Time Dependent Pulse Propagation and Scattering in Elastic Solids; an Asymptotic Theory

  • A. N. Norris
Conference paper
Part of the Review of Progress in Quantitative Nondestructive Evaluation book series (RPQN, volume 6 A)


Predictive modeling of ultrasonic pulse propagation in elastic solids is usually formulated in the frequency domain. Tractable solutions can then be obtained by using, for example, the powerful technique of geometrical elastodynamics and ray theory for wavefront propagation [1]. Recent advances [2,3] allow us to incorporate the finite pulse width by means of Gaussian profiles. However, a more realistic model should also include the fact that the pulse is of limited duration and therefore spatially localized in all directions. This paper outlines a theory for pulses in the form of a localized disturbance with a Gaussian envelope. The theory is valid if the associated carrier wavelength is short in comparison with typical length scales encountered in the solid. The method provides results explicitly in the time domain without the necessity of intermediate FFTs required by frequency domain methods. Applications to pulse propagation in smoothly varying inhomogeneous media, interface scattering and edge diffraction are discussed. The present theory contains an extra degree of freedom not explicitly considered before, i. e., the temporal width or duration of the pulse. An extensive treatment of the related problem for the scalar wave equation can be found in reference 4.


Rayleigh Wave Leaky Rayleigh Wave Gaussian Wave Packet Scalar Wave Equation Gaussian Envelope 
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    J.D. Achenbach, A.K. Gautesen and H. McMaken, Ray Methods for Waves in Elastic Solids. Pitman, Boston (1982).MATHGoogle Scholar
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    R.B. Thompson and E.F. Lopes, “A Model for the Effects of Aberrations on Refracted Ultrasonic Fields,” Review of Progress in Quantitative NDE5. D.O. Thompson, D.E. Chimenti, Eds., Plenum Press, NY (1986).Google Scholar
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    M.M. Popov, “A New Method of Computation of Wave Fields Using Gaussian Beams,” Wave Motion, 4, 85–97 (1982).CrossRefMATHMathSciNetGoogle Scholar
  4. 4.
    A.N. Norris, B.S. White and J.R. Schrieffer, “Gaussian Wave Packets in Inhomogeneous Media with Curved Interfaces” (unpublished).Google Scholar
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    H.L. Bertoni and T. Tamir, “Unified Theory of Rayleigh-Angle Phenomena for Acoustic Beams at Liquid-Solid Interfaces,” Appl. Phys., 2, 157–172 (1973).CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1987

Authors and Affiliations

  • A. N. Norris
    • 1
  1. 1.Department of Mechanics & Materials ScienceRutgers UniversityPiscatawayUSA

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