Hybrid space filling curve metamaterials for transmissive flow in Jet Engine inlets Jennifer Natalie Glove r [1] Loughborough University Loughborough University Epinal Way, Loughborough, Leicestershire, LE11 3TU, UK Dan John O’Boy [2] Loughborough University Loughborough University Epinal Way, Loughborough, Leicestershire, LE11 3TU, UK ABSTRACT Acoustic metamaterials research has grown exponentially in the past 10 years driven by the advances in manufacturing and an increased understanding of damaging environment noise. 2050 was the first noise reduction target as set by Advisory Council for Aircraft Research and Innovation in Europe with a relative 65% decrease. This ambitious target will not be met by current engine noise control technology; however, metamaterials offer an encouraging alterna- tive. Space Filling Curves (SFC) have the potential to provide a lightweight, thin, high perfor- mance acoustic liner. SFC have a history in mathematical geometry dating back to the 1890’s but are a comparatively new addition to acoustics. They are designed with a sub-wavelength curled cross-section creating a maze-like pattern which slows acoustic wave propagation through the liner, enabling characteristics such as negative refraction and low frequency atten- uation. This paper contains unique hybrid design combining some of the most promising SFC metamaterial acoustic liner designs, in terms of the fundamental theory of the design category and a discussion of the reflection, absorption and transmission characteristics in terms of a head on and grazing flow conditions. Experimental impedance tube testing compares 3D printed designs to the traditional Helmholtz resonator. The paper concludes with future appli- cation for aeroacoustics with particular focus on the engine inlet. 1. INTRODUCTION

As pressure grows for aircraft noise reduction, from organisations like the Advisory Council for Aircraft Research and Innovation in Europe (ACARE) there is an increased need for innovation in Aeroacoustic attenuation. The nature of noise means that a targeted approach to attenuation is far more effective in achieving overall observable noise reductions. Therefore, this project focuses on the dominant noise source, the engine, which accounts for approximately 68% at approach and at take-off approximately 98% of the total aircraft noise [1] (percentage of total logarithmic dB output). Any solution needs to cope with extreme operating conditions and low frequency noise not commonly controlled by traditional methods, due to the long wavelengths involved. This paper introduces inno- vative metamaterial acoustic liners as solutions for the jet engine inlet, tested in grazing conditions and builds on work by Glover and O’Boy 2020 [2], Glover and O’Boy 2021 [3] and Glover and O’Boy 2021 [4]. [1] J.Glover2@lboro.ac.uk

[2] D.J.Oboy@lboro.ac.uk

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Metamaterials demonstrate a huge resource for acoustic control whether passively in coiling- up, Helmholtz resonator like or membrane structured, as reviewed in the paper by Assouar et al [5]. Or actively with piezoelectric, mechanical, or electric and magnetic biasing as discussed in “A Re- view of Tuneable Acoustic Metamaterials” [6]. For this project, the metamaterials studied are Space Filling Curves (SFC) defined by their sub-wavelength structural, curled cross section. They are classed as a passive absorber acoustic liner. The SFC provides an elongated coiled propagation path able to attenuate much lower frequencies than an undivided cavity of the same dimensions. SFC offer subwavelength low frequency attenuation with the potential to provide a lightweight, thin, high per- formance acoustic liner [5]. The present paper contains a comparison of a unique hybrid metamaterial design which utilises SFC to a Helmholtz resonator in realistic working conditions. An evaluation was made in terms of the fundamental theory of the design and a discussion of the reflection, trans- mission, and absorption characteristics. The design of the original inspiration for this method are provided, then the paper contains a discussion of experimental testing to compare the unique SFC to traditional Helmholtz resonators in impedance tube measurements. Conclusions are also made as to the future application for aeroacoustics with particular focus on the engine inlet. These SFC where previously assessed in Glover and O’Boy 2020 [2] and Glover and O’Boy 2021 [3] under head-on flow conditions. 2. ACOUSTIC LINERS

