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Noise is always a serious factor affecting people's quality of life. The most common sound-absorbing materials are porous materials, which work based on the principle that sound waves entering into the pores inside the material are subjected to air friction and viscous resistance, thus converting sound energy into heat. Porous materials have excellent performance of absorbing medium-frequency and high-frequency sound , but they are required to be thick enough to control the low-frequency sound waves with large wavelengths, which limits the application of porous materials in low-frequency noise control. In recent years, acoustic artificial structures have become a research hotspot, which can realize exotic effective acoustic parameters based on periodical structure or local resonance. Acoustic artificial structure provides a new material basis for noise control, in which Helmholtz resonator plays an important role because of its simple geometry. In this study, a broadband muffler is designed based on the second-order neck embedded Helmholtz resonator. In order to achieve low-frequency and broadband sound insulation with a limited number of units and structure length, the second-order resonator is chosen as a basic structure unit, which has a stronger low-frequency noise reduction capability and has one high-frequency transmission loss peak more than a conventional Helmholtz resonator. The acoustic characteristics and insulation performance of second-order resonators are analyzed through theoretical calculation, simulation calculation and experimental test. Then, based on the theoretical model and empirical rules, a broadband muffler composed of nine second-order resonators is designed by carefully adjusting the geometry parameters of each resonator. The three-dimensional printed resonators are installed on the side wall of a square standing wave tube for experimental measurement. In the experiment, the transmission loss curve of the muffler is measured by the two-load method. The result shows that the designed muffler has good sound insulation performances in a frequency range of 267–927 Hz, with the whole transmission loss above 20 dB and the maximum sound insulation up to 60 dB. The experimental result is consistent with the calculation result and simulation result. The muffler has simple structure and high practicability, which will have a wide application prospect in noise control engineering.
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Liu Z E, Wu X C, Du S Z, Huang T, Lu Z H, Ruan J, Shao J Y, Liu G Q 2019 Digit. Manu. Sci. 6 143
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Google Scholar
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Google Scholar
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[33] 康钟绪 2009 博士学位论文 (太原: 山西大学)
Kang Z X 2009 Ph. D. Dissertation (Harbin: Harbin Engineering University) (in Chinese)
[34] 龙厚友 2019 博士学位论文 (南京: 南京大学)
Long H Y 2019 Ph. D. Dissertation (Nanjing: Nanjing University) (in Chinese)
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图 1 (a)二阶共鸣器的三维截面示意图; (b)二维结构示意图及几何参数
Figure 1. (a) 3D cross-sectional schematic diagram of second-order resonator; (b) 2D structure schematic diagram and geometrical parameters.
图 2 二阶共鸣器单元在波导管侧壁作为消声器的三维仿真示意图(a)和实验测量示意图(b); 1号(c)和2号(d)二阶共鸣器单元的数值计算、仿真计算与实验测量的传递损失结果对比数据图
Figure 2. 3D simulation schematic diagram (a) and experimental test diagram (b) of the second-order resonator as a muffler on the side of a waveguide; transmission loss results of the numerical calculation, simulation calculation and experimental measurement of No. 1 (c) and No. 2 (d) second-order resonators, respectively.
图 3 (a) 传统共鸣器; (b) 二阶共鸣器; (c) 仿真计算的传递损失结果对比图
Figure 3. (a) Schematic diagram of traditional resonator; (b) schematic diagram of second-order resonator; (c) transmission loss results of structures corresponding to (a), (b).
图 5 (a) 不同第一内插管半径
$ {r}_{\rm{n}}^{1} $ 的传输损失曲线; (b) 不同第一内插管长度$ {l}_{\rm{n}}^{1} $ 的传输损失曲线; (c) 不同第二内插管半径$ {r}_{\rm{n}}^{2} $ 的传输损失曲线; (d) 不同第二内插管长度$ {l}_{\rm{n}}^{2} $ 的传输损失曲线Figure 5. (a) Transmission loss curves of different
$ {r}_{\rm{n}}^{1} $ ; (b) transmission loss curves of different$ {l}_{\rm{n}}^{1} $ ; (c) transmission loss curves of different$ {r}_{\rm{n}}^{2} $ ; (d) transmission loss curves of different$ {l}_{\rm{n}}^{2} $ .
