Propagation of Low Frequency Elastic Disturbances in a Three-Dimensional Composite Material

[+] Author and Article Information
W. Kohn

Department of Physics, University of California, San Diego, La Jolla, Calif.

J. Appl. Mech 42(1), 159-164 (Mar 01, 1975) (6 pages) doi:10.1115/1.3423508 History: Received August 01, 1973; Revised July 01, 1974; Online July 12, 2010


This paper is a generalization to three dimensions of an earlier study for one-dimensional composites. We show here that in the limit of low frequencies the displacement vector u i (r ,t) can be written in the form ui (r ,t) = (∂ij + vijl (r ) ∂/∂xl + [[ellipsis]]) Uj (r ,t). Here Uj (r ,t) is a slowly varying vector function of r and t which describes the mean displacement of each cell of the composite. Its components satisfy a set of three coupled partial differential equations with constant coefficients. These coefficients are obtainable from the three-by-three secular equation which yields the low-lying normal mode frequencies, ω(k ). Information about local strains is contained in the function vijl (r ), which is characteristic of static deformations, and is discussed in detail. Among applications of this method is the structure of the head of a pulse propagating in an arbitrary direction.

Copyright © 1975 by ASME
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