Sound transmission through a periodic acoustic metamaterial grating

Abstract This study investigates into the sound transmission through a periodic acoustic metamaterial grating of finite size. The single-layer grating is constructed by periodically arranging sub-wavelength unit cells in a slab, as a part of a large baffle between two acoustic domains. The metamaterial unit cell consists of an open duct decorated with coiled resonators, which intends to suppress sound transmission using its acoustic stop-band. The space-coiling structure allows the metamaterial to operate at low frequency with a compact size. Analytical approach to predict the sound transmission loss (STL) of the combined baffle is developed, which is employed to study its sound attenuation under normal and oblique incidence. Results show that the unit cell geometry, the periodicity of grating elements, and the angle of incidence significantly affect the STL. The STL behavior of the acoustic grating is mainly governed by three physical effects, including the acoustic stop-band, the edge diffraction, and the destructive radiation interference behind the acoustic grating. Detailed mechanism studies for these effects are discussed using numerical examples. Experiment is conducted to validate the proposed numerical approach. This paper presents a theoretical framework to predict and study the performance of acoustic gratings comprised of metamaterial unit cells, which can be further extended to study phase tailoring acoustic metasurface.