Labyrinthine Acoustic Metamaterials with Space-Coiling Channels for Low-Frequency Sound Control

Abstract

We numerically analyze the performance of labyrinthine acoustic metamaterials with internal channels folded along a Wunderlich space-filling curve to control low-frequency sound in air. In contrast to previous studies, we perform direct modeling of wave propagation through folded channels, not introducing effective theory assumptions. As a result, we reveal that metastructures with channels, which allow wave propagation in the opposite direction to incident waves, have different dynamics as compared to those for straight slits of equivalent length. The differences are attributed to activated tortuosity effects and result in 100% wave reflection at band gap frequencies. This total reflection phenomenon is found to be insensitive to thermo-viscous dissipation in air. For labyrinthine channels generated by iteration levels, one can achieve broadband total sound reflection by using a metamaterial monolayer and efficiently control the amount of absorbed wave energy by tuning the channel width. Thus, the work contributes to a better understanding of labyrinthine metamaterials with potential applications for reflection and filtering of low-frequency airborne sound.

Between Science and Art: Thin Sound Absorbers Inspired by Slavic Ornaments

“…For the identical total length of every HR L HR = L r + L (k) n equal to 11.92 cm, the resonator eigenfrequencies are f (1) HR = 1 kHz, f (2) HR = 770 Hz, f (3) HR = 658 Hz, f (4) HR = 546 Hz, f (5) HR = 492 Hz, and f (6) HR = 464 Hz. We start from the evaluation of wave dispersion by applying the Floquet-Bloch conditions at the tube ends (Krushynska et al, 2018), imitating an infinite sequence of the HRs, and by neglecting any losses in the system. Figure 3A shows the corresponding dispersion relation with the band gaps shaded in gray.…”

“…This decrease can be explained by the use of Equations (1) and (2), which are, strictly speaking, not applicable for nonuniform cross-sections of the HR cavities. However, the insertion of the losses by means of the effective parameters (1) and (2) leads to a computationally cheaper problem as compared to the direct incorporation of thermal and viscous boundary layers into a finite-element model (Krushynska et al, 2018). Since the inaccuracy concerns only the first absorption peak, and the goal of this work is not the demonstration of some quantitative results, but understanding the physical mechanisms of the sound absorption, we proceed further by using the effective parameters for the folded HR cavities.…”

“…These fascinating properties have opened the way to the development of compact sound absorbing materials. For example, membrane-type (Yang et al, 2008(Yang et al, , 2015Park et al, 2011;Mei et al, 2012;Lu et al, 2016;Gao et al, 2017) or scape-coiling (Liang and Li, 2012;Li et al, , 2013Li et al, , 2014Li et al, , 2015Xie et al, 2013Xie et al, , 2014Molerón et al, 2016;Krushynska et al, 2018) metamaterials are capable of totally absorbing sound at frequencies, when the corresponding wavelength is up to two orders of magnitude larger than their thickness. Rigidly-backed structures with Helmholtz resonators (HRs) (Jiménez et al, 2016(Jiménez et al, , 2017a) also act as perfect absorbers, if the critical coupling conditions are satisfied (Theocharis et al, 2014;Merkel et al, 2015;Groby et al, 2016).…”

Fractal Acoustic Metamaterials with Subwavelength and Broadband Sound Insulation

“…If a structure with multiple resonance modes can be developed to form multiple bandgaps, it will provide a promising basis for achievement of broadband sound insulation. rough studies of labyrinthine fractal structures, researchers have found that multiple resonances appear in these structures [24][25][26][27][28][29] that can produce multiple bandgaps and thus broadband sound insulation. In these labyrinthine fractal structures, the sound waves propagate along the labyrinthine channels rather than in a straight line, which thus greatly increases their transmission paths and produces an ultraslow transmission effect.…”

“…In these labyrinthine fractal structures, the sound waves propagate along the labyrinthine channels rather than in a straight line, which thus greatly increases their transmission paths and produces an ultraslow transmission effect. Because of the increased lengths of their transmission paths, these metamaterials have high refractive indexes and demonstrate extraordinary physical properties, including multiple bandgaps [24][25][26][27][28][29], negative refraction [30,31], and acoustic focusing [32,33]. Liang et al constructed an extreme acoustic metamaterial by coiling up the space using zigzag channels, which caused their material to have negative refraction and sound tunneling properties [30].…”