### ASA 125th Meeting Ottawa 1993 May

## 2pPA1. Stop bands in periodic and random media.

**E. N. Economou
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*FORTH, P.O. Box 1527, 711 10 Heraklio, Crete, Greece
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In periodic media, frequency regions may exist at which no bounded at
infinity solution of the wave equation exists. In random systems frequency
regions may appear at which all bounded solutions are localized, i.e., decay
exponentially at infinity. Both regions give rise to stop bands. Such stop
bands appear easily for acoustic waves in bubbly liquids. They are also
predicted to exist for elastic waves in binary composites consisting of gold or
lead spherical inclusions periodically placed in a Si, Be, or SiO[sub 2] (for
gold inclusions only) matrix and occupying about 10% of the volume. The
midfrequency (omega)[sub g] of the stop band was found to satisfy the relation
(omega)[sub g]=yc[sub il]/R[sub i], where c[sub il] is the longitudinal
velocity in the inclusion material, R[sub i] is the radius of each inclusion,
and y is a number between 1 and 2.