SOUND ISOLATION FROM CUBIC ARRAYS OF AIR BUBBLES IN WATER

We present systematic and extensive evidence for the existence of comp lete, multiple, huge stop bands in the band structure for cubic arrays of air bubbles in water. We investigate face-centered cubic (fcc), bo dy-centered cubic (bcc), and simple-cubic (sc) arrangements using the Fourier series expansion method which does not require matching of the messy boundary conditions. The lowest stop bands are largest for a vo lume fraction f less than or equal to 10%, with a gap/midgap ratio of approximate to 1.8 for all the three geometries. Surprisingly interest ing but rigorously justifiable is the fact that the low-frequency flat passbands for the perfectly periodic systems correspond to the discre te modes of a single bubble. This is an artifact of the low filling fr action and huge density contrast in air and water. We stress that such a simple inhomogeneous system as made up of air bubbles in water exhi bits the widest stop bands ever reported for elastic/acoustic as well as dielectric composites. (C) 1998 Elsevier Science B.V.