Typical acoustic liners for a commercial jet engine use the principle of a Helmholtz Resonator (HR) where a mass of air oscillates on a spring of air trapped in a volume. HR implementations are cheap passive devices, are relatively lightweight and effective for one dominant frequency and most importantly, need a large depth to attenuate low frequencies. The issue of low frequency attenuation is due to the mass law. The effect is essentially, the lower the desired attenuation frequency the larger the liner depth needs to be [7] (and for the purposes of this paper the frequency range of interest is 200-1800Hz). By targeting one dominant frequency, any other frequencies are not substantially af- fected, and the same weight penalty remains. Hence, the choice of critical frequency and the potential for multiple frequency targeting is paramount.

The liners are proposed to control the dominant frequencies of jet engines, typically below 1000Hz, with the lowest at approximately 630Hz defined by Khardi [8]. Moreover, the industrial trend towards ultra-high bypass engines means there is a potential increase in bypass ratio from 8 to 15 [9]. Since ultra-high bypass fans result in an increase in weight and potential drag it is predicted that there will be a subsequent reduction in the thickness of the outer casing, meaning that any sound- proofing contained within needs to become thinner [9]. Therefore, in this paper the depth of the liners is tightly controlled below 50mm, the lower end of typical current liner depth. A successful met- amaterial acoustic liner would show a reduced weight and thickness compared to a traditional HR liner. The 2020 paper by Glover and O’Boy [2] and 2021 paper Glover and O’Boy 2021 [3] outline the two existing SFC design Hexagonal and Spider which were tested and refined through PhD re- search beyond the scope of this paper, to produce the final proposal unique hybrid metamaterial HexSpi double.

2.1 Helmholtz Resonator

Traditional HR are used to control steady, simple harmonic sound at a narrow frequency range. The main advantages of this resonator is it’s simplicity, although careful tuning is required for effec- tive noise attenuation [10]. The HR works as an acoustic stopband filter with the action of the volume

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of air in the cavity emulating a mass spring system [10]. However, this causes an undesirable back pressure which has a detrimental effect on the efficiency and performance of the engine. The limited narrow band can be improved with a range of tuned HRs, but this has a proportional increase in back pressure [7]. If frequency bands could be filtered out through an alternative method such as multi- resonant scattering, there would be a far smaller effect on engine efficiency which could be a designed in characteristics of metamaterial liners.

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Figure 1: Helmholtz Resonator 610Hz

Figure 2: Helmholtz Resonator 610Hz unit cell

For the purposes of comparison in this paper a baseline acoustic liner was designed using a hexagonal 610Hz tuned HR (Figure 1 and Figure 2), see formula in [9]. This design was also used in the 2020 [2] and 2021 [3] papers, although in this case an outer frame is used to reduced structural resonance. This was chosen to compromise between industry standard design, the working frequency range of the experimental impedance tube, and available 3D printing capabilities allowing rapid pro- totyping and experimental verification of trends. The hexagonal HR liner was a benchmark of success criteria for the SFC liners. Thus, a good liner would show a better absorption coefficient at a wider frequency range and ideally at a lower weight. The additional characteristics of a typical sandwich configuration was also applied to the SFCs for the following three reasons: 1) Allowing a direct com- parison to the two microphone work recorded in head-on conditions which utilised sandwich config- urations to great effect [2]. 2) A sandwich configuration is the current standard for soundproofing thus can be considered commercial. 3) The additional resonant conditions are predicted to improve absorption coefficients for the SFC samples. 2.2 SPACE FILLING CURVES

Space-filling curve metamaterials are designed with a sub-wavelength curled wave path cre- ating a mazelike pattern (Figure 3). SFC were developed from a purely mathematical problem where a line passes through every cell element of a grid, so that every cell is visited exactly once. They have been proposed in acoustics for a decade or so due to their potential ultra-thin, low frequency, broad- band attenuation overcoming the drawbacks of traditional HRs. In this paper, one hybrid design is presented combining two existing SFC recorded in previous publications (Hexagonal and Spider). These design were extensively refined for use in a commercial jet engine inlet, with additional design parameters introduced: double scale of flow path, top plates (TP), and a central void. This experi- mental assessment established if the HexSpi double with 8TP is a comparable alternative to HR at a significantly reduced weight and thickness.

