内插缝Helmholtz共振腔吸声超结构的机理分析与优化设计

贾静; 肖勇; 王勋年; 王帅星; 温激鸿

doi:10.7498/aps.73.20240250

摘要

低频噪声一直是噪声控制领域比较棘手的问题, 近年来吸声超结构的蓬勃发展为低频噪声控制提供了新理念. 本文提出了一种内插缝Helmholtz共振腔吸声超结构, 建立了其吸声特性计算的理论解析方法, 并与数值计算方法对比, 验证了解析方法的有效性. 随后, 从吸声曲线、简化等效模型、归一化声阻抗、声压云图与质点速度分布等多角度对吸声特性及吸声机理进行了深入分析. 进一步, 采用差分优化算法开展了多元胞并联耦合宽带优化设计, 优化后典型超结构实现了90 mm厚度下在170—380 Hz低频段内平均吸声系数达到0.86的优异吸声效果. 最后, 制备了若干样件, 开展吸声测试, 实验结果与理论结果符合良好, 验证了解析建模与优化设计方法的准确性. 本文提出的内插缝Helmholtz共振腔吸声超结构具有结构简单、低频吸声性能好, 且易于加工制造等特点, 在低频噪声控制领域具有广阔的应用前景.

关键词:

Abstract

Low-frequency noise has always been a thorny problem in the field of noise control. In recent years, the development of sound-absorbing metastructures has provided new ideas for controlling low-frequency noise. In this work, we propose a low-frequency sound-absorbing metastructure constructed by Helmholtz resonators with embedded slit. Analytical and numerical models are established to analyze the sound absorption performance and mechanism of the proposed sound-absorbing metastructure, and optimization design is conducted to achieve low-frequency wideband absorption performance. The analytical modeling method and the performance of the proposed sound-absorbing metastructure are also experimentally verified. The main conclusions are summarized as follows.1) By using transfer matrix method and finite element method, analytical and numerical models for calculating sound absorption coefficient are established. It is shown that analytical predictions are in good agreement with numerical calculations. It is demonstrated that a typical design of a 30-mm-thick single-cell metastructure can achieve a sound absorption coefficient of 0.88 at 404 Hz. Typical designs of two-cell parallel structure and the four-cell parallel structure (both with a thickness of 50 mm) can achieve two and four nearly perfect low-frequency sound absorption peaks in a frequency band of 200–400 Hz, respectively.2) The low-frequency sound absorption mechanisms of the proposed metastructures are explained from four aspects: simplified equivalent model parameters, normalized acoustic impedance, complex-plane zero/pole distribution, and sound pressure cloud image and particle velocity field distribution. It is demonstrated that the main sound absorption mechanism is related to the thermal viscous loss of sound waves, caused by the inner wall of embedded slit.3) The design for broadband low-frequency absorption performance is optimized by using differential evolution optimization algorithm. An optimized parallel-multi-cell coupled metastructure with multiple perfect sound absorption peaks below 500 Hz is realized. For a thickness of 90 mm, the sound absorption coefficient curve of an optimized metastructure exhibits 8 almost perfect sound absorption peaks and an average sound absorption coefficient of 0.86 in a frequency range of 170－380 Hz.4) Experimental samples are fabricated to test sound absorption. Experimental results are basically consistent with the analytical predictions. The results from analytical model, numerical calculations and experimental measurements are mutually verified.In summary, the sound-absorbing metastructures with a thickness of sub-wavelength, proposed in this work, exhibit outstanding sound absorption performance at low frequencies. We demonstrate that they are suitable for low frequency broadband sound absorption below 500 Hz. Owing to their thin thickness and relatively simple construction, they have broad application prospects in practical noise control engineering.

Keywords:

作者及机构信息

1.
中国空气动力研究与发展中心, 气动噪声控制重点实验室, 绵阳　621000

2.
国防科技大学智能科学学院, 装备综合保障技术重点实验室, 长沙　410073

通信作者: 肖勇, xiaoy@vip.sina.com ; 王勋年, 13890111856@139.com ; 温激鸿, wenjihong@vip.sina.com

基金项目: 国家自然科学基金面上项目(批准号：51875569)和国家自然科学基金重大项目(批准号:11991032)资助的课题.

Authors and contacts

1.
Key Laboratory of Aerodynamic Noise Control, China Aerodynamics Research and Development Center, Mianyang 621000, China

2.
Laboratory of Science and Technology on Integrated Logistics Support, College of Intelligence Science and Technology, National University of Defense Technology, Changsha 410073, China

Corresponding author: Xiao Yong, xiaoy@vip.sina.com ; Wang Xun-Nian, 13890111856@139.com ; Wen Ji-Hong, wenjihong@vip.sina.com

Funds: Project supported by the National Natural Science Foundation of China (Grant No. 51875569) and the Major Program of the National Natural Science Foundation of China (Grant No. 11991032).

