Sound insulation performance of Helmholtz cavity with thin film bottom

He Zi-Hou; Zhao Jing-Bo; Yao Hong; Chen Xin

doi:10.7498/aps.68.20191131

Abstract

Aiming at the isolation of low-frequency noise, an acoustic metamaterial is designed based on Helmholtz cavity and thin film structure. It consists of a Helmholtz cavity with film bottom and the mass block attached to the cavity. By the finite element method, the transmission losses and resonance frequencies of metamaterials in a frequency range of 20－1200 Hz are calculated and also verified experimentally. The results show that the metamaterial has great sound insulation performance in the frequency range. There are six sound insulation peaks, of which the two sound insulation peaks below 100 Hz have the transmission losses of 44.29 dB and 67.43 dB, respectively. The maximum transmission loss in the whole frequency range is 90.18 dB. Comparing with the normal Helmholtz cavity or thin film acoustic metamaterial or traditional material, the sound insulation performance of the metamaterial is improved greatly. By analyzing the resonance and vibration mode diagram at the sound insulation peaks comprehensively, the sound insulation mechanism of the metamaterial is further explored. The results show that many resonance modes have no effect on transmission loss only when the resonance mode can be coupled with the incident wave and is not an antisymmetric mode which can affect the transmission loss. The transmission and reflection coefficient of the metamaterial are calculated by the finite element method, and through the method for retrieving effective properties, the effective mass density and effective modulus are obtained. It is found that there is a negative effective mass density at the sound insulation peak, meanwhile the effective modulus is close to zero. The generation mechanism of abnormal equivalent parameters is analyzed from the energy view point. The acoustic impedance of the metamaterial is obtained by an equivalent circuit method, through which the first resonance frequency is calculated relatively accurately. According to the results of the previous study on sound insulation mechanism, the effect of the eccentric mass unit on the sound insulation performance of metamaterial is studied. It is found that the eccentric mass can greatly reduce the antisymmetric resonance mode and increase the sound insulation peak of the structure, which is also verified experimentally. The results provide a reference for designing the acoustic metamaterials.

Keywords:

Authors and contacts

1.
Graduate School, Air Force Engineering University, Xi’an 710051, China
2.
Department of Basic, Air Force Engineering University, Xi’an 710051, China

Corresponding author: Zhao Jing-Bo, chjzjb@163.com

Funds: Project supported by the National Natural Science Foundation of China (Grant No. 11504429) and the Pre-research Project of Department of Basic Sciences, Air Force Engineering University, China (Grant No. YNJC19070602)

