Acoustic Metamaterial Design by Phase Delay Derivation Using Transfer Matrix

Abstract

When acoustic elements such as quarter-wave, Helmholtz, labyrinthine-type or hook-type resonators are arranged sequentially, sound waves can be refracted in a specific frequency range. Thus, a metasurface may be designed to reduce noise by locating two sequentially arranged acoustic elements symmetrically. Phase delay, which can be calculated with a transfer function of the acoustic element, needs to be obtained to decide on acoustic element design parameters. However, in the case of a complex structure with labyrinthine-type or hook-type resonators, it can be difficult to calculate the phase delay accurately because each designer may have a different estimation method for the propagation direction of the sound wave. Therefore, this study presents a method for accurately deriving the phase delay required when designing a metasurface with a complex structure. The phase delay was calculated using the pressure and velocity derived from FEM and the transfer matrix of the main duct. Using the proposed method, a metasurface with symmetrically arranged acoustic elements was designed, and the noise reduction effect was confirmed through a speaker test. This study could be very helpful, since through it, any kinds of complex acoustic elements are able to be designed with accurate phase delay calculations.