Labyrinthine Resonator Design for Low-Frequency Acoustic Meta-Structures

Acoustic meta-structure represents a class of composite structure characterized by local resonators that improve the sound absorption. In recent years, the interest for these complex systems is tremendously risen, above all for their capacity to alter waves in low-frequency ranges. Local resonators are generally based on quarter-wavelength resonance, which leads to not negligible problems: the narrow bandwidth of influence and the fact that for low-frequency design, the quarter-wavelength means a wave path too big for conventional problems where limited thickness is a requirement. Labyrinth resonators (LRs) can be the perfect solution in order to overcome these problems: the tube follows a labyrinth path that enables the resonance effect without increasing too much the sample thickness. The whole length can be stretched in other directions rather than along the thickness. Even though the resonance behavior of quarter-wavelength tubes and labyrinth resonators is quite similar, the analytical formula of quarter-wavelength tubes is not overall able to predict the natural frequency of LRs. The scope of this project is to prove that labyrinth resonance frequency cannot be predicted through conventional quarter-wavelength formula, maynly because natural frequency depends just on tube length. Moreover, a new analytical formula is proposed by considering the main parameters of labyrinth resonators: number of labyrinth branches, dimension of the single-port air-inlet, and the total length of the labyrinth.