A theory, in the form of a coupled system of reduced parabolic wave equations (equations (42)), is developed for stress wave propagation studies through inhomogeneous, locally isotropic, linearly elastic solids. A parabolic wave theory differs from a complete wave theory in allowing propagation only in directions of increasing range. Thus, when applicable, it is well suited for numerical computation using a range-incrementing procedure. The parabolic theory considered here requires the propagation directions to be limited to a cone, centered about a principal propagation direction, which might be described as narrow-angled. Further, the theory requires that the effects of diffraction, refraction, and energy transfer between the dilatational and distortional modes are gradual enough that coupling between them can be ignored over a range of several wavelengths. Precise conditions for the applicability of the theory are summarized in a series of inequalities (equations (44)).
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September 1977
Research Papers
A Parabolic Theory of Stress Wave Propagation Through Inhomogeneous Linearly Elastic Solids
J. J. McCoy
J. J. McCoy
Department of Civil Engineering, The Catholic University of America, Washington, D. C.
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J. J. McCoy
Department of Civil Engineering, The Catholic University of America, Washington, D. C.
J. Appl. Mech. Sep 1977, 44(3): 462-468 (7 pages)
Published Online: September 1, 1977
Article history
Received:
June 1, 1976
Revised:
January 1, 1977
Online:
July 12, 2010
Citation
McCoy, J. J. (September 1, 1977). "A Parabolic Theory of Stress Wave Propagation Through Inhomogeneous Linearly Elastic Solids." ASME. J. Appl. Mech. September 1977; 44(3): 462–468. https://doi.org/10.1115/1.3424101
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