图 6 (a)由9个二阶共鸣器单元组成的抗性消声器仿真模型; (b) 实验测试图; (c) 实验测量与Comsol Multiphysics仿真、Matlab计算结果的传递损失对比图
Figure 6. (a) The simulation model of the resistant muffler composed of nine second-order resonators; (b) experimental measurement photo; (c) transmission loss curves of experimental measurement, simulation with Comsol Multiphysics and calculation with Matlab.
表 1 两个二阶共鸣器单元的几何参数表
Table 1. Geometrical parameters of two 2nd-order resonators.
NO. $ {S}_{\rm{c}} $/mm2 $ {l}_{\rm{n}}^{1} $, $ {l}_{\rm{n}}^{2} $/mm $ {l}_{\rm{c}}^{1} $/mm $ {l}_{\rm{c}}^{2} $/mm $ {r}_{\rm{n}}^{1} $/mm $ {r}_{\rm{n}}^{2} $/mm 1 100×100 10 70 30 40 20 2 115×100 10 70 30 42.5 20 
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表 2 图3(a), (b)中三维结构的几何参数及共振峰结果表
Table 2. Geometrical parameters and resonance peak results of the structures in Fig. 3(a), (b).
类型 $ {l}_{\rm{c}}^{1} $/mm $ {l}_{\rm{c}}^{2} $/mm $ {l}_{\rm{n}}^{1} $/mm $ {r}_{\rm{n}}^{1} $/mm $ {l}_{\rm{n}}^{2} $/mm $ {r}_{\rm{n}}^{2} $/mm $ {f}_{1} $/Hz $ {f}_{2} $/Hz $ {\rm{T}\rm{L}}_{f1} $/dB $ {\rm{T}\rm{L}}_{f2} $/dB 一阶 100 — 20 20 — — 299 — 29.4 — 二阶 50 50 20 20 20 10 201 500 29.3 37.1
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表 3 图4(a)—(c)中三维结构的几何参数及共振峰结果表
Table 3. Geometrical parameters and resonance peak results of the structures in Fig. 4(a)-(c).
No. $ {l}_{\rm{c}}^{1} $/mm $ {l}_{\rm{c}}^{2} $/mm $ {f}_{1} $/Hz $ {f}_{2} $/Hz $ {\rm{T}\rm{L}}_{f1} $/dB $ {\rm{T}\rm{L}}_{f2} $/dB 1 40 60 188 545 30.7 36.4 2 50 50 201 500 29.3 37.1 3 60 40 219 467 34.7 38.8
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表 4 9个二阶共鸣器单元的几何参数表
Table 4. Geometrical parameters of nine second-order resonators.
No. $ {S}_{\rm{c}} $/mm2 $ {r}_{\rm{n}}^{1} $/mm $ {r}_{\rm{n}}^{2} $/mm 1 100×100 40 20 2 115×100 42.5 20 3 130×100 42.5 21 4 145×100 43 21 5 160×100 43 21 6 175×100 43 20 7 190×100 41 20 8 205×100 41 15 9 220×100 41 15
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[1] Liu Z Y, Zhang X X, Mao Y W, Zhu Y Y, Yang Z Y, Chan C T, Sheng P 2000 Science 289 1734
Google Scholar
[2] Allard J, Atalla N 2009 Propagation of Sound in Porous Media: Modelling Sound Absorbing Materials (2nd Ed.) (Hoboken: John Wiley & Sons) p15
[3] Yang Z, Mei J, Yang M, Chan N H, Sheng P 2008 Phys. Rev. Lett. 101 204301
Google Scholar
[4] Yang Z, Dai H M, Chan N H, Ma G C, Sheng P 2010 Appl. Phys. Lett. 96 041906
Google Scholar
[5] Cheng Y, Zhou C, Yuan B G, Wu D J, Wei Q, Liu X J 2015 Nat. Mater. 14 1013
Google Scholar
[6] Soto G, Castro A, Vechiatti N, Lasi F, Armas A, Marcovich N E, Mosiewicki M A 2017 Polym. Test. 57 42
Google Scholar
[7] Cai X B, Guo Q Q, Hu G K, Yang J 2014 Appl. Phys. Lett. 105 121901
Google Scholar
[8] Chen C R, Du Z B, Hu G K, Yang J 2017 Appl. Phys. Lett. 110 221903
