Non-Hermitian elastic waveguides with piezoelectric feedback actuation: non-reciprocal bands and skin modes

In this work, we investigate non-Hermitian elastic waveguides with periodically applied proportional feedback efforts, implemented through piezoelectric sensors and actuators. Using onedimensional spectral models for longitudinal motion, it is shown that dispersion diagrams of family structures exhibit non-reciprocal imaginary frequency components, manifesting as wave attenuation or amplification along opposite directions all pass bands. The effects positive negative feedback, well local non-local actuation are investigated. Overall, switching the sign effort inverts direction, while increasing degree non-locality produces splitting bands into multiple interchanging behavior. Furthermore, skin modes localized at boundaries finite domains investigated successfully predicted by winding number complex These results contribute to recent efforts in designing metamaterials novel properties associated physics systems, which may find fruitful technological applications relying on vibration noise control, localization, filtering multiplexing.