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Aiming at the isolation of low-frequency sound, a kind of thin-film acoustic metamaterialis designed and obtained by implanting PZT into thin film. The finite element method (FEM) of the structure is built, and 1st–14th order eigenfrequencies and transmission loss between 20–1200 Hz are calculated. The reliability of finite element calculation is verified experimentally and the existence of adjustable sound insulation peak is monitored in the experiment. The results show that the acoustic metamaterial has good sound insulation performance in a frequency range between 20 and 1200 Hz, and has two sound insulation peaks of more than 50 dB, and there is a sound insulation peak which can be changed by adjusting the parameters of the outer circuit. By analyzing the first resonance mode of simple structure and building its equivalent model, the effect of structural parameter on the sound insulation performance of thin film acoustic metamaterial is investigated theoretically, and the rationality of the equivalent model is verified by the finite element calculation. The sound insulation mechanism of the structure is further illustrated by taking into consideration the eigenfrequencies, transmission loss curve and vibration mode diagrams at various frequencies. It is found that at the resonance frequency, the flapping motion of the film will cause the sound wave in the subsequent propagation to cancell the interference, therefore realizing the attenuation of the sound wave. Based on Fano resonance theory, the reasons for the different characteristics of transmission loss curves at different resonance points are investigated. The PZT and outer circuit can form a LC oscillator. At the resonant frequency of the oscillator, the vibration of the piezoelectric material can absorb the energy of sound wave to cause a sound insolation peak. The resonant frequency of the circuit can be adjusted by changing the parameters of the outer circuit, thereby realizing the adjustability of the sound insulation performance. The influence of eccentricity of piezoelectric mass block on sound insulation performance of material is explored, proving that the sound insulation performance can be further optimized by improving structure. And through the finite element calculation, it is proved that the sound insulation performance of material is adjustable by changing the parameters of the outer circuit. The results provide a theoretical reference for designing the thin film acoustic metamaterials.
[1] 邓吉宏, 王柯, 陈国平 2008 航空学报 29 1581
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Wang S, Lin S Y 2019 Acta Phys. Sin. 68 024303
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Du C Y, Yu D L, Liu J W, Wen J H 2017 Acta Phys. Sin. 66 140701
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Xing T, Li X H, Gai X L, Zhang B, Xie P 2016 Tech. Acoust. 35 2
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Chen S B 2014 Ph. D. Dissertation (Changsha: National University of Defense Technology)(in Chinese)
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Wang C H, Zhao Z Y 1981 Acta Acust. 4 263
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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.
图 2 腔体结构
Figure 2. Cavity structure.
图 3 传输损失曲线
Figure 3. Transmission loss curve.
图 4 实验示意图 (a)样件结构; (b)实验装置; (c)样件实物图
Figure 4. Experimental schematic diagram: (a) Sample structure; (b) experimental facility; (c) physical samples.
图 5 大电感 (a)电路图; (b)实物图
Figure 5. Large inductance: (a) Circuit diagram; (b) physical diagram.
图 6 传输损失曲线
Figure 6. Transmission loss curve.
图 7 简化结构示意图
Figure 7. Simplified structure sketch.
图 8 贝塞尔函数曲线
Figure 8. Bessel function curve.
图 9 等效模型示意图
Figure 9. Schematic diagram of equivalent model.
图 10 首阶特征频率
Figure 10. First natural frequency.
图 11 消声原理图
Figure 11. Anechoic schematic diagram.
图 12 隔声峰处的振动模式图 (a) 185 Hz; (b) 485.6 Hz; (c) 896 Hz
Figure 12. Vibration mode diagram at sound insulation peak: (a) 185 Hz; (b) 485.6 Hz; (c) 969 Hz.
图 13 隔声谷处的振动模式图 (a) 115 Hz; (b) 457Hz
Figure 13. Vibration mode diagram at sound insulation peak: (a) 115 Hz; (b) 457Hz.