To understand the advantages of metamaterials as a noise control method there needs to be an appreciation of the physical attenuation mechanisms. The primary physical mechanism of noise re- duction in both types is an extended pathlength compared to unit depth, which enables subwavelength attenuation. Different designs can offer multiple propagation paths, directions, and scattering. Hex- agonal and Spider SFC have been previously defined as maze-like types. The maze-like designs are better understood using Mie resonant theory as they offer multiple propagation directions and a high

4

reflective index. Mie resonance is commonly defined in light rather than sound, but it still applies when the size of the scattering sphere is comparable to the wavelength. Mie-resonance particles have a high refractive index relative to the background medium. They are initiated in this case due to the ultraslow relative propagation through the flow path compared to the in space dimensions (Figure 3) [11]. These liners often benefit from multiple resonances instigated at low frequency due to the high contrast of sound speed with the isotropic resonant frequency shown in Equation 5 [12]. The proposed Hexagonal is described as being an ultra-slow medium demonstrating the high contrast in wave speed needed to observe Mie resonance [13]. Unfortunately, Equation 1 is more suited to designs with the common centre or central focus point of Spider rather than Hexagonal.As a result, even though they are said to display Mie resonance this formula cannot be directly applied. However, future investiga- tion beyond the scope of this project could determine refractive index and wave speed through ex- perimentation of the Hexagonal and Labyrinthine liners, then the Mie resonance value could be found based on the work of Zhou et al.[14].

f = c πn ୰

ඨ 2η R ୧ (R −R ୧ ) ᇱ (1)

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Figure 3 : Ultra slow fluid medium representation of spider liner

2.2.1 Hexagonal

The first acoustic liner design investigated was proposed by Xia et al. [15] and termed a “Sym- metry-broken metamaterial”. The design was iterated by extending the one-dimensional chain to a two-dimensional lattice, a bi-periodic two-dimensional metamaterial can be realised by a so-called hexagonal lattice. The sample presented by Xia et al. [15] has tessellated hexagonal lattices with a central void tested using simulation in 2D on COMSOL only. The design creates a subwavelength monopole resonance 367Hz from in-phase propagation and dipole resonance 753 Hz through multiple scattering.

The Hexagonal liner sample design Figure 4 and sizing was inspired by Xia et al. [15] “Sym- metry-broken metamaterial”. It was progressed into 3D with a nominal depth matching that of the baseline HR. This test liner like all the designs investigated was tessellated to cover the whole 95mm diameter space available in the test rig (see Figure 7 ). No design had voids for consistency, although some origin papers such as this did. Xia et al. [15] recorded zero transmission at monopole and dipole and as the number of units present in the flow increases the overall average absorption increases. The double resonance and low frequency range are both aligned to the dominate frequencies of a jet engine inlet.

Ultraslow Background J medium 9 ay Core air

Figure 4 : Hexagonal unit cell

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Hexagonal is presented via sound transmission loss rather than absorption thus the peak values may not consistently associate. The absorption coefficient has two different formulas based on whether transmission is possible within the experimental setup (Equation 2 anechoic termination and Equation 3 rigid termination). Generally, absorption and reflection coefficients are mirror plots, but the transmission may not follow the same trend. As a result, the accuracy of this design recreation, will require the analyses of all three coefficients.

α = 1 −|R ୟ | ଶ −|T ୟ | ଶ (2) α = 1 −|R ୦ | ଶ (3)

2.2.2 Spider

The “Spider web-structured labyrinthine acoustic metamaterials” was developed by Krushyn- ska et al. is the second of the combined designs for hybridization [13]. This design configuration consists of a square external frame and a circular maze like path divided into eight independent cir- cular-shaped channels connected at the centre. (Figure 5).

