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Noise reduction is an interesting and important subject in the piping systems of many applications, in order to suppress noise in the pipe, many significative researches have been done. In recent years, the acoustic wave propagation in the phononic crystal pipe has received increasing attention. The characteristic band gaps in phononic crystal pipe can forbid wave to propagate within the band-gap frequency range, which provides a new way to control the noise in piping system. In this paper, the acoustic properties of phononic crystal pipe consisting of expansion chambers with the extended inlet/outlet are investigated theoretically and numerically. By combining the two-dimensional mode matching method and the transfer matrix method, the band structure and transmission loss, especially the band-gap properties of the phononic crystal structure are presented. The obtained results exhibit excellent agreement with the results from the finite element method. Then, this theoretical method is compared with the one-dimensional plane wave method, and it is found that the results from the proposed method are more accurate within the studied frequency range. Further, the effect of modal order in the band-gap frequency range is analyzed, which shows that the mode matching method has a good convergence.The wave scattering and resonance of the chamber will induce the Bragg and locally-resonant band gaps in the periodic pipe, respectively. Further analysis on the transmission coefficient in a band gap is conducted. It shows that the transmission coefficient decays exponentially with the periodic number increasing, which demonstrates that the suppression of the wave propagation in phononic crystal pipe is caused by the band-gap rather than the impedance mismatch. Then the effects of variable parameters including the lattice constant and the length of the insertion on the location and width of the band gaps are investigated. The results show that the lattice constant mainly controls the Bragg band gaps and the length of the insertion exerts a significant influence on the locally-resonant band gaps. Finally, the coupling behaviors of band gaps are studied to expand their widths. It is found that the Bragg band gaps can be coupled with the locally-resonant band gaps via changing the lattice constant and the length of the insertion, which can give rise to wider band gaps. Furthermore, the coupling between two locally-resonant band gaps is proposed by changing the length of the insertion, which also produces wider band gaps.This study can provide new ideas for designing the phononic crystal pipe to suppress the noise in piping system.
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Keywords:
- expansion chambers with extended inlet and outlet /
- two-dimensional mode matching method /
- band structure /
- coupled band gaps
[1] Liang X D 2010 NVC 30 127 (in Chinese) [梁向东 2010 噪声与振动控制 30 127]
[2] Shen H J, Li Y F, Su Y S, Zhang L K, Song Y B 2017 J. Vib. Shock 36 163 (in Chinese) [沈惠杰, 李雁飞, 苏永生, 章林柯, 宋玉宝 2017 振动与冲击 36 163]
