Active nonreciprocal metamaterial using an eigen-structure assignment control strategy.

Abstract

A class of active nonreciprocal metamaterials (ANMMs) is developed to control the flow and distribution of energy along periodic dynamical systems. Such a development constitutes a radical departure from the currently available approaches where the non-reciprocities are generated either by utilizing various sources of passive nonlinearities, gyroscopic circulators, spatiotemporal modulation, or active control of nonlinear systems. The proposed ANMM cell consists of a one-dimensional acoustic duct provided with linear active control capabilities. The controller is designed by simultaneous assignment of both the eigenvalues and eigenvectors, i.e., the entire eigen-structure, of the closed-loop system. Conventionally, the placement of the eigenvalues has been considered to improve the damping and system's response. However, in this study, the emphasis is placed also on tailoring the eigenvectors in order to enable the spatial control and redistribution of the wave propagation energy flow along the acoustic duct in such a manner that it can introduce non-reciprocity as well as control its direction and reversal. During this entire process, the system remains behaving in a linear fashion. Numerical examples are presented to demonstrate the basic features and non-reciprocal behavior, as well as the energy flow characteristics.