Acoustic band structure of periodic elastic composites

We present the first full band-structure calculations for periodic, elastic composites. For transverse polarization of the vibrations we obtain a ``phononic'' band gap which extends throughout the Brillouin zone. A complete acoustic gap or a low density of states should have important consequences for the suppression of zero-point motion and for the localization of phonons, and may lead to improvements in transducers and in the creation of a vibrationless environment.