Figure 5 Spider liner unit

Krushynska et al. tested the design using simulation in COMSOL only and demonstrated con- sistent low transmission for a frequency range 0-2000Hz. As stated, the Spider is classified as a maze- like SFC meaning there are multiple propagation routes rather than a singular flow direction. This design is also very difficult to predict through a numerical theory due to the presence of Mie scattering which is why the origin paper’s use of simulation is vital in predicting the acoustic performance. The design was inspired by garden spider Araneus diadematus. In addition, Krushynska et al. concluded the spider SFC is highly tuneable with activation or elimination of subwavelength band gaps and negative group-velocity modes can be refined by increasing/decreasing the edge cavity dimensions.

2.2.3 HexSpi Double

The concept of hybridising two designs was investigated as part of this project in order to combine the advantageous properties of two different SFC designs. It was predicted that as the sound waves travel through two different core patterns, the overall mean absorption of the hybrid design would be greater than the single SFC prototypes. This was desired because previous results had es- tablished that generally the SFCs have a lower mean absorption than the traditional HR. In addition, the property of dual resonance was hypothesized to be induced more reliably because, the two dis- tinctive designs within the unit induced their own resonant peaks. This characteristic is particularly relevant for jet engines as they have multiple dominant peaks and an alignment for this attenuation would result in a very effective sound reduction, another advantage is that single sized HR units are only tuned to single frequencies. The potential of hybrid design is a recent advancement due to addi- tive manufacture. Based on the extensive experimental research previously mentioned the two most promising designs for jet engine purposes (Hexagonal and Spider) were combined into one test unit, divided into four quarters, two for each SFC, see Figure 6. HexSpi double was created to include promising design parameters based on experimental study beyond the scope of this paper, which include a framing, double scale, and voids.

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Figure 6 HexSpi Double liner unit

3. IMPEDANCE TUBE RIG

A three tube impedance rig (Figure 7 ) was designed and built in this project to accurately measure sound reflection and absorption coefficients according to ISO10534-2 [16]. The tubes work as a plane wave is generated by the sound source. Measurements of acoustic pressure are taken at fixed locations depending on the number of microphones (see Figure 8 to Figure 10). The reflection off or absorption through the sample generates a standing wave that can be measured by the micro- phones. A white noise source is used with no external flow applied. Calculations are carried out using a complex transfer function to determine the normal incidence absorption and impedance ratios of the acoustic material (Equation 4 transfer matrix, Equation 5 transmission coefficient, Equation 6 reflection coefficient). The rig has a working frequency range of 400-1700Hz.

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Figure 7 Photograph of experimental rig

Microphones 4 Microphone Tube Loudspeaker Grazing Tube NI Module Signal Laptop Amplifier’ White noise generator

Figure 8 Two microphone impedance tube

Termination

Figure 9 Four microphone impedance tube

Termination

Figure 10 Grazing impedance tube

(4)

(5)

𝑇 ௔ = 2𝑒 ௝௞ௗ

൤ 𝑝 (௔) 𝑝 (௕)

𝑣 (௔) 𝑣 (௕) ൨

𝑇 ଵଵ + ቀ 𝑇 ଵଶ

௫ୀ଴

𝜌 ଴ 𝑐 ቁ+ 𝜌 ଴ 𝑐𝑇 ଶଵ + 𝑇 ଶଶ

= ൤ 𝑇 ଵଵ 𝑇 ଵଶ 𝑇 ଶଵ 𝑇 ଶଶ ൨൤𝑝 (௔) 𝑝 (௕)

𝑣 (௔) 𝑣 (௕) ൨

௫ୀௗ

𝑇 ଵଵ + ቀ 𝑇 ଵଶ

(6)

