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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  and
R.K. Kaul
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.

Keywords

Periodic StructureQuasi-Periodic SolutionsBrillouin ZoneHill's DiscriminantReflection SymmetryEigenvalue Equations
Type
Invited Paper
Information
Journal of Mechanics , Volume 16 , Issue 1 , March 2000 , pp. 9 - 14
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. 47–88 (1883).CrossRefGoogle Scholar
2Kaul, R. K. and Barone, R. C. A., “Factorization of Floquet's Characteristic Equation in the Case of Reflection Symmetry.” Second International Conference on Mathematical and Numerical Aspects of Wave Propagation, Conducted by SIAM, University of Delaware (1993).Google Scholar
3Kaul, R. K. and Herrmann, G., “Free Torsional Vibrations of an Elastic Cylinder with Laminated Periodic Structure,” Int. J. Solids and Structures, 12, pp. 449–466 (1976).CrossRefGoogle Scholar
4Kaul, R. K. and Lee, C. S., “Free Torsional Vibrations of a Hollow Cylinder with Laminated Periodic Structure,” Int. J. Solids and Structures, 18, pp. 297–314 (1982).CrossRefGoogle Scholar