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An Application of Elastodynamic Reciprocity to Reflection by an Obstacle in a Waveguide

Published online by Cambridge University Press:  05 May 2011

J.D. Achenbach
J.D. Achenbach*
Affiliation:
Center for Quality Engineering and Failure Prevention, Northwestern University, Evanston, IL 60208, U.S.A.
*
*professor
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Abstract

The reciprocal identity which connects two elastodynamic states, denoted by A and B, is used in this paper to obtain two results for an elastic layer. The first is an orthogonality condition for wave modes. For that case the states A and B are wave modes propagating in the same direction. The second result concerns reflection and transmission of wave motion by an obstacle in the layer. Now state A is defined by a superposition of incident wave modes and its reflection and transmission by the obstacle. Expressions for the reflection and transmission coefficients are obtained by selecting counter propagating wave modes for state B. It is also shown that the reflection by an obstacle in a layer can be extended to obtain the reflection and transmission coefficients for a planar array of obstacles in an unbounded elastic solid. For clarity all results are presented for horizontally polarized transverse wave motion.

Type
Articles
Information
Journal of Mechanics , Volume 16 , Issue 2 , June 2000 , pp. 97 - 101
Copyright
Copyright © The Society of Theoretical and Applied Mechanics, R.O.C. 2000

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References

REFERENCES

1deHoop, A. T., Handbook of Radiation and Scattering of Waves, Academic Press, London, p. 429 (1995).Google Scholar
2Love, A. E. H., A Treatise on the Mathematical Theory of Elasticity, Dover Publication, New York (1944).Google Scholar
3Betti, E., “Teori Della Elasticita,” Il Nuovo Ciemento, Ser. 2, pp. 7–10 (1872).Google Scholar
4Lord, Rayleigh, “Some General Theorems Relating to Vibration,” London Math. Soc. Proc., 4, pp. 366–368 (1873).Google Scholar
5Maxwell, J. C., “On the Calculation of the Equilibrium and Stiffness of Frames,” Phil. Mag, 27, p. 294 (1864).CrossRefGoogle Scholar
6Achenbach, J. D., Wave Propagation in Elastic Solids, North Holland/Elsevier (1973).Google Scholar
7Achenbach, J. D., Gautesen, A. K. and McMaken, H., Ray Methods for Waves in Elastic Solids, Pitman Advanced Publishing Program, Boston, p. 34 (1982).Google Scholar
8Achenbach, J. D. and Kitahara, M., “Reflection and Transmission of an Obliquely Incident Wave by an Array of Spherical Cavities,” J. Acoust. Soc. Am., 80, pp. 1209–1214 (1986).CrossRefGoogle Scholar
9Achenbach, J. D, Kitahara, M., Mikata, Y. and Sotiropoulos, D. A., “Reflection and Transmission of Plane Waves by a Layer of Compact Inhomo-geneities,” PAGEOPH, 128, pp. 101–118 (1988).CrossRefGoogle Scholar
10Angel, Y. C. and Achenbach, J. D., “Reflection and Transmission of Elastic Waves by a Periodic Array of Cracks,” J. of Applied Mech., 52, pp. 33–41 (1985).CrossRefGoogle Scholar
11Angel, Y. C. and Achenbach, J. D., “Reflection and Transmission of Elastic Waves by a Periodic Array of Cracks: Oblique Incidence,” Wave Motion, 7, pp. 375–397 (1985).CrossRefGoogle Scholar
12Mikata, Y. and Achenbach, J. D., “Interaction of Harmonic Waves with a Periodic Array of Inclined Cracks,” Wave Motion, 10, pp. 59–72 (1988).CrossRefGoogle Scholar