Plane wave propagation in finite 2-2 composites

A common practice in the study of wave propagation in stratified structures is to use the Floquet (or Bloch) condition to derive the dispersion relation, leading to the passband and stopband structures. However, the Floquet condition is valid only for an infinite system while a real system always has finite dimensions. We report a study on wave propagation in a finite 2-2 composite by using the transfer (T) matrix technique. Through introducing a new definition for the dispersion relation using the T matrix, the passbands and stopbands are calculated for a finite system without the Floquet condition. The formation of stopbands and passbands with the increase of composite size can now be clearly seen. The spatial profile of the vibration pattern inside a finite composite can also be calculated using this technique, which reveals strong edge effects. The effects of randomization on the wave localization in a 2-2 composite are also studied.