Two-dimensional pulse propagation in a two-parameter anisotropic elastic solid
Author:
Robert G. Payton
Journal:
Quart. Appl. Math. 27 (1969), 147-160
DOI:
https://doi.org/10.1090/qam/99832
MathSciNet review:
QAM99832
Full-text PDF Free Access
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References |
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Abstract: A perturbing body force, in the form of an impulsive point source, is suddenly introduced into an anisotropic elastic body. The anisotropic solid is characterized by two parameters. After placing suitable restrictions on these parameters, integral representations of the transient displacement components are found. Explicit expressions for the displacements are obtained along two perpendicular lines which are centered at the point of application of the point impulse and parallel to the coordinate axes. Wave front singularities are identified and graphical results for the wave shapes are presented.
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R. A. Scott and J. Miklowitz, Office of Naval Research, Project No. NR–064–487, Technical Report No. 4 (1966)
N. Cameron and G. Eason, Quart. J. Mech. Appl. Math. 20, 23 (1967)
R. Courant and D. Hilbert, Methods of mathematical physics, Vol. II, Wiley, New York, 1962
L. Cagniard, Reflection and refraction of progressive seismic waves, McGraw-Hill, New York, 1962
E. A. Kraut, Rev. Geophys. 1, 401 (1963)
M. J. Lighthill, Philos. Trans. Roy. Soc. A 252, 397 (1960)
F. John, Plane waves and spherical means applied to partial differential equations, Wiley, New York, 1955
I. M. Gelfand and G. E. Shilov, Generalized functions, Vol. I, Academic Press, New York, 1964
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Article copyright:
© Copyright 1969
American Mathematical Society
