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The suppression and absorption of low-frequency noise for a fluid-filled pipe system has become a challenging task. Inspired by the properties of acoustic metamaterials, we construct a fluid-filled periodic pipe system, consisting of small-size short acoustic pipes mounted on a fluid-filled main pipe system equidistantly along the axial direction of main pipe. The short acoustic pipe is filled with fluid and gas, and the fluid section is connected to the main pipe that is filled with the same liquid. In such a periodic pipe system, an ultra-low frequency and ultra-broad band gap of acoustic waves can be generated, making the acoustic waves transmitting in the pipe system effectively attenuated within the band gap frequency range. Since the attenuation effects of the band gap on the low-frequency sound are so strong (the acoustic waves almost cannot be transmitted through the pipe system) that the periodic pipe system is referred to as a dark acoustic metamaterial (DAM)-type fluid-filled pipe system. The formation mechanism of the first band gap can be ascribed to the co-resonance of the short acoustic pipe array in the piping system, and this band gap is categorized as resonant-type BG (RBG). The contribution of short acoustic pipes is to introduce a low-frequency and large impedances spatially into the system, whereupon the transmitting waves will experience a tempestuously resonance in the pipe. As a result, the transmission of acoustic waves within the RBG is stopped. The second band gap in a higher frequency range is classified as Bragg-type band gap (BBG), since it is induced by the effects of interference between the incident, the reflected and the transmitted acoustic waves existing in the periodic units. The interference effect on the suppression of wave transmission is strengthened by the ceaselessly repeating uniform cells. The lattice constant change can bring in a modulation effects on both the BBG and the upper band edge of RBG. Increasing the volume of gas chamber in the short acoustic pipe will result in a shift of lower band edge of RBG towards the low-frequency range but has no action on the upper band edge; similarly, the augment of the liquid volume of the short acoustic pipe also lowers the band edges of RBG, however, bandwidth of the RBG will be reduced. A membrane may be used to physically separate the gas from the fluid in the short acoustic pipe, rendering the design more feasible to be realized in practical engineering. The installation of membrane will not change the low-frequency band gap properties of the DAM pipe. The obtained results show that the proposed design in this study may provide a new way to solve the defiant problem of noise control in the low frequency range for fluid piping systems.
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Keywords:
- dark acoustic metamaterials /
- fluid-filled pipe /
- noise control /
- acoustic band gap
[1] 吴九汇, 马富银, 张思文, 沈礼 2016 机械工程学报 52 68
Wu J H, Ma F Y, Zhang S W, Shen L 2016 Chin. J. Mech. Eng. 52 68
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Google Scholar
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Cheng C, Wu F G, Zhang X, Yao Y W 2014 Acta Phys. Sin. 63 024301
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Gao H F, Zhang X, Wu F G, Yao Y W 2016 Acta Phys. Sin. 65 044301
Google Scholar
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Google Scholar
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Liu S G 2001 M. S. Thesis (Haerbin: Harbin Engineering University) (in Chinese)
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图 1 暗声学超材料管结构示意图
Figure 1. Sketch map of the 1D dark metamaterial pipe.
图 2 暗声学超材料管的声波能带结构图和声传递损失
Figure 2. Acoustic bang structure and sound transmission loss of the dark acoustic metamaterial-type pipe.
图 3 暗声学超材料管的声波透射系数与吸声系数
Figure 3. The transmission and absorption coefficients of acoustic waves in the dark acoustic metamaterial-type pipe.
图 4 带隙内若干频率处的管内声压分布图和等值面 (a) 34.5 Hz; (b) 95.5 Hz;(c) 305.5 Hz
Figure 4. Acoustic pressure distributions and isosurfaces inside the dark metamaterial pipe, for several frequencies which located within the band gaps: (a) 34.5 Hz; (b) 95.5 Hz; (c) 305.5 Hz.
图 5 充液声学短管周期管道的声传递损失
Figure 5. The sound transmission loss for a fluid-filled pipe system with short acoustic pipes attached periodically.
图 6 气液混合腔声学短管的归一化阻抗
Figure 6. The normalized acoustic impedance for the short pipe equipped with a gas-fluid hybrid chamber.
图 7 单个周期元胞在若干频率点处的声学模态
Figure 7. Acoustic modes of the periodic pipe cell at several frequency points.
图 8 不同晶格常数下暗声学超材料管的声传递损失
Figure 8. The sound transmission losses of the dark metamaterial pipe, for different lattice constants.
图 9 共振带隙上带边和Bragg带隙下带边随晶格常数的变化
Figure 9. The curves for the upper edge of resonance gap and the lower edge of Bragg gap, as functions of the increased lattice constant.