图 14 隔声谷与传输损失突变处的振动模式图 (a) 687 Hz; (b) 969 Hz; (c) 1129 Hz; (d) 1136 Hz
Figure 14. Vibration mode diagram at TL peak and TL sudden change: (a) 687 Hz; (b) 969 Hz; (c) 1129 Hz; (d) 1136 Hz
图 15 传输损失突变处的振动模式图 (a) 229 Hz; (b) 235 Hz
Figure 15. Vibration mode diagram at TL sudden change: (a) 229 Hz; (b) 235 Hz.
图 16 Fano共振
Figure 16. Fano resonance.
图 17 传输损失曲线m = 0.001, 0.004, 0.006 m
Figure 17. TL curve m = 0.001, 0.004, 0.006 m.
图 18 特征频率
Figure 18. Eigen frequencies.
图 19 第五阶共振模态 (a) m = 0.002 m; (b) m = 0.004 m; (c) m = 0.006 m
Figure 19. Fifth order vibration: (a) m = 0.002 m; (b) m = 0.004 m; (c) m = 0.006 m.
图 20 电路参数不同时隔声量的变化 (a)不同电阻; (b)不同电感
Figure 20. TL with different circuit parameters: (a) Different resistors; (b) different inductances.
表 1 压电材料参数
Table 1. Piezoelectric material parameters.
ρ/kg·m–3 $s_{11}^{\rm{E}}/{{\rm{m}}^3} \cdot {{\rm{N}}^{ - 1}}$ d31/C·m–2 $\varepsilon _{33}^{\rm{T}}/{\rm{F}} \cdot {{\rm{m}}^{ - 1}}$ 7500 1.65 × 10–11 –2.74 × 10–10 3.01 × 10–8 
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表 2 材料参数
Table 2. Material parameters.
Material ρ/kg·m–3 E/1010 Pa Possion rate Silastic 1300 1.175 × 10–5 0.469 Steel 7780 21.06 0.3
DownLoad: CSV
表 3 模态图
Table 3. Modal diagram.
阶数 频率/Hz 模态图 阶数 频率/Hz 模态图 1 111.77 
8 689.74 
2 135.84 
9 793.01 
3 147.67 
10 835.10 
4 185.63 
11 842.97 
5 201.65 
12 945.92 
6 231.21 
13 981.43 
7 458.62 
14 1148.40 
DownLoad: CSV
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[1] 邓吉宏, 王柯, 陈国平 2008 航空学报 29 1581
Google Scholar
Deng J H, Wang K, Chen G P 2008 Acta Aeronaut. Astronaut. Sin. 29 1581
Google Scholar
[2] Bolton J S, Shiau N M, Kang Y 1996 JSV 191 317
Google Scholar
[3] Liu Z, Zhang X X, Chan C T, Sheng P 2000 Science 289 1734
Google Scholar
[4] 张思文, 吴九汇 2013 物理学报 62 134302
Google Scholar
Zhang S W, Wu J H 2013 Acta Phys. Sin. 62 134302
Google Scholar
[5] 张帅, 郭书祥, 姚宏, 赵静波, 蒋娟娜, 贺子厚 2018 压电与声光 40 754
Google Scholar
Zhang S, Guo S X, Yao H, Zhao J B, Jiang J N, He Z H 2018 Piezoelectr. Acoustoopt. 40 754
Google Scholar
[6] 赵甜甜, 林书玉, 段祎林 2018 物理学报 67 224207
Google Scholar
Zhao T T, Lin S Y, Duan W L 2018 Acta Phys. Sin. 67 224207
Google Scholar
[7] 王莎, 林书玉 2019 物理学报 68 024303
Wang S, Lin S Y 2019 Acta Phys. Sin. 68 024303
[8] 张振方, 郁殿龙, 刘江伟, 温激鸿 2018 物理学报 67 074301
Google Scholar
Zhang Z F, Yu D L, Liu J W, Wen J H 2018 Acta Phys. Sin. 67 074301
Google Scholar
[9] 杜春阳, 郁殿龙, 刘江伟, 温激鸿 2017 物理学报 66 140701
Google Scholar
Du C Y, Yu D L, Liu J W, Wen J H 2017 Acta Phys. Sin. 66 140701