文章全文 : translate this paragraph

参考文献

[1]	Champoux Y, Allard J F 1991 J. Appl. Phys. 70 1975 Google Scholar
[2]	Panneton R 2007 J. Acoust. Soc. Am. 122 217 Google Scholar
[3]	Trompette N, Barbry J, Sgard F, Nelisse H 2009 J. Acoust. Soc. Am. 125 31 Google Scholar
[4]	Climente A, Torrent D, Sánchez-Dehesa J 2012 Appl. Phys. Lett. 100 144103 Google Scholar
[5]	Ma G C, Sheng P 2016 Sci. Adv. 2 1501595 Google Scholar
[6]	肖勇, 王洋, 赵宏刚, 郁殿龙, 温激鸿 2023 机械工程学报 59 277 Google Scholar Xiao Y, Wang Y, Zhao H G, Yu D L, Wen J H 2023 J. Mech. Eng. 59 277 Google Scholar
[7]	Cai X B, Guo Q Q, Hu G K, Yang J 2014 Appl. Phys. Lett. 105 121901 Google Scholar
[8]	Wang Y, Zhao H G, Yang H B, Zhong J, Zhao D, Lu Z L, Wen J H 2018 J. Appl. Phys. 123 185109 Google Scholar
[9]	Wu F, Xiao Y, Yu D, Zhao H, Wang Y, Wen J 2019 Appl. Phys. Lett. 114 151901 Google Scholar
[10]	吴飞, 黄威, 陈文渊, 肖勇, 郁殿龙, 温激鸿 2020 69 134303 Google Scholar Wu F, Huang W, Chen W Y, Xiao Y, Yu D L, Wen J H 2020 Acta Phys. Sin. 69 134303 Google Scholar
[11]	Zhao H G, Wang Y, Yu D L, Yang H B, Zhong J, Wu F, Wen J H 2020 Compos. Struct. 239 111978 Google Scholar
[12]	Jin Y B, Yang Y L, Wen Z H, He L S, Cang Y, Yang B, Djafari-Rouhani B, Li Y, Li Y 2022 Int. J. Mech. Sci. 226 107396 Google Scholar
[13]	Liu C R, Yang Z R, Liu X L, Wu J H, Ma F Y 2023 APL Mater. 11 101122 Google Scholar
[14]	白宇, 张振方, 杨海滨, 蔡力, 郁殿龙 2023 72 054301 Google Scholar Bai Y, Zhang Z F, Yang H B, Cai L, Yu D L 2023 Acta Phys. Sin. 72 054301 Google Scholar
[15]	Liu J W, Yu D L, Yang H B, Shen H J, Wen J H 2020 Chin. Phys. Lett. 37 34301 Google Scholar
[16]	Zhou Z L, Huang S B, Li D T, Zhu J, Li Y 2022 Natl. Sci. Rev. 9 171 Google Scholar
[17]	Almeida G D N, Vergara E F, Barbosa L R, Lenzi A, Birch R S 2021 Appl. Acoust. 183 108312 Google Scholar
[18]	Wu F, Ju Z G, Hu M, Zhang X, Li D, Liu K L 2023 J. Phys. D: Appl. Phys. 56 45401 Google Scholar
[19]	Ma G C, Yang M, Xiao S W, Yang Z Y, Sheng P 2014 Nat. Mater. 13 873 Google Scholar
[20]	Ge H, Yang M, Ma C, Lu M H, Chen Y F, Fang N, Sheng P 2018 Natl. Sci. Rev. 5 159 Google Scholar
[21]	Cummer S A, Christensen J, Alù A 2016 Nat. Rev. Mater. 1 16001 Google Scholar
[22]	Stinson M R 1991 J. Acoust. Soc. Am. 89 550 Google Scholar
[23]	Verdière K, Panneton R, Elkoun S D, Dupont T, Leclaire P 2013 J. Acoust. Soc. Am. 134 4648 Google Scholar
[24]	Guo J W, Zhang X, Fang Y, Jiang Z Y 2021 Compos. Struct. 260 113538 Google Scholar
[25]	Tam C K W, Ju H, Jones M G, Watson W R, Parrott T L 2005 J. Sound Vib. 284 947 Google Scholar
[26]	Zieliński T G, Chevillotte F, Deckers E 2019 Appl. Acoust. 146 261 Google Scholar
[27]	杜功焕, 朱哲民, 龚秀芬 2012 声学基础(南京: 南京大学出版社)第159页 Du G H, Zhu Z M, Gong X F 2012 Acoustics Foundation (Nanjing: Nanjing University Press) p159
[28]	Romero-García V, Theocharis G, Richoux O, Merkel A, Tournat V, Pagneux V 2016 Sci. Rep. 6 19519 Google Scholar
[29]	Lee F C, Chen W H 2001 J. Sound Vib. 248 621 Google Scholar
[30]	Liu J, Herrin D W 2010 Appl. Acoust. 71 120 Google Scholar
[31]	Ruiz H, Claeys C C, Deckers E, Desmet W 2016 Mech. Syst. Signal Pr. 70 904
[32]	Romero-García V, Sánchez-Pérez J V, Garcia-Raffi L M 2011 J. Appl. Phys. 110 14904 Google Scholar
[33]	Qamoshi K, Rasuli R 2016 Appl. Phys. A 122 788 Google Scholar
[34]	Storn R, Price K 1997 J. Global Optim. 11 341 Google Scholar

