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
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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 (1971), 642–658. MR 0288401, https://doi.org/10.1137/0120064
  • [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, Trans. ASME Ser. E. J. Appl. Mech. 32 (1965), 829–836. MR 0187472
  • [8] F. Erdogan, G. D. Gupta, and T. S. Cook, Numerical solution of singular integral equations, Mechanics of fracture, Vol. 1, Noordhoff, Leiden, 1973, pp. 368–425. MR 0471394
  • [9] B. Noble, Methods based on the Wiener-Hopf technique for the solution of partial differential equations, International Series of Monographs on Pure and Applied Mathematics. Vol. 7, Pergamon Press, New York-London-Paris-Los Angeles, 1958. MR 0102719
  • [10] N. I. Muskhelishvili, Singular integral equations, Wolters-Noordhoff Publishing, Groningen, 1972. Boundary problems of functions theory and their applications to mathematical physics; Revised translation from the Russian, edited by J. R. M. Radok; Reprinted. 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)

Similar Articles

Retrieve articles in Quarterly of Applied Mathematics with MSC: 73D99, 73M05

Retrieve articles in all journals with MSC: 73D99, 73M05

Additional Information

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

American Mathematical Society