Active Acoustic Metamaterials With Programmable Densities Using an H-∞ Controller

Abstract

Various types of acoustic metamaterials have been developed to control the flow of acoustical energy through these materials. Most of these metamaterials are passive in nature with pre-tuned and fixed material properties. In this paper, the emphasis is placed on the development of a class of one-dimensional acoustic metamaterials with programmable densities in order to enable the control the acoustic wave propagation in these media. With such unique capabilities, the proposed active acoustic metamaterials (AAMM) can be utilized to physically realize, for example, acoustic cloaks, wave shifters and focusers, tunable acoustic absorbers and reflectors, as well as non-reciprocal acoustic media. The theoretical analysis of this class of AAMM with programmable effective dynamical densities is presented for an array of cavities separated by piezoelectric boundaries. These boundaries provide means for controlling the stiffness of the individual cavity and, in turn, its dynamical densities. In this regard, a disturbance rejection strategy is considered which is based on an H-∞ robust controller. The time and frequency response characteristics of a unit cell of the AAMM are investigated for various parameters of the controller in an attempt to optimize the performance characteristics. Extension of this study to include active control capabilities of the bulk modulus of the metamaterials would enable the development of wide classes of AAMM that are only limited by our imagination.