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𝜌 ଴ 𝑐 ቁ−𝜌 ଴ 𝑐𝑇 ଶଵ −𝑇 ଶଶ

𝑅 ௔ =

𝑇 ଵଵ + ቀ 𝑇 ଵଶ

𝜌 ଴ 𝑐 ቁ+ 𝜌 ଴ 𝑐𝑇 ଶଵ + 𝑇 ଶଶ

4. EXPERIMENTAL ANALYSIS OF LINERS

4.1 Methodology The experimental analysis determined the reflection, transmission, and absorption coefficients of each liner by frequency and as a mean value over the valid frequency range. The data was then compared between the Hybrid SFC and HR designs. Liner samples were designed with a diameter of 95mm and a rigid backplate of 2.5mm. HexSpi Double’s containing frame had an outer diameter of 95 mm and an inner diameter of 93.5 mm, with a central void diameter of 25mm. The double scale is based on the origin SFC in section 2.2.1 and 2.2.2. This was to ensure fit between all three test rigs; two tubes are circular where the liner must touch fit the inner surface and, the rectangular tube which has an aperture that fits both 95mm circular and 90mm square samples. An additional element of a HR designed top plate and 8TP for HexSpi double of thickness 2.5 mm was applied. The variation of the impedance tube method is also compared to capture the full working conditions. Head on (2 mi- crophone), head on transmissive (4 microphone) and grazing (grazing microphone). The weights and thickness are in Table 1. Table 1 : Acoustic liner and top plate weights

Liners CORE WEIGHT (g) CORE THICKNESS (mm) Top Plates MASS (g)

Helmholtz Resonator

32 15 HRTP 20

HexSpi double 24 9.94 8TP 20

Mic1 Mic2 Mic3 Mic4 N N N N Termination , Y — Loudspeaker A+ c+

Table 2 : Top plate design

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Figure 11 : 19x 2mm top plate (HRTP)

Figure 12 8x 3mm top plate (8TP)

This perforated top plate is designed spe- cifically for the Helmholtz resonator.

This perforated top plate is designed to maintain per- centage open space of perforation, but with larger holes more suited to the hybrid SFC design.

4.2 Results

The HexSpi double 10mm was selected as the proposed hybrid SFC design for this project and paper. This experimental study aimed to quantify the success of the hybrid design for jet engine inlet. The HexSpi double in previous investigation as part of a PhD thesis, showed the potential of comparable acoustic parameter performance to the baseline HR, at both a reduced weight and depth. It was predicted that with the use of the 8TP, the liner could better achieve low frequency attenuation below that of 800Hz. The 8TP has the same percentage open space as the HRTP, but with a reduced hole number and increased hole diameter. This liner was expected to induce resonance near the lowest dominate frequency of a jet engine. A full TP optimisation study was not possible due to the project time constraints but would be a starting point for further study.

Figure 13 Absorption coefficient by frequency -all methods

Senegal caper ene bepetianen sae: 1400 1600 = = Hiared HRT 2 my a Hamed HRT me) = framed HRT (racing) Absorption coefficent_ ‘200 000 1200 400 7600 Frequency [Hz]

Figure 13 compared the absorption coefficients of HexSpi double 10mm 8TP in all testing conditions to HR 610Hz. Absorption was determined as the most effective measure of performance because, for jet engine conditions the ideal is absorbed noise rather than reflected or transmitted. Reflection and transmission of noise could induce pressure / backpressure in the engine reducing performance or would still be released to an observer thus not meeting reduction targets. The 8TP as predicted showed dual peaks, within the working frequency range for all conditions. The peaks of 460Hz and 850Hz (average across the 3 conditions) corresponded well to the predicted peaks of Xia et al. monopole resonance 367Hz propagation and dipole resonance 753Hz. HR performed as per expected from theory showing a single peak in the desired low frequency range. The second peak in 4 microphone testing is not consider dual resonance due to the core design but, because of part sized units at the edge of the liner due to tessellation and cut off at 95mm diameter.