FullText HTML : translate this paragraph

References

[1]	William B A, Lisa M M, Kelsey B, Stephen B, John L A 2019 Environ. Sci. Technol. 53 7126 Google Scholar
[2]	周榕 2017 硕士学位论文 (南京: 江苏大学) Zhou Y 2017 M. S. Thesis (Nanjing: Jiangsu University) (in Chinese)
[3]	Wu J H, Ma F Y, Zhang S W, Shen L 2006 J. Mech. Eng. 52 68
[4]	丁昌林, 董仪宝, 赵晓鹏 2018 67 194301 Ding C L, Dong Y B, Zhao X P 2018 Acta Phys. Sin. 67 194301
[5]	Lee S H, Park C M, Seo Y M, Wang Z G, Kim C K 2010 Phys. Rev. Lett. 104 054301 Google Scholar
[6]	沈惠杰, 郁殿龙, 汤智胤, 苏永生, 李雁飞, 刘江伟 2019 68 144301 Shen H J, Yu D L, Tang Z Y, Su Y S, Li Y F, Liu J W 2019 Acta Phys. Sin. 68 144301
[7]	Chen H J, Zhai S L, Ding C L, Liu S, Luo C R, Zhao X P 2015 J. Appl. Phys. 118 094901 Google Scholar
[8]	Mei J, Ma G C, Yang M, Yang Z Y, Wen W J, Sheng P 2012 Nat. Commun. 3 756 Google Scholar
[9]	Nemat-Nasser S, Willis J R, Srivastava A, Amirkhizi A V 2011 Phys. Rev. B 83 104103 Google Scholar
[10]	丁昌林, 赵晓鹏 2009 58 6351 Google Scholar Ding C L, Zhao X P 2009 Acta Phys. Sin. 58 6351 Google Scholar
[11]	Liu Z, Zhang X X, Chan C T, Sheng P 2000 Science 289 1734 Google Scholar
[12]	贺子厚, 赵静波, 姚宏, 蒋娟娜, 张帅, 陈鑫 2018 硅酸盐学报 47 983 He Z H, Zhao J B, Yao H, Jiang J N, Zhang S Chen X 2018 J. Chin. Ceramic Soc. 47 983
[13]	高南沙, 侯宏 2018 材料导报 32 322 Google Scholar Gao N S, Hou H 2018 Mater. Rev. 32 322 Google Scholar
[14]	王莎, 林书玉 2019 68 024303 Wang S, Lin S Y 2019 Acta Phys. Sin. 68 024303
[15]	刘娇, 侯志林, 傅秀军 2015 64 154302 Liu J, Hou Z L, Fu X J 2015 Acta Phys. Sin. 64 154302
[16]	Cheng Y, Xu J Y, Liu X J 2008 Appl. Phys. Lett. 92 051913 Google Scholar
[17]	贾晓珍 2018 硕士学位论文 (西安: 陕西师范大学) Jia X Z 2018 M. S. Thesis (Xi′an: Shaanxi Normal Univer-sity) (in Chinese)
[18]	Chen Y, Huang G, Zhou X, Hu G, Sun C 2014 J. Acoust. Soc. Am. 136 969 Google Scholar
[19]	Fang N, Xi D J, Xu J Y, Ambati M, Srituravanich W, Sun C, Zhang X 2006 Nature Mater. 5 452 Google Scholar
[20]	姜久龙, 姚宏, 杜军, 赵静波, 邓涛 2017 66 064301 Jiang J L, Yao H, Du J, Zhao J B, Deng T 2017 Acta Phys. Sin. 66 064301
[21]	Naify C J, Chang C M, Mcknight G, Nutt S 2011 J. Appl. Phys. 110 751
[22]	梅军, 马冠聪, 杨旻, 杨志宇, 温维佳, 沈平 2012 物理 41 425 Mei J, Ma G C, Yang M, Yang Z Y, Wen W J, Shen P 2012 Physics 41 425
[23]	Cheng Y, Zhou C, Yuan B G, Wu D J, Wei Q, Liu X J 2015 Nature Mater. 14 1013 Google Scholar
[24]	周榕, 吴卫国, 闻轶凡 2017 声学技术 36 297 Zhou Y, Wu W G, Wen Y F 2017 Tech. Acoust. 36 297
[25]	Abbad A 2016 SAE International 9th International Styrian Noise, Vibration & Harshness Congress Warrendale, United States, June 22, 2016 p2011
[26]	Long H, Cheng Y, Liu X 2018 Sci. Rep. 8 15678 Google Scholar
[27]	陈鑫, 姚宏, 赵静波, 张帅, 贺子厚, 蒋娟娜 2019 68 084302 Chen X, Yao H, Zhao J B, Zhang S, He Z H, Jiang J N 2019 Acta Phys. Sin. 68 084302
[28]	杜功焕, 朱哲民, 龚秀芬 2012 声学基础 (南京: 南京大学出版社) 第84页 Du G H, Zhu Z M, Gong X F 2012 Acoustic Basis (Nanjing: Nanjing University Press) p84
[29]	Fokin V, Ambati M, Sun C, Zhang X 2007 Phys. Rev. B 76 144302 Google Scholar
[30]	贺子厚, 赵静波, 姚宏, 张帅, 蒋娟娜, 陈鑫 2019 68 134302 Google Scholar He Z H, Zhao J B, Yao H, Zhang S, Jiang J N, Chen X 2019 Acta Phys. Sin. 68 134302 Google Scholar

Cited By

图 1 材料结构　(a)结构示意图; (b)结构参数

Figure 1. Material structure: (a) Structural sketch; (b) structure parameter.

DownLoad: Full-Size Img PowerPoint

图 2 腔体结构

Figure 2. Cavity structure.

DownLoad: Full-Size Img PowerPoint

图 3 传输损失曲线

Figure 3. Transmission loss curves.

