Engineering three-dimensional labyrinthine fractal acoustic metamaterials with low-frequency multi-band sound suppression.

Acoustic metamaterials are a class of artificially periodic structures with extraordinary elastic properties that cannot be easily found in naturally occurring materials and can be applied to regulate the sound propagation behavior. The fractal configuration can be widely found in the acoustic system, like characterizing the broadband or multi-band sound propagation. This work will engineer three-dimensional (3D) labyrinthine fractal acoustic metamaterials (LFAMs) to regulate the sound propagation on subwavelength scales. The dispersion relations of LFAMs are systematically analyzed by the Bloch theory and the finite element method (FEM). The multi-bands, acoustic modes, and isotropic properties characterize their acoustic wave properties in the low-frequency regime. The effective bulk modulus and mass density of the LFAMs are numerically calculated to explain the low-frequency bandgap behaviors in specific frequencies. The transmissions and pressure field distributions of 3D LFAMs have been used to measure the ability for sound suppression. Furthermore, when considering the thermo-viscous loss on the transmission properties, the high absorptions occur within the multi-band range for low-frequency sound. Hence, this research contributes to potential applications on 3D LFAMs for multi-bands blocking and/or absorption on deep-subwavelength scales.