Broadband low-frequency sound attenuation in duct with embedded periodic sonic black holes

This paper studies the sound wave propagation and attenuation characteristics in a new type of acoustic device, which is constructed by periodically embedding sonic black holes (SBHs) into an air-filled waveguide. The SBH is realized by cascading a set of rigid rings with linearly or quadratically changing inner radii into each unit cell section. Acoustic impedance variation rendered by this specially tailored profile progressively slows down the incident sound velocity to generate the SBH effects including wavelength compression, energy focalization, and dissipation with inherent damping in the duct. Upon developing and validating a model based on the transfer matrix method (TMM), the sound transmission loss (STL) of a finite-length periodic duct with different geometrical parameters is investigated. Different from a single SBH unit which can trigger the complete SBH process only above the cut-on frequency, the proposed periodic arrangement offers strong attenuation bands in the low-frequency range of the STL curve well below the frequency barrier imposed by the cut-on frequency of a single SBH unit. Mechanism studies reveal that these attenuation bands result from the interplay between the Bragg scattering and the SBH-specific slow-sound effects. The latter is shown to equivalently increase the effective lattice constant of the periodic duct, thus lowering the frequency of the Bragg bandgap. It is also shown that in contrast to conventional locally-resonant metamaterials, the proposed device exhibits far less dependence on the number of unit cells and the amount of rigid rings to activate a significant low-frequency stop-band. These appealing features could greatly simplify the design and application of SBH-based metamaterials, making it a promising solution for low-frequency wave manipulation and noise control.