DownLoad: Full-Size Img PowerPoint

图 4 共振模态(颜色条表示位移的取值, 单位为mm, 其余图同)　(a) 69.44 Hz; (b) 325.40 Hz

Figure 4. Resonance mode (color bar represents the displacement values, unit: mm): (a) 69.44 Hz; (b) 325.40 Hz.

DownLoad: Full-Size Img PowerPoint

图 5 共振模态　(a) 25.05 Hz; (b) 68.53 Hz; (c) 420.72 Hz; (d) 622.76 Hz; (e) 944.71 Hz; (f) 1075.80 Hz

Figure 5. Resonance mode: (a) 25.05 Hz; (b) 68.53 Hz; (c) 420.72 Hz; (d) 622.76 Hz; (e) 944.71 Hz; (f) 1075.80 Hz.

DownLoad: Full-Size Img PowerPoint

图 6 隔声峰处振动模式图　(a) 25.10 Hz; (b) 67.43 Hz; (c) 415.49 Hz; (d) 626.30 Hz; (e) 952.81 Hz; (f) 1080.08 Hz

Figure 6. Vibration mode diagrams at sound insulation peak: (a) 25.10 Hz; (b) 67.43 Hz; (c) 415.49 Hz; (d) 626.30 Hz; (e) 952.81 Hz; (f) 1080.08 Hz.

DownLoad: Full-Size Img PowerPoint

图 7 Helmholtz腔(a)及其等价电路模型(b)

Figure 7. Helmholtz cavity (a) and its equivalent circuit model

DownLoad: Full-Size Img PowerPoint

图 8 薄膜底面Helmholtz腔(a)及其等价电路模型(b)

Figure 8. Helmholtz cavity with thin film bottom (a) and its equivalent circuit model.

DownLoad: Full-Size Img PowerPoint

图 9 首阶共振频率

Figure 9. First resonance frequency.

DownLoad: Full-Size Img PowerPoint

图 10 实验示意图　(a), (b)样件实物图; (c)实验装置

Figure 10. Experimental schematic diagrams: (a), (b) Sample structure; (c) experimental facility.

DownLoad: Full-Size Img PowerPoint

图 11 实验测得的传输损失曲线与数值计算结果的对比

Figure 11. Comparison between experimentally measured transmission loss curve and the results obtained by the finite element method.

DownLoad: Full-Size Img PowerPoint

图 12 (a)透射系数; (b)反射系数

Figure 12. (a) Transmission coefficient; (b) reflection coefficient.

DownLoad: Full-Size Img PowerPoint

图 13 等效参数　(a)等效密度; (b)等效模量

Figure 13. Effective parameters: (a) Effective mass density; (b) effective modulus.

DownLoad: Full-Size Img PowerPoint

图 14 结构示意图

Figure 14. Structural sketch.

DownLoad: Full-Size Img PowerPoint

图 15 (a)偏心质量单元与中心质量单元的传输损失曲线; (b)当 l 值不同时, 超材料的传输损失曲线

Figure 15. (a) Comparison of transmission loss between eccentric mass unit and central mass unit; (b) transmission loss curves when l is different.

DownLoad: Full-Size Img PowerPoint

图 16 振动模式图　(a) 28.03 Hz; (b) 61.27 Hz; (c) 71.29 Hz; (d) 328.22 Hz; (e) 396.30 Hz; (f) 466.81 Hz

Figure 16. Vibration mode: (a) 28.03 Hz; (b) 61.27 Hz; (c) 71.29 Hz; (d) 328.22 Hz; (e) 396.30 Hz; (f) 466.81 Hz.

DownLoad: Full-Size Img PowerPoint

图 17 中心质量单元设计时, 68.83 Hz共振频率所对应共振模态图

Figure 17. Resonance modal diagram with the resonance frequency of 68.83 Hz when the mass unit is at the center.

DownLoad: Full-Size Img PowerPoint

图 18 实验验证　(a)样件图; (b)传输损失曲线

Figure 18. Experimental verification: (a) Sample structure; (b) transmission loss curves.

DownLoad: Full-Size Img PowerPoint

表 1 材料参数

Table 1. Material parameters.