The hybrid liner also benefits from low frequency peaks with the first peak earlier than any absorption peaks seen in previous publications [2]–[4]. The potential drawback of 8TP orifice patten was the narrow peaks produced, but due to the noise profile of a jet engine, frequency positioning is more important than broad frequency attenuation. Across all conditions the peaks of 8TP are very consistent with peak 1 within 50Hz and the second peak 40Hz; demonstrating a very consistent at- tenuation performance. HR ranged much more with 85Hz for peak 1 and an inconsistent second peak. For instance in grazing conditions, HR has no second peak. The 8TP had a largest absorption peak below 1000Hz. However, none of the TP’s peaks aligned precisely with the desired acoustic profile. On the other hand, the absorption plots show the optimisation potential of acoustic liner design and a basis for future work to meet the success criteria of this project.

Table 3 : All conditions impedance tube mean coefficient results summary

2 micro-

phone HR framed HRTP HexSpi double framed 8TP

Mean absorption Mean reflection Mean absorption Mean reflection

400- 1700Hz 0.39 0.77 0.28 0.83

4 micro-

phone HR framed HRTP HexSpi double framed 8TP

Mean ab-

Mean re-

Mean trans-

Mean ab-

Mean re-

Mean trans-

sorption

flection

mission

sorption

flection

mission

400- 1700Hz 0.49 0.71 0.08 0.28 0.81 0.13

Phase 3 HR framed HRTP HexSpi double framed 8TP

Mean ab-

Mean re-

Mean trans-

Mean ab-

Mean re-

Mean trans-

sorption

flection

mission

sorption

flection

mission

400- 1700Hz 0.19 0.15 0.89 0.14 0.26 0.87

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The mean acoustic characteristics are shown in Table 3 . This highlighted the compromise in acoustic liner performance, of HR and HexSpi double. HR consistently shows a higher mean absorp- tion and smaller reflection coefficient. Although this characteristic was desired for the hybrid SFC to give a good overall performance across the acoustic range of a jet engine a targeted approach to attenuation is preferred. In head on transmissive and grazing transmissive flow HexSpi double has higher peak absorptions than HR making it a more effective attenuator at specific resonances. This when applied to jet engine inlets has a greater reduction effect. However, refinement is needed to better align the resonant peaks of the hybrid SFC with commercial jet engines; although they are already in the low frequency range and only small adjustments are needed.

5. CONCLUSION

This paper aimed to define a SFC acoustic liner, that provided a comparable mean acoustic performance to a baseline HR, at a reduced weight and depth. The HexSpi double was the combina- tion of most promising SFC design, based on the current acoustic liner study in Glover and O’Boy 2020 [2], Glover and O’Boy 2021 [3] and Glover and O’Boy 2021 [4]. The hybrid liner core was 25% lighter and 34% thinner than the baseline HR and attenuated at a lower frequency. The chosen 8TP was effective at reducing the resonant peaks of the HexSpi double 10mm, with the first peak at 450Hz and second at 860Hz.

Although these peaks do not both align with the acoustic profile of a jet engine inlet this variable change demonstrated the frequency peak dependence on TP design. Acoustic liner design is a compromise between broadband and specific frequency performance. The HexSpi double 8TP proved to be an effective concession. Demonstrating the potential for future refinements in a profile matched TP, enabling the HexSpi double to become an effectual acoustic solution, and exceeding that of the baseline HR. Overall, the HexSpi double 10mm is a valid and innovative replacement for a traditional HR acoustic liner, capable of meeting the demands of the challenging noise reduction targets of aviation authorities, and the demands of the adverse working conditions in a commercial jet engine inlet.

