Transmission Characteristics in Tubular Acoustic Metamaterials Studied with Fluid Impedance Theory

Tubular acoustic metamaterials with negative densities composed of periodical membranes set up along pipes are studied with the fluid impedance theory. In addition to the conventional forbidden bands induced by the Bragg-scattering due to the periodic distributions of different acoustic impedances, the low-frequency forbidden band (LFB) with the low-frequency limit of zero Hertz is studied, in which the LFB is explained with acoustic impedance matching and the Bloch theory. Furthermore, the influences of the structural parameters of the tubular acoustic metamaterials on the transmission characteristics, such as the transmission coefficients, dispersion curves, widths of forbidden and pass bands, fluctuations in pass bands, etc., are evaluated, which can be used in the optimization of the acoustic insulation ability of the metamaterials.