Session: 01-01-04: Elastic and Acoustic Metamaterial

Paper Number: 99106

99106 - Polarized Source Model for Active Metamaterials With Extreme Acoustic Properties 

Over the past decades, passive metamaterials have been the primary focus of efforts to physically fabricate transformation acoustics devices. The careful design of subwavelength structures has enabled spatially dependent, anisotropic, and by leveraging resonance, extreme effective properties. However, this class of material has fallen short of providing precise wave control in bulk media due to some fundamental obstacles. Passive unit cells cannot be implemented as independent building blocks; their behavior will depend on their neighbors and therefore their properties will vary with the overall assembly geometry, making the design of a device like a cloak exceedingly complex. Even in a single cell, the bulk modulus and mass density tend to be coupled and the reliance on resonance restricts operation to a narrow frequency band.

An alternate approach is the use of active components. Rather than a specialized feedback control system or a device with a few adjustable modes of operation, we are interested in a highly general active metamaterial. One suitable architecture consists of unit cells composed of sensors and drivers connected through electronics having a scalar gain so that each sensor-driver pair produces a coherent response to impinging waves. It has been shown experimentally that cells acting as monopole sources with amplitude proportional to the local pressure can be characterized by an effective bulk modulus and cells with dipole moments proportional to the local particle velocity can be characterized by an effective mass density. These demonstrations have been limited to only a single cell or a few cells oriented in a line such that they avoid sensing the responses of their neighbors. To realize bulk active metamaterials, it is necessary to model how these cells interact and analytically relate their gains to their effective properties, but such a description still needs to be derived.

Here, we present a polarized source model for active metamaterials composed of sensor-driver pairs that prescribes the gains between connected sensors and drivers for achieving desired effective acoustic properties. We consider a 2D time harmonic system in which a sensor-driver meta-atom is modeled as a source unit cell consisting of a monopole and a dipole in each Cartesian direction. The source amplitudes are related to the local field through their polarizabilities, which are representative of the physical sensor-driver gains. By equating the plane wave response of a source unit cell to the scattering of a subwavelength fluid cylinder, we find explicit functions relating the monopole polarizability to the cylinder bulk modulus and the dipole polarizability to the cylinder mass density. We then use the homogenization of an array of cylinders to determine the polarizabilities necessary for an array of source unit cells to act as a continuous bulk medium with given effective properties.

To verify the accuracy of the property relationships we found, we compare the scattered fields of sample continuous media to those of the equivalent polarized source metamaterial. The scattered fields of continuous media were found through the finite element method, while for the polarized source metamaterials they were determined by summing the contributions of all of the sources. The amplitude of each source was solved from a linear system comprised of the background field, source polarizabilities, and all inter-cell interactions. We specifically demonstrate the challenging case of full cloaking devices that require extreme mass anisotropy, and large effective mass and bulk moduli gradients, but the method is applicable to arbitrary geometries, property distributions, and background fields. We conclude that appropriately designed physical sensor-driver cells could potentially also realize such devices.

Presenting Author: Dylan Kovacevich University of Michigan

Presenting Author Biography: Dylan Kovacevich is a PhD Candidate in the Department of Mechanical Engineering at the University of Michigan. He currently researches active acoustic metamaterials under the advisement of Prof. Bogdan-Ioan Popa. He received his BS and MS in mechanical engineering from Rutgers University.

Authors:

Dylan Kovacevich University of Michigan
Bogdan-Ioan Popa University of Michigan