Research on pass band with negative phase velocity in tubular acoustic metamaterial

The tubular acoustic metamaterial with the double negativity based on the membranes and side holes periodically distributed along a pipe is studied with the Bloch theory. The results are verified by the full-wave simulation method and are used to explain the related experimental phenomena: the low-frequency forbidden band starting from the zero Hertz and the relations between the cutoff frequencies of the forbidden and pass bands in the single negativity metamaterials and the double negativity metamaterial composed of them. Based on the Bloch theory, the structural parameters of the membranes and side holes in the metamaterial are optimized to achieve the maximum pass band with the negative phase velocity (PBNV) since the PBNV is determined by the coactions of the membranes and side holes. Furthermore, the structures of the metamaterials are improved in order to broaden the PBNV further and achieve the balanced condition simultaneously.