Acoustic metamaterials are structures with exotic acoustic properties, with promising applications in acoustic beam steering, focusing, impedance matching, absorption and isolation. Recent work has shown that the efficiency of many acoustic metamaterials can be enhanced by controlling an additional parameter known as Willis coupling, which is analogous to bianisotropy in electromagnetic metamaterials. The magnitude of Willis coupling in a passive acoustic meta-atom has been shown theoretically to have an upper limit, however the feasibility of reaching this limit has not been experimentally investigated. Here we introduce a meta-atom with Willis coupling which closely approaches this theoretical limit, that is much simpler and less prone to thermo-viscous losses than previously reported structures. We perform two-dimensional experiments to measure the strong Willis coupling, supported by numerical calculations. Our meta-atom geometry is readily modeled analytically, enabling the strength of Willis coupling and its peak frequency to be easily controlled.

Noise mitigation of stage machinery can be quite demanding and requires innovative solutions. In this work, an acoustic metamaterial capsule is proposed to reduce the noise emission of several stage machinery drive trains, while still allowing the ventilation required for cooling. The metamaterial capsule consists of c-shape meta-atoms, which have a simple structure that facilitates manufacturing. Two different metamaterial capsules are designed, simulated, manufactured, and experimentally validated that utilize an ultra-sparse and air-permeable reflective meta-grating. Both designs demonstrate transmission loss peaks that effectively suppress gear mesh noise or other narrow band noise sources. The ventilation by natural convection was numerically verified, and was shown to give adequate cooling, whereas a conventional sound capsule would lead to overheating. The noise spectra of three common stage machinery drive trains are numerically modelled, enabling one to design meta-gratings and determine their noise suppression performance. The results fulfill the stringent stage machinery noise limits, highlighting the benefit of using metamaterial capsules of simple c-shape structure.