Material ρ/kg·m^–3 E/10¹⁰ Pa Possion rate

Tungsten 19100 35.41 0.35
Silastic 1300 1.175 × 10^–5 0.469
Steel 7780 21.06 0.3

DownLoad: CSV

map

[1]	William B A, Lisa M M, Kelsey B, Stephen B, John L A 2019 Environ. Sci. Technol. 53 7126 Google Scholar
[2]	周榕 2017 硕士学位论文 (南京: 江苏大学) Zhou Y 2017 M. S. Thesis (Nanjing: Jiangsu University) (in Chinese)
[3]	Wu J H, Ma F Y, Zhang S W, Shen L 2006 J. Mech. Eng. 52 68
[4]	丁昌林, 董仪宝, 赵晓鹏 2018 67 194301 Ding C L, Dong Y B, Zhao X P 2018 Acta Phys. Sin. 67 194301
[5]	Lee S H, Park C M, Seo Y M, Wang Z G, Kim C K 2010 Phys. Rev. Lett. 104 054301 Google Scholar
[6]	沈惠杰, 郁殿龙, 汤智胤, 苏永生, 李雁飞, 刘江伟 2019 68 144301 Shen H J, Yu D L, Tang Z Y, Su Y S, Li Y F, Liu J W 2019 Acta Phys. Sin. 68 144301
[7]	Chen H J, Zhai S L, Ding C L, Liu S, Luo C R, Zhao X P 2015 J. Appl. Phys. 118 094901 Google Scholar
[8]	Mei J, Ma G C, Yang M, Yang Z Y, Wen W J, Sheng P 2012 Nat. Commun. 3 756 Google Scholar
[9]	Nemat-Nasser S, Willis J R, Srivastava A, Amirkhizi A V 2011 Phys. Rev. B 83 104103 Google Scholar
[10]	丁昌林, 赵晓鹏 2009 58 6351 Google Scholar Ding C L, Zhao X P 2009 Acta Phys. Sin. 58 6351 Google Scholar
[11]	Liu Z, Zhang X X, Chan C T, Sheng P 2000 Science 289 1734 Google Scholar
[12]	贺子厚, 赵静波, 姚宏, 蒋娟娜, 张帅, 陈鑫 2018 硅酸盐学报 47 983 He Z H, Zhao J B, Yao H, Jiang J N, Zhang S Chen X 2018 J. Chin. Ceramic Soc. 47 983
[13]	高南沙, 侯宏 2018 材料导报 32 322 Google Scholar Gao N S, Hou H 2018 Mater. Rev. 32 322 Google Scholar
[14]	王莎, 林书玉 2019 68 024303 Wang S, Lin S Y 2019 Acta Phys. Sin. 68 024303
[15]	刘娇, 侯志林, 傅秀军 2015 64 154302 Liu J, Hou Z L, Fu X J 2015 Acta Phys. Sin. 64 154302
[16]	Cheng Y, Xu J Y, Liu X J 2008 Appl. Phys. Lett. 92 051913 Google Scholar
[17]	贾晓珍 2018 硕士学位论文 (西安: 陕西师范大学) Jia X Z 2018 M. S. Thesis (Xi′an: Shaanxi Normal Univer-sity) (in Chinese)
[18]	Chen Y, Huang G, Zhou X, Hu G, Sun C 2014 J. Acoust. Soc. Am. 136 969 Google Scholar
[19]	Fang N, Xi D J, Xu J Y, Ambati M, Srituravanich W, Sun C, Zhang X 2006 Nature Mater. 5 452 Google Scholar
[20]	姜久龙, 姚宏, 杜军, 赵静波, 邓涛 2017 66 064301 Jiang J L, Yao H, Du J, Zhao J B, Deng T 2017 Acta Phys. Sin. 66 064301
[21]	Naify C J, Chang C M, Mcknight G, Nutt S 2011 J. Appl. Phys. 110 751
[22]	梅军, 马冠聪, 杨旻, 杨志宇, 温维佳, 沈平 2012 物理 41 425 Mei J, Ma G C, Yang M, Yang Z Y, Wen W J, Shen P 2012 Physics 41 425
[23]	Cheng Y, Zhou C, Yuan B G, Wu D J, Wei Q, Liu X J 2015 Nature Mater. 14 1013 Google Scholar
[24]	周榕, 吴卫国, 闻轶凡 2017 声学技术 36 297 Zhou Y, Wu W G, Wen Y F 2017 Tech. Acoust. 36 297
[25]	Abbad A 2016 SAE International 9th International Styrian Noise, Vibration & Harshness Congress Warrendale, United States, June 22, 2016 p2011
[26]	Long H, Cheng Y, Liu X 2018 Sci. Rep. 8 15678 Google Scholar
[27]	陈鑫, 姚宏, 赵静波, 张帅, 贺子厚, 蒋娟娜 2019 68 084302 Chen X, Yao H, Zhao J B, Zhang S, He Z H, Jiang J N 2019 Acta Phys. Sin. 68 084302
[28]	杜功焕, 朱哲民, 龚秀芬 2012 声学基础 (南京: 南京大学出版社) 第84页 Du G H, Zhu Z M, Gong X F 2012 Acoustic Basis (Nanjing: Nanjing University Press) p84
[29]	Fokin V, Ambati M, Sun C, Zhang X 2007 Phys. Rev. B 76 144302 Google Scholar
[30]	贺子厚, 赵静波, 姚宏, 张帅, 蒋娟娜, 陈鑫 2019 68 134302 Google Scholar He Z H, Zhao J B, Yao H, Zhang S, Jiang J N, Chen X 2019 Acta Phys. Sin. 68 134302 Google Scholar