施引文献

图 1 内插缝Helmholtz共振吸声结构单元胞示意图

Fig. 1. Schematic of single slit-embedded Helmholtz resonator.

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图 2 矩形截面管道声传播示意图

Fig. 2. Diagram of sound propagation in a rectangular section pipe.

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图 3 并联结构示意图

Fig. 3. Schematic diagram of parallel structure.

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图 4 有限元模型　(a) 三维狭窄声学模型; (b) 二维狭窄声学模型; (c) 二维热黏性声学模型

Fig. 4. Finite element model: (a) Three-dimensional simulation model of narrow acoustic; (b) two-dimensional simulation model of narrow acoustic; (c) two-dimensional simulation model of thermoviscous acoustic.

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图 5 单元胞三维图

Fig. 5. Three dimensional diagram of single cell.

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图 6 单元胞吸声系数曲线

Fig. 6. Sound absorption coefficient curve of single cell.

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图 7 吸声系数曲线　(a) 随缝宽的变化; (b) 随缝高的变化

Fig. 7. Sound absorption coefficient curve: (a) Vary with width of slit; (b) vary with height of slit.

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图 8 双元胞与四元胞并联示意图

Fig. 8. Three-dimensional diagram of two cells and four cells in parallel.

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图 9 吸声系数曲线　(a) 双元胞并联结构; (b) 四元胞并联结构

Fig. 9. Sound absorption coefficient curve: (a) Two cells in parallel; (b) four cells in parallel.

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图 10 吸声频谱　(a) 随缝宽的变化; (b) 随缝高的变化

Fig. 10. Absorption spectrum: (a) Vary with width of slit; (b) vary with height of slit.

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图 11 归一化声阻抗曲线

Fig. 11. Normalized acoustic impedance curve.

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图 12 归一化声阻抗曲线　(a) 双元胞并联结构; (b) 四元胞并联结构

Fig. 12. Normalized acoustic impedance curve: (a) Two cells in parallel; (b) four cells in parallel.

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图 13 单元胞复平面反射系数与声压速度场分布

Fig. 13. Zero-pole distribution of single cell on complex plane and distribution of sound pressure and velocity field.

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图 14 反射系数在复平面的分布　(a) 双元胞结构; (b) 四元胞结构

Fig. 14. Distribution of reflection coefficient log|r|²: (a) Two cells in parallel; (b) four cells in parallel.

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图 15 声压及速度场分布　(a) 257 Hz; (b) 294 Hz; (c) 275 Hz

Fig. 15. Sound pressure and velocity field distribution: (a) 257 Hz; (b) 294 Hz; (c) 275 Hz.

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图 16 差分进化算法流程图

Fig. 16. Flow chart of differential evolution algorithm.

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图 17 八元胞并联三维图(厚度90 mm)

Fig. 17. Three-dimensional diagram of eight cells in parallel (thickness 90 mm).

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图 18 吸声系数曲线及复平面零极点分布

Fig. 18. Sound absorption coefficient curve and distribution of reflection coefficient log|r|².

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图 19 实验测试系统示意图

Fig. 19. Schematic diagram of experimental setup.

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图 20 实验测试系统实物图

Fig. 20. Photo of experimental setup.

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图 21 实验样件实物照片

Fig. 21. Photo of the experimental sample.

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图 22 单元胞结构理论解析与实验测试吸声系数(样件1, 厚30 mm)

Fig. 22. Comparison of theoretical and experimental sound absorption coefficient of single cell (Sample 1, thickness 30 mm).

