Polarized source model for the design of bulk active metamaterials

Abstract

Active acoustic metamaterials have the potential for the broadband realization of complex property distributions, such as those prescribed by transformation acoustics. Especially promising are metamaterials composed of unit cells consisting of paired sensors and drivers that generate a programmed acoustic response to the local pressure and particle velocity. Previous experimental works have used this approach to implement active metamaterials of theoretically controllable effective bulk modulus and mass density, but were limited to only one or a few non-interacting cells and were not applicable to general bulk media. Here, we further develop some of the theory necessary to overcome these limitations and enable the design of bulk active metamaterials with desired properties, including steep gradients and mass density anisotropy. We present a highly simplified model of sensor-driver unit cells as interacting polarized sources that allow us to derive closed-form expressions directly relating the effective acoustic properties to the required gains, or polarizabilities. We validate our model for several example geometries and property distributions by comparing the scattered fields of the theoretical metamaterials with those of the equivalent continuous media. In particular, we show compatibility with transformation acoustics and demonstrate cylindrical cloaks using polarized sources.