Active Feedback Control of One-Dimensional Willis Metamaterials for Directional Elastic Wave Manipulation
摘要
Willis metamaterials offer unique opportunities for the manipulation of elastic waves due to their additional constitutive coupling. However, in most passive designs, the effective properties are fixed once the microstructure is selected. This paper introduces a one-dimensional active Willis metamaterial that incorporates acceleration and velocity feedback control into an asymmetric locally resonant mass-spring lattice. A first-order Taylor expansion homogenization technique is developed to derive the effective Willis constitutive relations, demonstrating that the feedback gains serve as independent parameters for tuning the effective properties, including the Willis coupling coefficient. By formulating the scattering matrix, we show that Willis coupling leads to direction-dependent reflection amplitude and phase. Optimization of the feedback gains enables unidirectional zero reflection (UZR) at prescribed frequencies in both purely lossy and gain-containing configurations. This UZR condition is linked to an exceptional point (EP) in the non-Hermitian scattering matrix, with the eigenvalue response near the EP showing enhanced sensitivity to frequency perturbations. The design is extended to multi-cell configurations under lossy conditions to achieve unidirectional perfect absorption (UPA) by exploiting bandgap-induced transmission suppression and distributed dissipation. The proposed feedback-controlled approach provides a flexible method for adaptive wave manipulation, advancing the development of non-Hermitian wave-control devices, including sensors and directional absorbers.