Low-frequency broadband sound absorption performance of butterfly-like arc resonant cavity acoustic metamaterials
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摘要: 针对目前亥姆霍兹共振器低频吸声效果不理想的问题，提出了一种仿蝴蝶弧形共振腔型声学超材料结构，将阶梯式圆孔引入亥姆霍兹共振器的颈管，同时改变传统的负泊松比内凹夹芯结构，使结构在不改变整体尺寸的前提下，有效地为吸声器提供低频吸声所需的声阻抗，从而降低共振频率。利用有限元软件COMSOL 6.1对结构进行了仿真并通过驻波管吸声测试实验进行了验证，实验与仿真的结果具有较高的一致性。结果表明：仿蝴蝶弧形共振腔型声学超材料结构可以有效降低亥姆霍兹共振器的吸收峰值频率，使得该结构在650~1050 Hz频率范围内有着优秀的吸声性能，平均吸声系数大于0.9，实现了对声波的准完美吸收。吸声结构在740 Hz共振吸收系数峰值为0.962509，此时结构的厚度仅为吸收峰频率对应波长的1/15，体现了其深亚波长尺寸的特征。当结构的高度为30 mm时，仍有一个较宽的吸声频带，带宽比为62% (吸声系数>0.5)。不同仿蝴蝶弧形负泊松比的胞元参数对吸声性能也有一定的影响，当弧形胞元的圆弧半径r为11.8 mm、阶梯式圆孔的阶梯数n为4，以及阶梯式圆孔管径da和管长la为试件尺寸时，可以使亥姆霍兹共振器在低频宽带条件下有着优秀的吸声性能。Abstract: A novel acoustic metamaterial structure, inspired by the shape of butterfly arc, is proposed to address the issue of low-frequency absorption performance in Helmholtz resonators. In this paper, a butterfly-like arc resonance cavity acoustic metamaterial structure is proposed, and a stepped round hole is introduced into the neck tube of the Helmholtz resonator, and the traditional negative Poisson's ratio concave sandwich structure is changed, so that the structure can effectively provide the acoustic impedance required for low-frequency sound absorption for the sound absorber without changing the overall size, so as to reduce the resonance frequency. The structure was numerically simulated using COMSOL 6.1 finite element software and validated through a standing wave tube absorption test experiment, showing a high level of consistency between the experimental and simulated results. The results demonstrate that butterfly-like arc resonance cavity acoustic metamaterial structure can effectively reduce the absorption peak frequency of Helmholtz resonators, achieving excellent sound absorption performance in the frequency range of 650~1050 Hz, with an average sound absorption coefficient greater than 0.9. The structure achieves near-perfect absorption of sound waves. At the resonance absorption peak of 740 Hz, the structure thickness is only 1/15 of the corresponding wavelength, highlighting its deep subwavelength characteristics. Even at a height of 30 mm, the structure still exhibits a wide absorption bandwidth with a bandwidth ratio of 62% (Sound absorption coefficient > 0.5). The sound absorption performance is also influenced by different parameters of the butterfly arc-shaped negative Poisson's ratio unit cell. When the circular arc radius (r) of the arc-shaped cell is 11.8 mm, the number of steps (n) in the step-like circular hole is 4, and the diameter (da) and length (la) of the step-like circular hole correspond to the specimen size, the Helmholtz resonator exhibits excellent sound absorption performance over a wide low-frequency band.
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图 2 仿蝴蝶弧形共振腔型声学超材料结构示意图：(a) 整体结构；(b) 胞元结构示意图；(c) 胞元截面示意图
Figure 2. Schematic diagram of the structure of an acoustic metamaterial in an arc-like resonant cavity imitation butterfly: (a) Overall structure; (b) Cell structure; (c) Cell cross-section
ttop—Thickness of the microperforated plat; tbot—Thickness of the lower panel; t—Wall thickness of the cavity; a—Distance from the central axis of the inner extension tube to the concave wall; d—Stepped decreasing thickness; L—Cavity height; da—Diameter of the extension tube; la—Length of the extension tube.
