Nonlocal active metamaterial with feedback control for tunable bandgap and broadband nonreciprocity

Abstract

In this paper, a nonlocal active metamaterial with feedback control is proposed. For a metamaterial with a symmetric feedback signal, the tunable bandgap and negative effective stiffness are discussed. Symmetric displacement feedback control significantly broadens the bandgap, and combined with velocity feedback control can rapidly attenuate the vibration amplitude. In the metamaterial with an asymmetric feedback signal, the spatial symmetries of the control force are broken by the asymmetrical feedback signal. The non-Hermitian skin effects are achieved by asymmetrical feedback signal. The modes of localized are determined by topological properties with winding number, and the asymmetrical feedback control gain can change the topological properties with winding number. The imaginary parts of the wavenumber are also asymmetrically distributed in space. Theoretical analysis shows that nonlocal active metamaterials with asymmetric feedback signals can achieve nonreciprocal wave propagation and directional amplification across a broad frequency range. Numerical results verify that this metamaterial possesses the characteristics of nonreciprocal wave propagation and directional amplification. The nonlocal active metamaterials in this paper can not only achieve superior bandgap tuning, but also nonreciprocal wave propagation and directional amplification. Function switching between bandgap control and nonreciprocity can be realized by switching the feedback control signal.