Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X

   
 

 

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
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Abstract | References | Additional Information

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.


References [Enhancements On Off] (What's this?)

  • [1] R. A. Scott and J. Miklowitz, Office of Naval Research, Project No. NR-064-487, Technical Report No. 4 (1966)
  • [2] N. Cameron and G. Eason, Quart. J. Mech. Appl. Math. 20, 23 (1967)
  • [3] R. Courant and D. Hilbert, Methods of mathematical physics. Vol. II, Wiley Classics Library, John Wiley & Sons, Inc., New York, 1989. Partial differential equations; Reprint of the 1962 original; A Wiley-Interscience Publication. MR 1013360
  • [4] L. Cagniard, Reflection and refraction of progressive seismic waves, McGraw-Hill, New York, 1962
  • [5] E. A. Kraut, Rev. Geophys. 1, 401 (1963)
  • [6] M. J. Lighthill, Studies on magneto-hydrodynamic waves and other anisotropic wave motions, Philos. Trans. Roy. Soc. London Ser. A 252 (1960), 397–430. MR 0148337, https://doi.org/10.1098/rsta.1960.0010
  • [7] Fritz John, Plane waves and spherical means applied to partial differential equations, Interscience Publishers, New York-London, 1955. MR 0075429
  • [8] I. M. Gel’fand and G. E. Shilov, Generalized functions. Vol. I: Properties and operations, Translated by Eugene Saletan, Academic Press, New York-London, 1964. MR 0166596


Additional Information

DOI: https://doi.org/10.1090/qam/99832
Article copyright: © Copyright 1969 American Mathematical Society


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