A Micropolar Metabeam With Nonlocal Feedback Control Circuits

Active control schemes provide emergent wave properties and flexible tunability in mechanical systems. Here, we propose both analytically and numerically a non-Hermitian metamaterial system enabled by piezoelectric patches and electronic non-local feedback control. The metamaterial system is physically realized by a non-local microploar beam with non-local feedback control. Since the non-local feedback control breaks spatial reciprocity, the proposed metabeam supports not only non-reciprocal flexural wave amplification and attenuation, but also non-Hermitian skin effect featuring bulk localized eigenmodes in the finite structure. The non-reciprocal amplification and attenuation phenomena are quantitatively predicted by band structure analyses under both the continuum and discrete spring-mass representation, which can be attributed to the work exchange between mechanical and electric works. The non-Hermitian skin effect and the associated bulk localized eigenmodes are characterized by a topological invariant. In addition, direction-dependent bending stiffness is also demonstrated in the non-local micropolar piezoelectric metabeam with proper transfer functions. The electronically controllable non-Hermitian metabeam could pave the ways for designing future systems such as synthetic biofilaments and membranes with feed-back control schemes.