6. FUTURE WORK

The progression for this work is an optimization study on orifice diameter, using multiple hole size and positioning within the TP to manipulate the resonant peaks as required, for the specific noise problem. Also, the experimental progression would be an analysis of the hybrid prototype with mul- tiple units present and induced flow in the impedance tube. This would capture the effect of coupling between multiple units and likely result in an increase mean absorption. The introduction of flow in the impedance tube would also more effectively reflect the conditions of a jet engine. As well as introducing additional acoustic features such as bias flow in the orifices. The result would be a more representative acoustic parameters conclusion for the hybrid SFC.

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7. REFERENCES [1] N. Pignier, “The impact of traffic noise on economy and environment: a short literature study,” Stockholm, 2015. [2] J. N. Glover and D. J. O’Boy, “A review of acoustic space filling curve metamaterials for jet engine inlets.,” in Acoustics 2020, Institute of Acoustics , 2020. [3] J. N. Glover and D. J. O’Boy, “Low Filling Ratio Acoustic Space Filling Curve Metamaterials for Jet Engine Inlets,” Eng. Integr. , no. 50, pp. 10–20, 2021. [4] J. N. Glover and D. J. O’Boy, “Acoustic space filling curve metamaterials for grazing flow in jet engine inlets,” Proc. INTER-NOISE 2021 - 2021 Int. Congr. Expo. Noise Control Eng. , 2021. [5] B. Assouar, B. Liang, Y. Wu, Y. Li, J. C. Cheng, and Y. Jing, “Acoustic metasurfaces,” Nat. Rev. Mater. , vol. 3, no. 12, pp. 460–472, 2018. [6] S. Chen et al. , “A review of tunable acoustic metamaterials,” Appl. Sci. , vol. 8, no. 9, pp. 1– 21, 2018. [7] S. . Faruq, “An Experimental Investigation on Noise Reduction by Using Modified Helmholtz Resonator,” Bangladesh University of Engineering and Technology, 2014. [8] S. Khardi, “An Experimental Analysis of Frequency Emission and Noise Diagnosis of Com- mercial Aircraft on Approach,” Jounal Acoust. Emiss. , vol. 26, no. 2008, pp. 290–310, 2008. [9] Y. Wang et al. , “A renewable low-frequency acoustic energy harvesting noise barrier for high- speed railways using a Helmholtz resonator and a PVDF film,” Appl. Energy , vol. 230, pp. 52–61, 2018. [10] D. Wu, N. Zhang, C. M. Mak, and C. Cai, “Noise Attenuation Performance of a Helmholtz Resonator Array Consist of Several Periodic Parts,” Sensors MDPI , vol. 5, no. 17, 2017. [11] J. Li and C. T. Chan, “Double-negative acoustic metamaterial,” Phys. Rev. E - Stat. Physics, Plasmas, Fluids, Relat. Interdiscip. Top. , vol. 70, no. 5, pp. 1–4, 2004. [12] Y. Jia, Y. Luo, D. Wu, Q. Wei, and X. Liu, “Enhanced Low-Frequency Monopole and Di- pole Acoustic Antennas Based on a Subwavelength Bianisotropic Structure,” Adv. Mater. Technol. , vol. 5, no. 4, pp. 1–6, 2020. [13] A. O. Krushynska, F. Bosia, M. Miniaci, and N. M. Pugno, “Spider web-structured labyrin- thine acoustic metamaterials for low-frequency sound control,” New J. Phys. , vol. 19, no. 10, 2017. [14] C. Zhou, B. Yuan, Y. Cheng, and X. Liu, “Precise rainbow trapping for low-frequency acoustic waves with micro Mie resonance-based structures,” Appl. Phys. Lett. , vol. 108, no. 6, 2016. [15] B. Xia, H. Dai, and D. Yu, “Symmetry-broken metamaterial for blocking, cloaking, and su- pertunneling of sound in a subwavelength scale,” Appl. Phys. Lett. , vol. 108, 2016. [16] International organisation of standards, “ISO 10534-2 Acoustics-Determination of sound ab- sorption coefficient and impedance in impedance tubes- Part 2: Transfer-function method,” Geneve, 1998.

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