Google Scholar
[10] Mei J, Yang M, Yang Z Y, Chan N H, Shen P 2018 Phys. Rev. Lett. 101 204301
[11] Mei J, Ma G C, Yang M, Yang Z Y, Wen W J, Shen P 2012 Nat. Commun. 3 756
Google Scholar
[12] 梅军, 马冠聪, 杨旻 2012 物理 41 425
Google Scholar
Mei J, Ma G C, Yang M 2012 Physics 41 425
Google Scholar
[13] Chen Y, Huang G, Zhou X, Hu G, Sun C 2014 J. Acoust. Soc. Am. 136 969
Google Scholar
[14] Langfeldt F, Gleine W, von Estorff O 2015 JSV 349 315
Google Scholar
[15] 张佳龙, 姚宏, 杜军, 赵静波, 董亚科, 祁鹏山 2016 人工晶体学报 45 2549
Google Scholar
Zhang J L, Yao H, Du J, Zhao J B, Dong Y K, Qi P S 2016 J. Synth. Cryst. 45 2549
Google Scholar
[16] 叶超, 苏继龙 2017 噪声与振动控制 37 163
Google Scholar
Ye C, Su J L 2017 Noise Vibr. Control 37 163
Google Scholar
[17] 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
[18] 邢拓, 李贤徽, 盖晓玲, 张斌, 谢鹏 2016 声学技术 35 2
Xing T, Li X H, Gai X L, Zhang B, Xie P 2016 Tech. Acoust. 35 2
[19] Zhang Y, Wen J 2012 JASA 131 3372
[20] Preumont A 2011 Vibration Control of Active Structures (Berlin: Springer) pp21–59
[21] Chen S B, Wen J H, Yu D L, Wang G, Wen X 2011 Chin. Phys. B 20 014301
Google Scholar
[22] Zhang H, Wen J, Xiao Y, Wang G, Wen X 2015 JSV 343 104
Google Scholar
[23] 董亚科, 姚宏, 杜军, 赵静波, 姜久龙 2018 压电与声光 40 860
Google Scholar
Dong Y K, Yao H, Du J, Zhao J B, Jiang J L 2018 Piezoelectr. Acoustoopt. 40 860
Google Scholar
[24] 廖涛, 孙小伟, 宋婷, 田俊红, 康太凤, 孙伟彬 2018 物理学报 67 214208
Google Scholar
Liao T, Sun X W, Song T, Tian J H, Kang T F, Sun W B 2018 Acta Phys. Sin. 67 214208
Google Scholar
[25] 孙炜海, 张超群, 鞠桂玲, 潘晶雯 2018 物理学报 67 194303
Google Scholar
Sun W H, Zhang C Q, Jü G L, Pan J W 2018 Acta Phys. Sin. 67 194303
Google Scholar
[26] Yubao S, Leping F, Jihong W, Dianlong Y, Xisen W 2015 Phys. Lett. A 379 1449
Google Scholar
[27] 陈圣兵 2014 博士学位论文(长沙: 国防科技大学)
Chen S B 2014 Ph. D. Dissertation (Changsha: National University of Defense Technology)(in Chinese)
[28] 汪承灏, 赵哲英 1981 声学学报 4 263
Wang C H, Zhao Z Y 1981 Acta Acust. 4 263
[29] 贺子厚, 赵静波, 姚宏, 蒋娟娜, 张帅 2019 压电与声光 41 40
Google Scholar
He Z H, Zhao J B, Yao H, Jiang J N, Zhang S 2019 Piezoelectr. Acoustoopt. 41 40
Google Scholar
[30] Fano U 1961 Phys. Rev. 124 1866
Google Scholar
[31] 潘庭婷, 曹文, 邓彩松, 王鸣, 夏巍, 郝辉 2018 物理学报 67 157301
Google Scholar
Pan T T, Cao W, Deng C S, Wang M, Xia W, Hao H 2018 Acta Phys. Sin. 67 157301
Google Scholar
[32] Mikhail F, Mikhail V, Alexander N, Yuri S 2017 Nat. Photon. 11 543
Google Scholar
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