Harmonic Wave Propagation in a Periodically Layered, Infinite Elastic Body: Plane Strain, Analytical Results

[+] Author and Article Information
T. J. Delph, G. Herrmann

Division of Applied Mechanics, Department of Mechanical Engineering, Stanford University, Stanford, Calif. 94305

R. K. Kaul

State University of New York at Buffalo, Buffalo, N. Y. 14214

J. Appl. Mech 46(1), 113-119 (Mar 01, 1979) (7 pages) doi:10.1115/1.3424481 History: Received January 01, 1978; Revised July 01, 1978; Online July 12, 2010


The problem of harmonic wave propagation in an unbounded, periodically layered elastic body in a state of plane strain is examined. The dispersion spectrum is shown to be governed by the roots of an 8 × 8 determinant, and represents a surface in frequency-wave number space. The spectrum exhibits the typical stopping band characteristic of wave propagation in a periodic medium. The dispersion equation is shown to uncouple along the ends of the Brillouin zones, and also in the case of wave propagation normal to the layering. The significance of this uncoupling is examined. Also, the asymptotic behavior of the spectrum for large values of the wave numbers is investigated.

Copyright © 1979 by ASME
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