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图 25 多元胞并联理论解析与实验测试吸声系数(样件4, 厚90 mm)

Fig. 25. Comparison of theoretical and experimental sound absorption coefficient of multiple cells in parallel (Sample 4, thickness 90 mm).

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图 23 双元胞并联结构理论解析与实验测试吸声系数(样件2, 厚50 mm)

Fig. 23. Comparison of theoretical and experimental sound absorption coefficient of two cells in parallel (Sample 2, thickness 50 mm).

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图 24 四元胞并联结构理论解析与实验测试吸声系数(样件3, 厚50 mm)

Fig. 24. Comparison of theoretical and experimental sound absorption coefficient of four cells in parallel (Sample 3, thickness 50 mm).

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表 1 单个内插缝Helmholtz共振腔结构参数

Table 1. Structural parameters of single slit-embedded Helmholtz resonator.

长L/mm 宽D/mm 高H/mm 缝宽d/mm 缝高l_r/mm

100 100 30 2 10

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表 2 双元胞并联结构参数

Table 2. Structural parameters of two cells in parallel.

长L/mm 宽D/mm 高H/mm 缝宽d₁/mm 缝高l_r1/mm 缝宽d₂/mm 缝高l_r2/mm

50 50 50 1.2 17.3 1.1 9.8

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表 3 四元胞并联结构参数

Table 3. Structural parameters of four cells in parallel.

长L/mm 宽D/mm 高H/mm 缝宽d₁/mm 缝高l_r1/mm 缝宽d₂/mm 缝高l_r2/mm 缝宽d₃/mm 缝高l_r3/mm 缝宽d₄/mm 缝高l_r4/mm

50 50 50 2.7 42.3 1.7 17.9 1.3 8 1.3 4.7

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表 4 多元胞并联结构参数

Table 4. Structural parameters of multivariate cells in parallel.

元胞 1 2 3 4 5 6 7 8

缝宽d/mm 1.5 1.4 1.7 1.4 1.1 1.2 1.1 1.5
缝高l_r/mm 84 35.1 70.6 10.6 10.3 23.5 15.3 50.6

