3D Hilbert fractal acoustic metamaterials: low-frequency and multi-band sound insulation

Abstract

In this letter, we present a class of three-dimensional (3D) labyrinthine acoustic metamaterials with self-similar fractal technique, which can produce multiple frequency-band sound insulation in deep-subwavelength scale. By simultaneously exploiting the multi-frequency bandgaps and the low-frequency characteristics, the Hilbert cubes are explored to design the 3D Hilbert fractal acoustic metamaterials (HFAMs). The multiple-band features of the HFAMs are examined by the finite element method and the effective medium theory, in which the negative bulk modulus and the mass density are responsible for the formation of the multi-bandgaps. These multi-frequency properties are induced by the Fabry-Perot multi-resonance of 3D HFAMs, which possess an ultra-high refractive index. Hence, the multi-band sound insulations of 3D HFAMs with the negative effective property are achieved below 500Hz. These properties of the designed 3D HFAMs provide an effective way for acoustic metamaterials to achieve multi-band filtering and noise attenuation in the low-frequency regime.

Recent Advances in Acoustic Metamaterials for Simultaneous Sound Attenuation and Air Ventilation Performances

“…The concept of acoustic metamaterials is not limited only to locally resonant materials or periodic structures. Several other types of acoustic metamaterials have been reported, such as coiling-up space type AMs [59,60], split-ring type AMs, topological acoustics [61], fractal acoustic metamaterials [62][63][64][65][66], helical-structured metamaterials [67,68], and acoustic metasurfaces [69,70]. For coiling-up space type acoustic metamaterials, the incident acoustic waves are confined in coiled subwavelength cross-section channels, thereby resulting in extraordinary acoustic properties such as double negativity and near-zero index to a high effective refractive index of unit cells [71,72].…”

Review and prospects of metamaterials used to control elastic waves and vibrations

“…These biological systems-inspired materials offer a completely new approach to the structural design of acoustic metamaterials. In addition, many researchers have introduced fractal geometry into phononic crystals to obtain better dynamic properties, such as Hilbert fractal [29,30], Koch fractal [31,32]. However, the related acoustic metamaterials mentioned above are all passive metamaterials, and the structural invariance of passive metamaterials limits their performance, function, and tunability.…”

Sound absorption in Hilbert fractal and coiled acoustic metamaterials

“…27,28 The description is made via impedance tube experiments and numerical simulations. The space-filling curve used in this work is the Hilbert fractal 29,30 [Figs. 1(f) and 1(g)].…”