Bandgap characteristics of a duct embedded with multiple membrane-cavity resonators in the presence of mean flow

Bandgap characteristics of periodic structures can be investigated by the effective material properties via reflection and transmission coefficients. In this paper, for the first time, corresponding effective properties such as mass density, relative impendence and refractive index are presented for a duct embedded with membrane-cavity resonators in its sidewalls. Around the membrane or cavity resonant frequencies, the effective density varies drastically with the negative values, implying that its acceleration has opposite phase with the dynamic pressure load, within which almost a total sound pressure reflection can be obtained. Moreover, the presence of flow will cause a significant decrease in both the amplitude of relative impedance and refractive index, especially for the resonant peaks. Mean flow effect on bandgap characteristics of periodic resonant cells is conducted in the last part. Significant decrease and slight shift can be observed in the Bragg reflection and locally resonant bandgaps, and their dispersion curve (phase change per cell) cannot reach zero or +/-pi within these bandgaps. It implies that the presence of flow in duct is similar to the damping effect which leads to the dispersion branch that cannot cover the entire Brillouin zone.