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Helmholtz resonator(HR) has already been demonstrated both theoretically and experimentally to be a metamaterial with negative mass density and negative bulk modulus simultaneously. The HR can resonate at a frequency corresponding to a wavelength much longer than its geometrical parameters. At this time, the incident acoustic energy can be located. Therefore, the HR structures are considered to be good choices for controlling low-frequency sound waves. Furthermore, existing results indicate that the wide forbidden band could be formed by a one-dimensional structure shunted with detuned HRs. Based on these aforementioned theories, a man-made acoustical structure with broadband low-frequency sound insulation effect is designed by circularly inbuilt HRs. Beyond this structure's surface, a two-dimensional quiet zone can be created. With the same simulated model, an experimental structure is fabricated based on PVC plastic material. The structure consists of five layerd circular plates. In the top four plates, two kinds of holes are drilled. The smaller holes in the top plate act as shot necks of the HR, while the bigger holes in the middle three plates serve as the cavities of the HR. They can construct 60 resonators with different resonant frequencies. Experiments are carried out to study its sound insulation properties. In the experiments, three kinds of HRs with resonant frequencies 785, 840 and 890 Hz from inner loop to outer loop, respectively, are formed. The experimental results are very coincident with the simulation results from the software of COMSOL Multiphysics based on finite element method, which shows that this structure has an excellent sound insulation effect in a frequency band of 680-1050 Hz, and the maximum insulation sound pressure level can reach 41 dB. Meanwhile, the distribution of the two-dimensional sound field is measured. The results point out that the range of the insulation area can be changed with the incident frequency. In addition, the sound insulation effect is sensitive to the resonant state of the HRs. When all of the resonators at the same loop resonate simultaneously, the insulation sound pressure level will be higher. On the contrary, the insulation sound pressure level will be lower because of the energy leaking through the positions where the HRs do not resonate with the others. This work will be of help for designing new sound protection devices for low-frequency sound waves.
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Keywords:
- Helmholtz resonator /
- low-frequency insulation /
- two-dimensional acoustic field distribution /
- sound protection
[1] Kushwaha M S, Halevi P, Dobrzynski L, Djafari-Rouhani B 1993 Phys. Rev. Lett. 71 2022
[2] Liu Z Y, Zhang X X, Mao Y W, Zhu Y Y, Yang Z Y, Chan C T, Sheng P 2000 Science 289 1734
[3] Zhu R, Liu X N, Hu G K, Sun C T, Huang G L 2014 Nat. Commun. 5 5510
[4] Zhang S, Xia C G, Fang N 2011 Phys. Rev. Lett. 106 024301
[5] Zhu X F, Liang B, Kan W W, Zou X Y, Cheng J C 2011 Phys. Rev. Lett. 106 014301
[6] Kan W W, Garcia-Chocano V M, Cervera F, Liang B, Zou X Y, Yin L L, Cheng J C, Sanchez-Dehesa J 2015 Phys. Rev. Appl. 3 064019
[7] Wu L Y, Chen L W, Liu C M 2009 Appl. Phys. Lett. 95 013506
[8] Norris A N, Wickham G 1993 J. Acoust. Soc. Am. 93 617
