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Diffraction of impulsive elastic waves by a fluid cylinder

Published online by Cambridge University Press:  24 October 2008

Ramanand Jha
Ramanand Jha
Affiliation:
Department of Applied Mathematics and Theoretical Physics University of Cambridge
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Abstract

In this paper, the problem of diffraction of an impulsive P wave by a fluid circular cylinder has been considered. The cylinder is embedded in an unbounded isotropic homogeneous elastic medium and it is filled with inviscid fluid material. The line source, giving rise to the incident front, is situated outside the cylinder parallel to its axis.

The exact solution of the problem is obtained by using the method of dual integral transformations. The solution is evaluated approximately to obtain the motion on the wave front in the shadow zone of the elastic medium. Further, we interpret the approxi mate solutions in terms of Keller's geometrical theory of diffraction. Our result also gives a correction to an earlier investigation of the similar problem by Knopoff and Gilbert(s).

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 75 , Issue 3 , May 1974 , pp. 391 - 404
Copyright
Copyright © Cambridge Philosophical Society 1974

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References

REFERENCES

(1)ErdéLyi, A. and others. Tables of integral transforms (Mcgraw Hill Book Co., 1954).Google Scholar
(2)Friedlander, F. G.Comm. Pure. Appl. Math. 7 (1954), 705–732.CrossRefGoogle Scholar
(3)Friedlander, F. G.Sound pulses (Cambridge, 1958).Google Scholar
(4)Friedman, B.Principles and techniques of applied mathematics (John Wiley, 1956).Google Scholar
(5)Gilbert, F. and Knopoff, L.J. Acoust. Soc. America 31 (1959), 1169–75.CrossRefGoogle Scholar
(6)Gilbert, F.J. Acoust. Soc. America 32 (1960), 841–57.CrossRefGoogle Scholar
(7)Keller, J. B.Proc. Eighth. Symp. Appl. Math. of Am. Math. Soc. (Mcgraw Hill Bk. Co., 1958).Google Scholar
(8)Knoroff, L. and Gilbert, F.Bull. Seiasmol. Soc. America 51 (1961), 35–49.Google Scholar
(9)Mishra, S. K.Proc. Cambridge Philos. Soc. 60 (1964), 295–312.CrossRefGoogle Scholar
(10)Miklowitz, J.Proc. Int. Cong. Appl. Mechanics (Munich 1964).Google Scholar
(11)Olver, F. W. J.Philos. Trans. Roy. Soc. London Ser A, 247 (1954), 328–68.Google Scholar
(12)Peck, J. C. and Miklowitz, J.Shadow zone…by a circular cavity. Internat. J. Solids and Structures 5 (1969), 437–454.CrossRefGoogle Scholar
(13)Ragas, F. M.Comm. Pure Appl. Math. 11 (1958), 115.Google Scholar
(14)Teng, T. and Richards, P. G.J. Geophys. Res. 74, (1969).Google Scholar
(15)Watson, G. N.Theory of Bessel functions (Camb. Univ. Press, 1944).Google Scholar