[1]	Xu Qiang-Rong, Zhu Yang, Lin Kang, Shen Cheng, Lu Tian-Jian. Low-frequency sound insulation performance of novel membrane acoustic metamaterial with dynamic negative stiffness. Acta Physica Sinica, 2022, 71(21): 214301. doi: 10.7498/aps.71.20221058
[2]	Xu Qi, Sun Xiao-Wei, Song Ting, Wen Xiao-Dong, Liu Xi-Xuan, Wang Yi-Wen, Liu Zi-Jiang. Novel one-dimensional optomechanical crystal nanobeam with high optomechanical coupling rate under different defect states. Acta Physica Sinica, 2021, 70(22): 224210. doi: 10.7498/aps.70.20210925
[3]	Cao Ming-Peng, Wu Xiao-Peng, Guan Hong-Shan, Shan Guang-Bao, Zhou Bin, Yang Li-Hong, Yang Yin-Tang. Electrothermal coupling analysis of three-dimensional integrated microsystem based on dual cell method. Acta Physica Sinica, 2021, 70(7): 074401. doi: 10.7498/aps.70.20201628
[4]	Sun Wei-Bin, Wang Ting, Sun Xiao-Wei, Kang Tai-Feng, Tan Zi-Hao, Liu Zi-Jiang. Defect states and vibration energy recovery of novel two-dimensional piezoelectric phononic crystal plate. Acta Physica Sinica, 2019, 68(23): 234206. doi: 10.7498/aps.68.20190260
[5]	He Zi-Hou, Zhao Jing-Bo, Yao Hong, Jiang Juan-Na, Chen Xin. Sound insulation performance of thin-film acoustic metamaterials based on piezoelectric materials. Acta Physica Sinica, 2019, 68(13): 134302. doi: 10.7498/aps.68.20190245
[6]	Dong Wei, Wang Zhi-Bin. Improved hybrid plasmonic microcavity laser. Acta Physica Sinica, 2018, 67(19): 195204. doi: 10.7498/aps.67.20180242
[7]	Zhao Yun-Jin, Tian Meng, Huang Yong-Gang, Wang Xiao-Yun, Yang Hong, Mi Xian-Wu. Renormalization of photon dyadic Green function by finite element method and its applications in the study of spontaneous emission rate and energy level shift. Acta Physica Sinica, 2018, 67(19): 193102. doi: 10.7498/aps.67.20180898
[8]	Chen Yan, Zhou Gui-Yao, Xia Chang-Ming, Hou Zhi-Yun, Liu Hong-Zhan, Wang Chao. Analysis of a novel dual-mode large-mode-area micro-structured fiber. Acta Physica Sinica, 2014, 63(1): 014701. doi: 10.7498/aps.63.014701
[9]	Wang Yue, Liu Li-Wei, Hu Si-Yi, Li Qi-Yang, Sun Zhen-Hao, Miao Xin-Hui, Yang Xiao-Chuan, Zhang Xi-He. Simulation study based on the COMSOL Mutiphysics to the surface plasmon resonance of Cu2S quantum dots. Acta Physica Sinica, 2013, 62(19): 197803. doi: 10.7498/aps.62.197803
[10]	Yuan Ling, Sun Kai-Hua, Cui Yi-Ping, Shen Zhong-Hua, Ni Xiao-Wu. Experimental and theoretical analysis of the dispersion of laser-induced surface acoustic wave due to surface roughness. Acta Physica Sinica, 2012, 61(1): 014210. doi: 10.7498/aps.61.014210
