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In this work, we investigate non-Hermitian acoustic waveguides designed withperiodically applied feedback efforts using electrodynamic actuators.One-dimensional spectral (infinite-dimensional) and finite element(finite-dimensional) models for plane acoustic waves in ducts are used. It isshown that dispersion diagrams of this family of metamaterials exhibitnon-reciprocal imaginary frequency components, manifesting as wave attenuationor amplification along opposite directions for all pass bands. The effects ofdifferent feedback laws are investigated. Furthermore, the non-Hermitian skineffect manifesting as topological modes localized at the boundaries of finitedomains is investigated and successfully predicted by the topology of thereciprocal space. This work extends previous numerical results obtained for apiezoelectric rod system and contributes to recent efforts in designing activemetamaterials with novel properties associated with the physics ofnon-Hermitian systems, which may find fruitful technological applicationsrelated to noise control, wave localization, filtering and multiplexing.

Non-Hermitian acoustic waveguides with periodic electroacoustic feedback