Google Scholar
[9] 刘志恩, 吴旭昌, 杜松泽, 黄涛, 卢炽华, 阮杰, 邵炯炀, 刘国强 2019 数字制造科学 6 143
Liu Z E, Wu X C, Du S Z, Huang T, Lu Z H, Ruan J, Shao J Y, Liu G Q 2019 Digit. Manu. Sci. 6 143
[10] Shao C, Zhu Y Z, Long H Y, Liu C, Cheng Y, Liu X J 2022 Appl. Phys. Lett. 120 083504
Google Scholar
[11] Gu Y, Long H Y, Cheng Y, Deng M X, Liu X J 2021 Phys. Rev. Appl. 16 014021
Google Scholar
[12] Nguyen H, Wu Q, Xu X C, Chen H, Tracy S, Huang G L 2020 Appl. Phys. Lett. 117 134103
Google Scholar
[13] Sun M, Fang X S, Mao D X, Wang X, Li Y 2020 Phys. Rev. Appl. 13 044028
Google Scholar
[14] Shao C, Xiong W, Long H Y, Tao J C, Cheng Y, Liu X J 2021 J. Acoust. Soc. Am. 150 1044
Google Scholar
[15] Dong R Z, Mao D X, Wang X, Li Y 2021 Phys. Rev. Appl. 15 024044
Google Scholar
[16] Long H Y, Shao C, Cheng Y, Tao J C, Liu X J 2021 Appl. Phys. Lett. 118 263502
Google Scholar
[17] Shen L, Zhu Y F, Mao F L, Gao S Y, Su Z H, Luo Z T, Zhang H, Assouar B 2021 Phys. Rev. Appl. 16 064057
Google Scholar
[18] Gao Y X, Cheng Y, Liang B, Li Y, Yang J, Cheng J C 2021 Sci. China-Phys. Mech. Astron. 64 1
[19] Liu C K, Wang H J, Liang B, Cheng J C, Lai Y 2022 Appl. Phys. Lett. 120 231702
Google Scholar
[20] Yu Y C, Yang Y Z, Zhao H, Shi Q Q, Kong P, Yang J, Deng K 2022 J. Appl. Phys. 131 135102
Google Scholar
[21] Zhu Y Z, Long H Y, Liu C, Zhang H X, Cheng Y, Liu X J 2022 Appl. Phys. Lett. 120 141701
Google Scholar
[22] Selamet A, Lee I 2003 J. Acoust. Soc. Am. 113 1975
Google Scholar
[23] Ji J, Li D T, Li Y, Jing Y 2020 Front. Mech. Eng-Switz. 6 94
[24] Huang S B, Fang X S, Wang X, Assouar B, Cheng Q, Li Y 2019 J. Acoust. Soc. Am. 145 254
Google Scholar
[25] Romero-Garc V, Theocharis G, Richoux O, Pagneux V 2016 J. Acoust. Soc. Am. 139 3395
Google Scholar
[26] Long H Y, Liu C, Shao C, Cheng Y, Tao J C, Qiu X J, Liu X J 2020 J. Sound Vib. 479 115371
Google Scholar
[27] Li Y, Assouar B M 2016 Appl. Phys. Lett. 108 063502
Google Scholar
[28] Ryoo H, Jeon W 2018 Appl. Phys. Lett. 113 121903
Google Scholar
[29] Chen J S, Chen Y B, Cheng Y H, Chou L C 2020 Phys. Lett. A 384 126887
Google Scholar
[30] Liu C R, Wu J H, Ma F Y, Chen X, Yang Z R 2019 J. Phys. D: Appl. Phys. 52 105302
Google Scholar
[31] Huang S B, Zhou Z L, Li D T, Liu T, Wang X, Zhou J, Li Y 2020 Sci. Bull. 65 373
Google Scholar
[32] Jiménez N, Groby J P, Romero-García V 2021 Acoustic Waves in Periodic Structures, Metamaterials, and Porous Media (Cham: Springer International Publishing) p103
[33] 康钟绪 2009 博士学位论文 (太原: 山西大学)
Kang Z X 2009 Ph. D. Dissertation (Harbin: Harbin Engineering University) (in Chinese)
[34] 龙厚友 2019 博士学位论文 (南京: 南京大学)
Long H Y 2019 Ph. D. Dissertation (Nanjing: Nanjing University) (in Chinese)
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