sih and J. F. Loeber, Torsional vibration of an elastic solid containing a penny-shaped crack, J. Acoust. Soc. Amer. 44, 1237-1245 (1968)
  • [3] G. C. Sih and J. F. Loeber, Normal compression and radial shear waves scattering at a penny-shaped crack in an elastic solid, J. Acoust. Soc. Amer. 46, 711-721 (1969)
  • [4] A. K. Mal, Interaction of elastic waves with a penny-shaped crack, Int. J. Engng. Sci. 8, 381-388 (1970)
  • [5] D. L. Jain and R. P. Kanwal, An integral equation method for solving mixed boundary value problems, SIAM J. Appl. Math. 20, 642-658 (1971) MR 0288401
  • [6] Y. Shindo, Diffraction of torsional waves by a flat annular crack in an infinite elastic medium, J. Appl. Mech. 46, 827-831 (A79)
  • [7] F. Erdogan, Stress distribution in bonded dissimilar materials containing circular or ring-shaped cavities, J. Appl. Mech. 32, 829-836 (1965) MR 0187472
  • [8] F. Erdogan, G. D. Gupta and T. S. Cook, Methods of analysis and solutions of crack problems, Noordhoff International Publishing, Leyden, 1973, p. 368 MR 0471394
  • [9] B. Noble, Methods based on the Wiener-Hopf technique, Pergamon Press Inc., New York, 1958 MR 0102719
  • [10] N. I. Muskhelishvili, Singular integral equations, Noordhoff, Groningen, 1946 MR 0355494
  • [11] T. Shibuya, I. Nakahara and T. Koizumi, The axisymmetric distribution of stresses in an infinite elastic solid containing a flat annular crack under internal pressure, ZAMM 55, 395-402 (1975)

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DOI: https://doi.org/10.1090/qam/636237
Article copyright: © Copyright 1981 American Mathematical Society

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