Fractal labyrinthine acoustic metamaterial in planar lattices

Labyrinthine acoustic metamaterial provides a flexible and unprecedented ability to manipulate the sound wave propagation, such as sound blocking, cloaking, supertunneling etc. However, the design of labyrinthine acoustic metamaterial with excellent properties remains challenging with a traditional zigzag channel. Here, we develop a class of fractal-inspired labyrinthine acoustic metamaterials with hierarchical zigzag channels and highlight the influences of the self-similar fractal hierarchies on their band structures. Band structures of fractal-inspired labyrinthine acoustic metamaterials in the five representative Bravais lattices are also investigated. Our results show that the self-similar fractal can be effectively used to widen the total band gaps and lower the frequency of the first bandgap. Furthermore, for the second order fractal labyrinthine acoustic metamaterial arranged in different Bravais lattices, several excellently wide bandgaps appear in the different frequency ranges. By actively-tuning the Bravais lattice, we have a chance to yield excellently wide and tunable bandgaps. Thus, this work provides an insight into the critical role of the self-similar fractal on the band structure of the labyrinthine acoustic metamaterial, and gives a guidance for the selection of Bravais lattices with a desired band structure.