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Application of Fourier Elastodynamics to Direct and Inverse Problems for the Scattering of Elastic Waves from Flaws Near Surfaces

  • J. M. Richardson
  • K. W. FertigJr.
Part of the Library of Congress Cataloging in Publication Data book series (volume 2A)

Abstract

In ultrasonic inspection one frequently encounters situations in which flaws lie too close to surfaces (or interfaces) for the applications of the conventional theory of scattering in an infinite host medium. One approach, pursued by Varadan, Pillai, and Varadan, is to rework scattering theory with a Green function suitably modified for the presence of surfaces. Our approach uses a Fourier elastodynamics formalism in which the scattering process is represented by the generalized transfer function for a slab of material containing the flaw. A sufficiently simple elastodynamic system can be built up of separately characterizable subsystems defined by intervals on the z-axis. Fortunately, it turns out that, in the case of propagating waves the generalized transfer function can be simply related to the scattering amplitude, the representation of scattering in the conventional theory. In the case where evanescent waves are present, the generalized transfer function can also be simply related to the scattering amplitude in which the incident and scattered direction \(\mathop e\limits^{{ \to _1}}\) and \(\mathop e\limits^{{ \to _S}}\) have been analytically continued from real to complex forms. In some cases it may be a good approximation to ignore completely the effects of evanescent waves. An integral equation has been derived whose solution gives the scattering from a system composed of a flaw and a nearby surface or interface. The computational results pertain to the scattering from spherical voids and inclusions in plastic at various distances from the plastic-water interface with the incident wave propagating through the water.

Keywords

Green Function Incident Wave Scattered Wave Evanescent Wave Mode Conversion 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. Auld, B.A. (1973), “Acoustic Fields and Waves in Solids,” New York, Wiley.Google Scholar
  2. Goodman, J.W. (1968), “Introduction to Fourier Optics, ” San Francisco, McGraw-Hill.Google Scholar
  3. Varadan, V.V., T.A.K. Pillai, and V.K. Varadan (1982), “Wave Scattering by Obstacles in Joined Fluid-Solid Half Space,” paper in the present proceedings.Google Scholar

Copyright information

© Plenum Press, New York 1983

Authors and Affiliations

  • J. M. Richardson
    • 1
  • K. W. FertigJr.
    • 1
  1. 1.Rockwell International Science CenterThousand OaksUSA

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