Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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



Diffraction of elastic waves by a penny-shaped crack

Author: A. K. Mal
Journal: Quart. Appl. Math. 26 (1968), 231-238
MSC: Primary 73.35
DOI: https://doi.org/10.1090/qam/231573
MathSciNet review: 231573
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Abstract: The diffraction of axisymmetric, harmonic elastic waves by a circular crack is considered. It is shown that the potential functions for the diffracted waves can be obtained from the solution of a pair of dual integral equations. The dual equations are transformed into integral equations of the second kind suitable for iteration at low frequencies. The principle of contraction mapping is used to discuss the convergence of the iteration scheme. The solution satisfies an edge condition.

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

  • [1] A. K. Mal, D. D. Ang and L. Knopoff, Diffraction of elastic waves by a rigid circular disc, Proc. Camb. Phil. Soc. 1967 (In press)
  • [2] Ian N. Sneddon, Fourier Transforms, McGraw-Hill Book Co., Inc., New York, Toronto, London, 1951. MR 0041963

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DOI: https://doi.org/10.1090/qam/231573
Article copyright: © Copyright 1968 American Mathematical Society

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