Hostname: page-component-586b7cd67f-gb8f7 Total loading time: 0 Render date: 2024-11-26T14:41:49.663Z Has data issue: false hasContentIssue false
  • English
  • Français

Two-dimensional anisotropic elastic waves emanating from a point source

Published online by Cambridge University Press:  24 October 2008

Robert G. Payton
Robert G. Payton
Affiliation:
Mathematics Department, Adeiphi University, Garden City, New York 11530
Get access Rights & Permissions [Opens in a new window]

Abstract

A two (spatial) dimensional initially strained elastic body is excited by a point impulse. Expressions are found for the various displacement components in a form which is readily evaluated by residues. The solid itself is characterized by three parameters which depend on the material properties and the initial deformation. For the case when two of these parameters are equated, explicit expressions for the displacements are given along the Cartesian axes passing through the origin of the point impulse. Wave front singularities and lacunas are identified and discussed. Some typical numerical results are given.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 70 , Issue 1 , July 1971 , pp. 191 - 210
Copyright
Copyright © Cambridge Philosophical Society 1971

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

(1)Green, A. E., Rivlin, R. S. and Shield, R. T.Proc. Roy. Soc. A 211, (1952), 128.-Google Scholar
(2)Payton, R. G.Arch. Rational Mech. Anal. 32 (1969), 311.CrossRefGoogle Scholar
(3)Payton, R. G.Arch. Rational Mech. Anal. 35 (1969), 402.CrossRefGoogle Scholar
(4)Weitzner, H.Phys. Fluids 4 (1961), 1238.CrossRefGoogle Scholar
(5)Burridge, R.Proc. Cambridge Philos. Soc. 63 (1967), 819.CrossRefGoogle Scholar
(6)Petrowsky, I.Rec. Math [Mat. Sbornik] 17 (1945), 289.Google Scholar
(7)Bazer, J. and Yen, D. H. Y.Comm. Pure Appl. Math. 22 (1969), 279.CrossRefGoogle Scholar
(8)Green, A. E. and Zerna, W.Theoretical elasticity (London: Oxford University Press, 1954).Google Scholar
(9)John, F.Plane waves and Spherical means applied to partial differential equations (New York: John Wiley and Sons, 1965).Google Scholar
(10)Gel'fand, I. M. and Shilov, G. E.Generalizedfunctions, vol. I. (New York: Academic Press, 1964).Google Scholar
(11)Truesdell, C. and Noil, W.The non-linear field theories of mechanics (Berlin-Heidelberg-New York: Springer, 1965).Google Scholar
(12)Courant, R. and Hilbert, D.Methods of mathematical physics, vol. II (New York: John Wiley and Sons, 1962).Google Scholar