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We investigate non-Hermitian elastic lattices characterized by non-localfeedback control interactions. In one-dimensional lattices, we show that theproportional control interactions produce complex dispersion relationscharacterized by gain and loss in opposite propagation directions. Depending onthe non-local nature of the control interactions, the resulting non-reciprocityoccurs in multiple frequency bands characterized by opposite non-reciprocalbehavior. The dispersion topology is also investigated with focus on windingnumbers and non-Hermitian skin effect, which manifests itself through bulkmodes localized at the boundaries of finite lattices. In two-dimensionallattices, non-reciprocity is associated with directional dependent waveamplification. Moreover, the non-Hermitian skin effect manifests as modeslocalized at the boundaries of finite lattice strips, whose combined effect intwo directions leads to the presence of bulk modes localized at the corners offinite two-dimensional lattices. Our results describe fundamental properties ofnon-Hermitian elastic lattices, and open new possibilities for the design ofmetamaterials with novel functionalities related to selective wave filtering,amplification and localization. The results also suggest that feedbackinteractions may be a useful strategy to investigate topological phases ofnon-Hermitian systems.

Dynamics and topology of non-Hermitian elastic lattices with non-local feedback control interactions