Eur. Phys. J. B 3, 155-161 (1998)
https://doi.org/10.1007/s100510050296

Sonic stop-bands for cubic arrays of rigid inclusions in air

Laboratoire de Dynamique et Structures des Matériaux Moléculaires (URA CNRS No. 801) , U.F.R. de Physique, Université de Lille I, 59655 Villeneuve d'Ascq Cedex, France

Corresponding author: ^a manvir@sirio.ifuap.buap.mx

Received: 24 October 1997
Revised: 1 December 1997
Accepted: 6 March 1998
Published online: 15 May 1998

Abstract

Extensive band structures have been computed for cubic arrays of rigid spheres and cubes in air. Complete stop bands are obtained for the face-centered-cubic (fcc) structure; however, there is no gap for the body-centered-cubic (bcc) and simple-cubic (sc) structures. These gaps start opening up for a filling fraction of ≈54%(27% ) for spherical (cubic) inclusions and tend to increase with the filling fraction, exhibiting a maximum at the close-packing. We also propose a tandem structure that allows the achievement of an ultrawideband filter for environmental or industrial noise in the desired frequency range. This work is motivated by the recent experimental measurement of sound attenuation on the sculpture, by Eusebio Sempere, exhibited at the Juan March Foundation in Madrid (Nature 378, 241 (1995)) and complements the corresponding theoretical work (Appl. Phys. Lett. 70, 3218 (1997)).