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A Factorization Algorithm for Wave Propagation in Periodic Structures with Application to Torsional Waves in an Infinite Cylinder

Published online by Cambridge University Press:  05 May 2011

R.C.A. Barone*
Affiliation:
Genesee Community College, Batavia, NY 14020-9704, U.S.A.
R.K. Kaul*
Affiliation:
State University of New York at Buffalo, Buffalo, NY 14260-2050, U.S.A.
*
*Professor
*Professor
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Abstract

In this paper we introduce a fundamentally new concept in the field of wave-propagation in periodic structures. We show that a phenomenal amount of simplification can be achieved by using symmetry arguments. Problems which ordinarily lead to (2n × 2n) determinantal eigenvalue equations, can effectively be reduced to two (n × n) determinantal equations. We state the final result in the form of a factorization theorem and then with the help of a simple problem, we show the superiority of this new result over the traditional methods of solution.

Type
Invited Paper
Copyright
Copyright © The Society of Theoretical and Applied Mechanics, R.O.C. 2000

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References

REFERENCES

1Floquet, G., Sur les équations différentielles linéaires á coefficients périodiques, Ann. Ecole. Norm. Sup., 12, pp. 4788 (1883).CrossRefGoogle Scholar
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3Kaul, R. K. and Herrmann, G., “Free Torsional Vibrations of an Elastic Cylinder with Laminated Periodic Structure,” Int. J. Solids and Structures, 12, pp. 449466 (1976).CrossRefGoogle Scholar
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