Far Field Radiation of a Point Source on the Free Surface of Semi-Infinite Anisotropic Solids

  • Kunyu Wu
  • Peter B. Nagy
  • Laszlo Adler
Part of the Review of Progress in Quantitative Nondestructive Evaluation book series


A common approach to study the acoustic field in an isotropic elastic half-space has been to use the equations of linear, isotropic elasticity together with Fourier or Hankel transforms [1,2]. The result is a definiteintegral representation of the field at an arbitrary point in the half-space owing to a prescribed stress applied to the free surface. The complicated integral can be evaluated asymptotically to give the far field radiation. Furthermore, the theoretical expressions for the directivity patterns from a variety of acoustic sources, radiating into an isotropic elastic half-space have been presented by several authors [1–4]. A similar theoretical analysis applied to an anisotropic solid medium fails because the potential theory method is not applicable to the anisotropic problem.


Free Surface Point Source Reflection Coefficient Anisotropic Medium Directivity Pattern 
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  1. 1.
    R.L. Roderick, Ph.D. dissertation, Brown University, RI (1971).Google Scholar
  2. 2.
    G.F. Miller and H. Pursey, Proc. R. Soc. (London) A223 (1954).Google Scholar
  3. 3.
    L. Filipczynski, Proc. Conf. Ultrason. 2nd, Warsaw, 29 (1956).Google Scholar
  4. 4.
    D.A. Hutchins, R.J. Dewhurst, S.B. Palmer, J. Acoust. Soc. Am. 70 (1981).Google Scholar
  5. 5.
    J.W. Strutt (Lord Rayleigh), Theory of Sound (Dover Publ. Inc., New York, 1945), Vol. 1.MATHGoogle Scholar
  6. 6.
    L. Ya. Gutin, Sov. Phys. Acoust. 9 (1964)Google Scholar
  7. L. Ya. Gutin, Zh. Tekhn. Fiz. 21 (1951).Google Scholar
  8. 7.
    A.E. Lord, Jr., J. Acoust. Soc. Am. 39 (1966).Google Scholar
  9. 8.
    B.A. Auld, Acoustic Fields and Waves in Solids (Wiley-Interscience, New York, 1973 ), Vols. 1 and 2.Google Scholar
  10. 9.
    M.J.P. Musgrave, Crystal Acoustics ( Holden Day, San Francisco, 1970 ).MATHGoogle Scholar
  11. 10.
    A. Tverdokhlebov and J. Rose, J. Acoust. Soc. Am. 83 (1988).Google Scholar
  12. 11.
    H. Lamb, Phil. Trans. Roy. Soc. A203 (1903).Google Scholar

Copyright information

© Springer Science+Business Media New York 1990

Authors and Affiliations

  • Kunyu Wu
    • 1
  • Peter B. Nagy
    • 1
  • Laszlo Adler
    • 1
  1. 1.The Ohio State UniversityColumbusUSA

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