Abstract
Acoustic and ultrasonic waves are powerful probes for many macroscopic systems ranging from the oceanic environment to devices under mechanical stress. From the technological point of view, tools must be developed in order to understand the propagation of acoustic waves through inhomogeneous media. In this work, a variational method is developed to study the acoustic response of three-dimensional systems with periodically distributed scatterers. The dispersion relations of the corresponding acoustic bands are obtained. They determine the stop bands. Also, it is shown that symmetry plays an important role in the full problem of transmitting acoustic waves through a periodic structure. If the symmetry of the external wave does not match with the band at its corresponding frequency, the acoustic energy cannot be transmitted. The existence of these bands has been previously reported in two-dimensional sonic crystals [J. V. Sánchez-Pérez et al., Phys. Rev. Lett. 80, 3080–3083 (1998)]. [Work supported by CICyT of Spain.]
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