  In this work, we investigate non-Hermitian acoustic waveguides designed with
periodically 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 is
shown that dispersion diagrams of this family of metamaterials exhibit
non-reciprocal imaginary frequency components, manifesting as wave attenuation
or amplification along opposite directions for all pass bands. The effects of
different feedback laws are investigated. Furthermore, the non-Hermitian skin
effect manifesting as topological modes localized at the boundaries of finite
domains is investigated and successfully predicted by the topology of the
reciprocal space. This work extends previous numerical results obtained for a
piezoelectric rod system and contributes to recent efforts in designing active
metamaterials with novel properties associated with the physics of
non-Hermitian systems, which may find fruitful technological applications
related to noise control, wave localization, filtering and multiplexing.

Applied Physics