[9] Sugimoto N, Horioka T 1995 J. Acoust. Soc. Am. 97 1446
[10] Hu X H, Chan C T 2005 Phys. Rev. E 71 055601
[11] Fang N, Xi D J, Xu J Y, Ambati M, Srituravanich W, Sun C, Zhang X 2006 Nat. Mater. 5 452
[12] Cheng Y, Xu J Y, Liu X 2008 J. Phys. Rev. B 77 045134
[13] Ding C L, Zhao X P 2009 Acta Phys. Sin. 58 6351 （in Chinese)[丁昌林, 赵晓鹏2009 58 6351]
[14] Gao D B, Zeng X W, Zhou Z M, Tian Z F 2013 Acta Phys. Sin. 62 094304 （in Chinese)[高东宝, 曾新吾, 周泽民, 田章福2013 62 094304]
[15] Gao D B, Zeng X W, Zhou Z M, Tian Z F 2014 Proceedings of the 21th Inter. Congress on Sound and Vib. Beijing, China, July 13-17, 2014 p2679
[16] Cheng Y, Xu J Y, Liu X J 2008 Appl. Phys. Lett. 92 051913
[17] Cheng Y, Liu X J 2012 Appl. Phys. A 109 805
[18] Liu J, Hou Z L, Fu X J 2015 Acta Phys. Sin. 64 154302 （in Chinese)[刘娇, 侯志林, 傅秀军2015 64 154302]
[19] Fey J, Robertson M 2011 J. Appl. Phys. 109 114903
[20] Du G H, Zhu Z M, Gong X F 2001 Fundamentals of Acoustics（Nanjing:Nanjing University Press) pp279-283(in Chinese)[杜功焕, 朱哲民, 龚秀芬2001声学基础(南京:南京大学出版社)第279–283页]
[21] Zhu X F, Liang B, Kan W W, Peng Y G, Cheng J C 2016 Phys. Rev. Appl. 5 054015
[22] Zhu X F, Li K, Zhang P, Zhu J, Zhang J T, Tian C, Liu S C 2016 Nat. Commun. 7 11731
[23] Zhu X F, Ramezani H, Shi C Z, Zhu J, Zhang X 2014 Phys. Rev. X 4 031042
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[1] Kushwaha M S, Halevi P, Dobrzynski L, Djafari-Rouhani B 1993 Phys. Rev. Lett. 71 2022
[2] Liu Z Y, Zhang X X, Mao Y W, Zhu Y Y, Yang Z Y, Chan C T, Sheng P 2000 Science 289 1734
[3] Zhu R, Liu X N, Hu G K, Sun C T, Huang G L 2014 Nat. Commun. 5 5510
[4] Zhang S, Xia C G, Fang N 2011 Phys. Rev. Lett. 106 024301
[5] Zhu X F, Liang B, Kan W W, Zou X Y, Cheng J C 2011 Phys. Rev. Lett. 106 014301
[6] Kan W W, Garcia-Chocano V M, Cervera F, Liang B, Zou X Y, Yin L L, Cheng J C, Sanchez-Dehesa J 2015 Phys. Rev. Appl. 3 064019
[7] Wu L Y, Chen L W, Liu C M 2009 Appl. Phys. Lett. 95 013506
[8] Norris A N, Wickham G 1993 J. Acoust. Soc. Am. 93 617
[9] Sugimoto N, Horioka T 1995 J. Acoust. Soc. Am. 97 1446
[10] Hu X H, Chan C T 2005 Phys. Rev. E 71 055601
[11] Fang N, Xi D J, Xu J Y, Ambati M, Srituravanich W, Sun C, Zhang X 2006 Nat. Mater. 5 452
[12] Cheng Y, Xu J Y, Liu X 2008 J. Phys. Rev. B 77 045134
[13] Ding C L, Zhao X P 2009 Acta Phys. Sin. 58 6351 （in Chinese)[丁昌林, 赵晓鹏2009 58 6351]
[14] Gao D B, Zeng X W, Zhou Z M, Tian Z F 2013 Acta Phys. Sin. 62 094304 （in Chinese)[高东宝, 曾新吾, 周泽民, 田章福2013 62 094304]
[15] Gao D B, Zeng X W, Zhou Z M, Tian Z F 2014 Proceedings of the 21th Inter. Congress on Sound and Vib. Beijing, China, July 13-17, 2014 p2679
[16] Cheng Y, Xu J Y, Liu X J 2008 Appl. Phys. Lett. 92 051913
[17] Cheng Y, Liu X J 2012 Appl. Phys. A 109 805
[18] Liu J, Hou Z L, Fu X J 2015 Acta Phys. Sin. 64 154302 （in Chinese)[刘娇, 侯志林, 傅秀军2015 64 154302]
[19] Fey J, Robertson M 2011 J. Appl. Phys. 109 114903
[20] Du G H, Zhu Z M, Gong X F 2001 Fundamentals of Acoustics（Nanjing:Nanjing University Press) pp279-283(in Chinese)[杜功焕, 朱哲民, 龚秀芬2001声学基础(南京:南京大学出版社)第279–283页]
[21] Zhu X F, Liang B, Kan W W, Peng Y G, Cheng J C 2016 Phys. Rev. Appl. 5 054015
[22] Zhu X F, Li K, Zhang P, Zhu J, Zhang J T, Tian C, Liu S C 2016 Nat. Commun. 7 11731
[23] Zhu X F, Ramezani H, Shi C Z, Zhu J, Zhang X 2014 Phys. Rev. X 4 031042
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