Effects of periodicity perturbations on the transmission by underwater phononic crystals.

The effects of periodicity perturbations in underwater phononic crystal layers composed of noninterpenetrating rows of identical shells are investigated. The results for one row are obtained by using a multiple scattering method between shells. Then, taking into account the multiple reflections and transmissions between two adjacent rows, a Debye series method is used to calculate the reflection and transmission coefficients by a finite number of rows. The paper focuses on three kinds of perturbations: (i) variation of the inner radius of shells from row to row, (ii) increase in the spacing from row to row and of the number of rows, and (iii) substitution of simple steel rows by steel-polyethylene bilayers. It is shown by studying the transmission coefficient that the case (i) permits the insertion of narrow pass bands in the stop band while the two other cases (ii) and (iii) widen the stop band. The study intends to model simple underwater acoustic filters.