图 10 不同充气腔长度下暗声学超材料管的声传递损失
Figure 10. The sound transmission losses of the dark metamaterial pipe, for different lengths of gas-filled section of the attached short pipe.
图 11 不同充液腔长度下暗声学超材料管的声传递损失
Figure 11. The sound transmission losses of the dark metamaterial pipe, for different lengths of the fluid-filled section of the attached short pipe.
图 12 声学短管液腔和气腔加橡胶隔膜条件下暗声学超材料管的声传递损失
Figure 12. The sound transmission losses of the dark metamaterial pipe under the condition when a rubber membrane is installed to separate the liquid and gap inside the attached short pipe.
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[1] 吴九汇, 马富银, 张思文, 沈礼 2016 机械工程学报 52 68
Wu J H, Ma F Y, Zhang S W, Shen L 2016 Chin. J. Mech. Eng. 52 68
[2] 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
[3] 曹晓丰, 郁殿龙, 刘江伟, 温激鸿 2016 振动与冲击 35 20
Cao X F, Yu D L, Liu J W, Wen J H 2016 J. Vib. Shock 35 20
[4] Liu B, Liu J, Wei W, Shen H, Wei Z 2018 AIP Adv. 8 115322
Google Scholar
[5] Chiang Y K, Choy Y S, Tang S K 2017 J. Acoust. Soc. Am. 141 1999
Google Scholar
[6] Jiang C Y, Huang L X 2018 J. Sound Vib. 418 79
Google Scholar
[7] Kopiev V F, Mironov M A, Yakovets M A 2015 Acoust. Phys. 61 49
[8] Cambonie T, Mbailassem F, Gourdon E 2018 Appl. Acoust. 131 87
Google Scholar
[9] Zhang T, Zhang Y O, Ouyang H 2015 Int. J. Press. Ves. Pip. 125 66
Google Scholar
[10] Bravo T, Maury C, Pinhède C 2017 J. Sound Vib. 395 201
Google Scholar
[11] Koh J, Lyu S, Lee T 2015 Proceedings of the 22ND International Congress on Sound and Vibration Florence, Italy, July 12–16, 2015 p12
[12] Zhu Y W, Zhu F W, Zhang Y S, Wei Q G 2017 Appl. Acoust. 116 9
Google Scholar
[13] Xiang L, Zuo S, Wu X, Liu J 2017 Appl. Acoust. 122 35
Google Scholar
[14] Williams P, Kirby R, Hill J, Åbom M, Malecki C 2018 Appl. Acoust. 131 61
Google Scholar
[15] Zhao X, Cai L, Yu D, Lu Z, Wen J 2017 AIP Adv. 7 065211
Google Scholar
[16] Li D, Kang Y, Ding X, Wang X, Liu W 2017 J. Mech. Sci. Technol. 31 1203
Google Scholar
[17] Chaitanya P, Munjal M L 2011 Appl. Acoust. 72 65
Google Scholar
[18] Mimani A, Munjal M L 2012 Wave Motion 49 271
Google Scholar
[19] Liu J, Yu D, Wen J, Zhang Z 2018 J. Theor. Comp. Acoust. 26 1850026
[20] Yu D L, Shen H J, Liu J W, Yin J F, Zhang Z F, Wen J H 2018 Chin. Phys. B 27 064301
Google Scholar
[21] 程聪, 吴福根, 张欣, 姚源卫 2014 物理学报 63 024301
Google Scholar
Cheng C, Wu F G, Zhang X, Yao Y W 2014 Acta Phys. Sin. 63 024301
Google Scholar
[22] 高汉峰, 张欣, 吴福根, 姚源卫 2016 物理学报 65 044301
Google Scholar
Gao H F, Zhang X, Wu F G, Yao Y W 2016 Acta Phys. Sin. 65 044301
Google Scholar
[23] 梁彬, 袁樱, 程建春 2015 物理学报 64 094305
Google Scholar
Liang B, Yuan Y, Cheng J C 2015 Acta Phys. Sin. 64 094305
Google Scholar
[24] Lu M H, Yan L F, Chen F 2009 Mater. Today 12 34
[25] Tang Y, Xin F, Huang L, Lu T 2017 EPL 118 44002
Google Scholar
[26] Liu Z, Zhang X, Mao Y, Zhu Y Y, Yang Z, Chan C T, Sheng P 2000 Science 289 1734
Google Scholar
[27] Mei J, Ma G, Yang M, Yang Z, Wen W, Sheng P 2012 Nat. Comm. 3 756
Google Scholar
[28] 刘侍刚 2001 硕士学位论文(哈尔滨: 哈尔滨工程大学)
Liu S G 2001 M. S. Thesis (Haerbin: Harbin Engineering University) (in Chinese)
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