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map

[1]	Champoux Y, Allard J F 1991 J. Appl. Phys. 70 1975 Google Scholar
[2]	Panneton R 2007 J. Acoust. Soc. Am. 122 217 Google Scholar
[3]	Trompette N, Barbry J, Sgard F, Nelisse H 2009 J. Acoust. Soc. Am. 125 31 Google Scholar
[4]	Climente A, Torrent D, Sánchez-Dehesa J 2012 Appl. Phys. Lett. 100 144103 Google Scholar
[5]	Ma G C, Sheng P 2016 Sci. Adv. 2 1501595 Google Scholar
[6]	肖勇, 王洋, 赵宏刚, 郁殿龙, 温激鸿 2023 机械工程学报 59 277 Google Scholar Xiao Y, Wang Y, Zhao H G, Yu D L, Wen J H 2023 J. Mech. Eng. 59 277 Google Scholar
[7]	Cai X B, Guo Q Q, Hu G K, Yang J 2014 Appl. Phys. Lett. 105 121901 Google Scholar
[8]	Wang Y, Zhao H G, Yang H B, Zhong J, Zhao D, Lu Z L, Wen J H 2018 J. Appl. Phys. 123 185109 Google Scholar
[9]	Wu F, Xiao Y, Yu D, Zhao H, Wang Y, Wen J 2019 Appl. Phys. Lett. 114 151901 Google Scholar
[10]	吴飞, 黄威, 陈文渊, 肖勇, 郁殿龙, 温激鸿 2020 69 134303 Google Scholar Wu F, Huang W, Chen W Y, Xiao Y, Yu D L, Wen J H 2020 Acta Phys. Sin. 69 134303 Google Scholar
[11]	Zhao H G, Wang Y, Yu D L, Yang H B, Zhong J, Wu F, Wen J H 2020 Compos. Struct. 239 111978 Google Scholar
[12]	Jin Y B, Yang Y L, Wen Z H, He L S, Cang Y, Yang B, Djafari-Rouhani B, Li Y, Li Y 2022 Int. J. Mech. Sci. 226 107396 Google Scholar
[13]	Liu C R, Yang Z R, Liu X L, Wu J H, Ma F Y 2023 APL Mater. 11 101122 Google Scholar
[14]	白宇, 张振方, 杨海滨, 蔡力, 郁殿龙 2023 72 054301 Google Scholar Bai Y, Zhang Z F, Yang H B, Cai L, Yu D L 2023 Acta Phys. Sin. 72 054301 Google Scholar
[15]	Liu J W, Yu D L, Yang H B, Shen H J, Wen J H 2020 Chin. Phys. Lett. 37 34301 Google Scholar
[16]	Zhou Z L, Huang S B, Li D T, Zhu J, Li Y 2022 Natl. Sci. Rev. 9 171 Google Scholar
[17]	Almeida G D N, Vergara E F, Barbosa L R, Lenzi A, Birch R S 2021 Appl. Acoust. 183 108312 Google Scholar
[18]	Wu F, Ju Z G, Hu M, Zhang X, Li D, Liu K L 2023 J. Phys. D: Appl. Phys. 56 45401 Google Scholar
[19]	Ma G C, Yang M, Xiao S W, Yang Z Y, Sheng P 2014 Nat. Mater. 13 873 Google Scholar
[20]	Ge H, Yang M, Ma C, Lu M H, Chen Y F, Fang N, Sheng P 2018 Natl. Sci. Rev. 5 159 Google Scholar
[21]	Cummer S A, Christensen J, Alù A 2016 Nat. Rev. Mater. 1 16001 Google Scholar
[22]	Stinson M R 1991 J. Acoust. Soc. Am. 89 550 Google Scholar
[23]	Verdière K, Panneton R, Elkoun S D, Dupont T, Leclaire P 2013 J. Acoust. Soc. Am. 134 4648 Google Scholar
[24]	Guo J W, Zhang X, Fang Y, Jiang Z Y 2021 Compos. Struct. 260 113538 Google Scholar
[25]	Tam C K W, Ju H, Jones M G, Watson W R, Parrott T L 2005 J. Sound Vib. 284 947 Google Scholar
[26]	Zieliński T G, Chevillotte F, Deckers E 2019 Appl. Acoust. 146 261 Google Scholar
[27]	杜功焕, 朱哲民, 龚秀芬 2012 声学基础(南京: 南京大学出版社)第159页 Du G H, Zhu Z M, Gong X F 2012 Acoustics Foundation (Nanjing: Nanjing University Press) p159
[28]	Romero-García V, Theocharis G, Richoux O, Merkel A, Tournat V, Pagneux V 2016 Sci. Rep. 6 19519 Google Scholar
[29]	Lee F C, Chen W H 2001 J. Sound Vib. 248 621 Google Scholar
[30]	Liu J, Herrin D W 2010 Appl. Acoust. 71 120 Google Scholar
[31]	Ruiz H, Claeys C C, Deckers E, Desmet W 2016 Mech. Syst. Signal Pr. 70 904
[32]	Romero-García V, Sánchez-Pérez J V, Garcia-Raffi L M 2011 J. Appl. Phys. 110 14904 Google Scholar
[33]	Qamoshi K, Rasuli R 2016 Appl. Phys. A 122 788 Google Scholar
[34]	Storn R, Price K 1997 J. Global Optim. 11 341 Google Scholar

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[13]	赵宏刚, 温激鸿, 杨海滨, 吕林梅, 温熙森. 一种含柱形空腔结构橡胶层的吸声机理及优化. , 2014, 63(13): 134303. doi: 10.7498/aps.63.134303
[14]	梁国龙, 庞福滨, 张光普. 吸声材料对水下小平台上矢量传感器声学特性的影响研究. , 2014, 63(3): 034303. doi: 10.7498/aps.63.034303
[15]	于利刚, 李朝晖, 王仁乾, 马黎黎. 含玻璃微球的黏弹性复合材料覆盖层的水下吸声性能分析. , 2013, 62(6): 064301. doi: 10.7498/aps.62.064301
[16]	杨海滨, 李岳, 赵宏刚, 温激鸿, 温熙森. 一种含圆柱形谐振散射体的黏弹材料低频吸声机理研究. , 2013, 62(15): 154301. doi: 10.7498/aps.62.154301
[17]	于利刚, 李朝晖, 马黎黎. 0-3型压电复合材料覆盖层水下吸声性能的理论研究. , 2012, 61(2): 024301. doi: 10.7498/aps.61.024301
[18]	吕林梅, 温激鸿, 赵宏刚, 孟浩, 温熙森. 内嵌不同形状散射子的局域共振型黏弹性覆盖层低频吸声性能研究. , 2012, 61(21): 214302. doi: 10.7498/aps.61.214302
[19]	孙广荣, 魏荣爵. 甘蔗纤维板穿孔吸声的初步研究. , 1963, 19(3): 151-159. doi: 10.7498/aps.19.151
[20]	魏荣爵, 余崇智. 国产吸声材料的吸声系数测定的初步报告. , 1957, 13(5): 365-387. doi: 10.7498/aps.13.365

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内插缝Helmholtz共振腔吸声超结构的机理分析与优化设计