[11]	Yu Ge, Han Qi-Gang, Li Ming-Zhe, Jia Xiao-Peng, Ma Hong-An, Li Yue-Fen. Finite element analysis of the high-pressure tungsten carbide radius-anvil. Acta Physica Sinica, 2012, 61(4): 040702. doi: 10.7498/aps.61.040702
[12]	Qi Yue-Feng, Qiao Han-Ping, Bi Wei-Hong, Liu Yan-Yan. Heat transfer characteristics in fabrication of heat method in photonic crystal fiber grating. Acta Physica Sinica, 2011, 60(3): 034214. doi: 10.7498/aps.60.034214
[13]	Liu Quan-Xi, Zhong Ming. Analysis on thermal effect of laser-diode array end-pumped composite rod laser by finite element method. Acta Physica Sinica, 2010, 59(12): 8535-8541. doi: 10.7498/aps.59.8535
[14]	Han Qi-Gang, Ma Hong-An, Xiao Hong-Yu, Li Rui, Zhang Cong, Li Zhan-Chang, Tian Yu, Jia Xiao-Peng. Finite element method study on the temperature distribution in the cell of large single crystal diamond. Acta Physica Sinica, 2010, 59(3): 1923-1927. doi: 10.7498/aps.59.1923
[15]	Han Qi-Gang, Jia Xiao-Peng, Ma Hong-An, Li Rui, Zhang Cong, Li Zhan-Chang, Tian Yu. Finite element simulations of thermal-stress on cemented tungsten carbide anvil used in cubic high pressure apparatus. Acta Physica Sinica, 2009, 58(7): 4812-4816. doi: 10.7498/aps.58.4812
[16]	Wang Chun-Can, Zhang Fan, Tong Zhi, Ning Ti-Gang, Jian Shui-Sheng. Study on the suppression of the stimulated Brillouin scattering in high-power single-frequency multicore fiber amplifier. Acta Physica Sinica, 2008, 57(8): 5035-5044. doi: 10.7498/aps.57.5035
[17]	Zhang Hong-Wu, Wang Jin-Bao, Ye Hong-Fei, Wang Lei. Generalized parametric constitutive law for van der Waals force simulation and its applications in computation of nanotubes. Acta Physica Sinica, 2007, 56(3): 1422-1428. doi: 10.7498/aps.56.1422
[18]	Zheng Kai, Chang De-Yuan, Fu Yong-Jun, Wei Huai, Yan Feng-Ping, Jian Wei, Jian Shui-Sheng. Erbium-doped hole-assisted lightguide fiber: structural study and optimization. Acta Physica Sinica, 2007, 56(2): 958-967. doi: 10.7498/aps.56.958
[19]	. Numerical simulation of laser-generated ultrasonic waves in steel with gradient changes of near-surface elastic property. Acta Physica Sinica, 2007, 56(12): 7058-7063. doi: 10.7498/aps.56.7058
[20]	Tian Jin-Shou, Zhao Bao-Sheng, Wu Jian-Jun, Zhao Wei, Liu Yun-Quan, Zhang Jie. Theoretical calculation of the modulation transfer function in a femoto-second electron diffraction system. Acta Physica Sinica, 2006, 55(7): 3368-3374. doi: 10.7498/aps.55.3368

Catalog

Vol. 68, Issue 21 - 2019-11-05

Metrics

Abstract views: 11380
PDF Downloads: 254
Cited By: 0

姓名
邮箱
手机号码
标题
留言内容
验证码

Search

Article

留言板