图 4 仿蝴蝶弧形共振腔型声学超材料结构的频率-吸声系数曲线
Figure 4. Frequency-acoustic absorption coefficient curve of butterfly-like arc resonant cavity acoustic metamaterial structure
图 5 740 Hz处共振发生时结构内部的质点速度分布
Figure 5. Particle velocity distribution inside the structure when resonance occurs at 740 Hz
图 6 (a) B&K驻波管测量设备；仿蝴蝶弧形共振腔型声学超材料结构实验样品结构制备流程：(b) 仿蝴蝶弧形夹芯层；(c) 含阶梯式圆孔内嵌管的微穿孔板； (d) 下面板；(e) 具有嵌入阶梯式圆孔的实验样品；(f) 含传统直管式内嵌管的微穿孔板；(g) 具有传统直管式内嵌管的实验样品
Figure 6. (a) B&K VSWT measurement equipment; Fabrication process of experimental samples for a resonator-type acoustic metamaterial with a mimicked butterfly-shaped: (b) Mimicked butterfly-shaped sandwich layer; (c) Micro-perforated plate with stepped round bore inline tubes; (d) Lower panel; (e) Experimental sample with embedded stepped round holes; (f) Micro-perforated plate with traditional straight inline tubes; (g) Experimental sample with traditional straight tubes
图 7 仿蝴蝶弧形共振腔型声学超材料结构的实验与仿真吸声系数对比图
Figure 7. Comparison of experimental and simulated absorption coefficients for mimetic butterfly arc-shaped resonant cavity acoustic metamaterial structure
图 8 基于传统直管式的仿蝴蝶弧形共振腔型声学超材料结构的实验与仿真吸声系数对比图
Figure 8. Comparison of experimental and simulated absorption coefficients for the conventional straight tube-based mimetic butterfly arc-shaped resonant cavity acoustic metamaterial structure
图 9 仿蝴蝶弧形共振腔型声学超材料弧形半径r示意图
Figure 9. Schematic diagram of the arc radius r of the acoustic metamaterial of the arc resonance cavity type of imitation butterfly
图 10 仿蝴蝶弧形共振腔型声学超材料不同弧形半径的频率-吸声系数曲线
Figure 10. Frequency-absorption coefficient curves of butterfly-like arc resonant cavity acoustic metamaterials with different arc radii
图 11 仿蝴蝶弧形共振腔型声学超材料不同阶梯数n的频率-吸声系数曲线
Figure 11. Frequency-absorption coefficient curves of butterfly-like arc resonant cavity acoustic metamaterials with different step numbers n
图 12 仿蝴蝶弧形共振腔型声学超材料不同阶梯数的总声压((a)~(c))和总热黏性功耗密度((d)~(f))图
Figure 12. Diagram of total sound pressure ((a)-(c)) and total thermoviscous power dissipation density ((d)-(f)) of different step numbers of butterfly-like arc resonant cavity acoustic metamaterials
图 13 仿蝴蝶弧形共振腔型声学超材料不同阶梯式圆孔管径的频率-吸声系数曲线
Figure 13. Frequency-sound absorption coefficient curves of different stepped circular hole diameters of butterfly-like arc resonant cavity acoustic metamaterials
图 14 仿蝴蝶弧形共振腔型声学超材料不同阶梯式圆孔管径的阻抗实部Real(Z/Z0)对比
Figure 14. Comparison of the impedance real parts Real(Z/Z0) of different stepped circular hole pipe diameters of butterfly-like arc resonant cavity acoustic metamaterials
Z—; Z0—
图 15 仿蝴蝶弧形共振腔型声学超材料不同阶梯式圆孔管径的阻抗虚部Imag(Z/Z0)对比
Figure 15. Comparison of the impedance imaginary parts Imag(Z/Z0) of different stepped circular hole pipe diameters of butterfly-like arc resonance cavity acoustic metamaterials
图 16 仿蝴蝶弧形共振腔型声学超材料不同阶梯式圆孔管长的频率-吸声系数曲线
Figure 16. Frequency-sound absorption coefficient curves of different stepped round hole tube lengths of butterfly-like arc resonant cavity acoustic metamaterials
图 17 仿蝴蝶弧形共振腔型声学超材料不同阶梯式圆孔管长的阻抗实部对比
Figure 17. Comparison of the impedance real parts of different stepped round bore tube lengths
图 18 仿蝴蝶弧形共振腔型声学超材料不同阶梯式圆孔管长的阻抗虚部对比
Figure 18. Comparison of the impedance imaginary parts of different stepped round hole tube lengths of butterfly-like arc-shaped resonant cavity acoustic metamaterials
表 1 试件参数
Table 1. Specimen parameters
$ {{t}}_{\text{top}} $/mm $ {{t}}_{\text{bot}} $/mm $ {t} $/mm $ {d} $/mm $ {L} $/mm $ {a} $/mm $ {r} $/mm $ {n} $ (piece) 2 1 0.5 0.5 30 5.8 11.8 4 Notes: $ {r} $—Radius of the arc; $ {n} $—Number of steps. 
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表 2 试件内延伸管的直径$ {{d}}_{\text{a}} $和管长$ {{l}}_{\text{a}} $参数
Table 2. Parameters of diameter $ {{d}}_{\text{a}} $ and length $ {{l}}_{\text{a}} $of the extension tube in the specimen
Unit $ {{d}}_{\text{a}} $/mm $ {{l}}_{\text{a}} $/mm 1 5.6 11.5 2 5.9 11.5 3 6.6 11.5 4 6.2 11.5 5 7 11.5 6 7 8.9 7 5.7 1.4 8 6.6 5.3 9 5.5 0 10 5.7 11.5
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表 3 仿蝴蝶弧形共振腔型声学超材料不同阶梯式圆孔管径da的参数(mm)
Table 3. Parameters of different stepped circular hole diameter da of butterfly-like arc resonant cavity acoustic metamaterials (mm)
Unit 1 2 3 4 5 6 7 8 9 10 Sample1 5.2 5.5 6.2 5.8 6.6 6.6 5.3 6.2 5.1 5.3 Sample2 5.6 5.9 6.6 6.2 7.0 7.0 5.7 6.6 5.5 5.7 Sample3 6.0 6.3 7.0 6.6 7.4 7.4 6.1 7.0 5.9 6.1
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表 4 仿蝴蝶弧形共振腔型声学超材料不同阶梯式圆孔管长la的参数(mm)
Table 4. Parameters of different stepped round hole tube length la of butterfly-like arc resonant cavity acoustic metamaterials (mm)
Unit 1 2 3 4 5 6 7 8 9 10 Sample4 13.5 13.5 13.5 13.5 13.5 10.9 3.4 7.3 2.0 13.5 Sample5 11.5 11.5 11.5 11.5 11.5 8.9 1.4 5.3 0.0 11.5 Sample6 9.5 9.5 9.5 9.5 9.5 6.9 1.4 3.3 0.0 9.5
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