Performance and stability constraints of an active acoustic metamaterial

Abstract

Metamaterials are the subject of significant interest due to their ability to reproduce behaviour beyond what is possible with naturally occurring media such as the appearance of high levels of wave attenuation at specified frequencies, known as band gaps. These band gaps can be tuned to appear at low frequencies, providing isolation performance at long wavelengths where the performance of traditional passive isolation techniques is generally poor. However, due to the resonant nature of the band gaps they tend to only extend over a very narrow frequency range. The application of active control within a metamaterial structure can provide an effective solution to this since the natural material response can be modified to enable attenuation over a much broader frequency region. This paper presents an active acoustic metamaterial, consisting of an array of active Helmholtz resonators. An actuator embedded within the resonators is used with a feedback controller to regulate the velocity of the air within the neck of the resonator elements, thereby enhancing their natural performance. The attainable performance of such an active metamaterial, however, is constrained by the requirement to maintain closed loop stability and formal constraints are presented and illustrated in the paper. Constrained non-linear optimisation is then employed to design a practical feedback controller consisting of an FIR filter, and its performance analysed.

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