Band gap characteristics of radial wave in a two-dimensional cylindrical shell with radial and circumferential periodicities

A two-dimensional cylindrical shell (2DCS) structure with radial and circumferential periodicities is proposed in this paper. The band gap characteristics of radial wave propagating radically from the inner circle of the structure are investigated numerically. According to the calculation and discussion of wave transmission behavior, radial wave in the structure is found to show distinct attenuation in certain frequency region, i.e. wave band gap. The internal mechanism of the band gap is then investigated and the Bragg scattering effect is illustrated. Furthermore, the detailed behaviors of radial wave within the band gap are studied, especially for the transmission peaks. Special localization phenomenon is observed where the mechanical energy localizes strongly in a certain circle of scatterers. Consistency is then found by comparing these localization modes of the whole 2DCS with those of corresponding single scatterers, which indicates that the localization phenomenon is essentially resulted from the local resonance behavior of certain scatterers.