Experimental realization of an active non-reciprocal metamaterial using an eigen-structure assignment control strategy.

Abstract

This paper presents a class of active non-reciprocal metamaterials (ANMMs) in an attempt to control the flow of acoustic waves along a one-dimensional acoustic duct. The proposed method distinguishes itself from the available approaches where the non-reciprocities are generated either actively or passively by various sources of nonlinearities, circulators and gyroscopic/gyrator components, and/or spatiotemporal modulation. The proposed method relies in its operation on a controller that is designed by simultaneous allocation of both the eigenvalues and eigenvectors. In other words, the entire eigen-structure of the closed-loop system is assigned as deemed necessary. Conventionally, the placement of the eigenvalues has been employed to enhance both the damping and response of the system. However, in this study, the focus is placed on adjusting the eigenvectors in a way that enables the spatial control and redistribution of the wave propagation along the acoustic duct in order to produce any desirable non-reciprocal behavior. During this entire process, the system continues to behave in a linear fashion. The theory governing the operation of this proposed approach is introduced, and a comprehensive experimental validation effort is presented to demonstrate the basic features, non-reciprocal behavior, and control characteristics. Generalization of the presented strategies to two-dimensional acoustic systems is a natural extension of the present work.