[3] Coulon J M, Atalla N, Desrocher A 2016 Appl. Acoust 113 109
[4] Xiang L Y, Zuo S G, Wu X D, Zhang J, Liu J F 2016 J. Vib. Shock 35 29 (in Chinese) [方智, 季振林, 刘成洋 2016 振动与冲击 35 29]
[5] Fang Z, Ji Z L, Liu C Y 2016 J. Vib. Shock 35 29 (in Chinese) [方智, 季振林, 刘成洋 2016 振动与冲击 35 29]
[6] Guo R, Wang L T, Tang W B, Han S 2017 Appl. Acoust 127 105
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[10] Xiao Y, Wen J H, Wen X S 2012 J. Sound Vib. 331 5408
[11] Yu D L, Wen J H, Zhao H G 2011 J. Sound Vib. 133 014502
[12] Liu Y Z, Meng H, Li L, Wen J H 2008 J. Vib. Shock 27 47 (in Chinese) [刘耀宗, 孟浩, 李黎, 温激鸿 2008 振动与冲击 27 47]
[13] Cao Y J, Hou Z L, Liu Y Y 2004 Phys. Lett. A 327 247
[14] Wang G, Wen J H, Han X Y, Zhao H G 2003 Acta Phys. Sin. 52 1943 (in Chinese) [王刚, 温激鸿, 韩小云, 赵宏刚 2003 52 1943]
[15] Liu J W, Yu D L, Wen J H, Shen H J, Zhang Y F 2016 J. Vib. Shock 35 141 (in Chinese) [刘江伟, 郁殿龙, 温激鸿, 沈惠杰, 张亚峰 2016 振动与冲击 35 141]
[16] Wen J H, Wang G, Liu Y Z, Yu D L 2004 Acta Phys. Sin. 53 3384 (in Chinese) [温激鸿, 王刚, 刘耀宗, 郁殿龙 2004 53 3384]
[17] Hou Z L, Fu X J, Liu Y Y 2004 Phys. Rev. B 70 2199
[18] Xiao Y 2012 Ph. D. Dissertation (Changsha: National University of Defense Technology) (in Chinese) [肖勇 2012博士学位论文 (长沙: 国防科学技术大学)]
[19] Wu J, Bai X C, Xiao Y, Geng M X, Yu D L, Wen J H 2016 Acta Phys. Sin. 65 064602 (in Chinese) [吴健, 白晓春, 肖勇, 耿明昕, 郁殿龙, 温激鸿 2016 65 064602]
[20] Fang X, Wen J H, Bonello B, Yin J F, Yu D L 2017 Nat. Commun. 8 1288
[21] Wang X N, Choy Y S, Cheng L, N X 2012 J. Acoust. Soc. Am. 132 3778
[22] Wang X N, Zhu W Y, Zhou Y D 2016 J. Acoust. Soc Am. 139 202
[23] Wu D Z, Zhang N, Mak C M, Cai C Z 2017 Sensors 17 1029
[24] Cai C Z, Mak C M 2016 J. Acoust. Soc Am. 140 471
[25] Yu D L, Du C Y, Shen H J, Liu J W, Wen J H 2017 Chin. Phys. Lett. 34 190
[26] Shen H J 2015 Ph. D. Dissertation (Changsha: National University of Defense Technology) (in Chinese) [沈惠杰 2015博士学位论文 (长沙: 国防科学技术大学)]
[27] Shi X F, Mak C M 2017 Appl. Acoust 1 15
[28] Cao X F, Yu D L, Liu J W, Wen J H 2016 J. Vib. Shock 35 20 (in Chinese) [曹晓丰, 郁殿龙, 刘江伟, 温激鸿 2016 振动与冲击 35 20]
[29] Li Y F, Shen H J, Zhang L K, Su Y S, Yu D L 2016 Phys. Lett. A 380 2322
[30] Selamet A, Ji Z L 1999 J. Sound Vib. 223 197
[31] Selamet A, Xu M, Lee I, Huff N 2005 J. Acoust. Soc Am. 117 2078
[32] Selamet A, Lee I J 2003 J. Acoust. Soc Am. 113 1975
[33] Cao X F 2016 M. S. Dissertation (Changsha: National University of Defense Technology) (in Chinese) [曹晓丰 2016硕士学位论文 (长沙: 国防科学技术大学)]
[34] Fang Z 2014 Ph. D. Dissertation (Harbin: Harbin Engineering University) (in Chinese) [方智 2014 博士学位论文 (哈尔滨: 哈尔滨工程大学)]
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[1] Liang X D 2010 NVC 30 127 (in Chinese) [梁向东 2010 噪声与振动控制 30 127]
[2] Shen H J, Li Y F, Su Y S, Zhang L K, Song Y B 2017 J. Vib. Shock 36 163 (in Chinese) [沈惠杰, 李雁飞, 苏永生, 章林柯, 宋玉宝 2017 振动与冲击 36 163]
[3] Coulon J M, Atalla N, Desrocher A 2016 Appl. Acoust 113 109
[4] Xiang L Y, Zuo S G, Wu X D, Zhang J, Liu J F 2016 J. Vib. Shock 35 29 (in Chinese) [方智, 季振林, 刘成洋 2016 振动与冲击 35 29]
[5] Fang Z, Ji Z L, Liu C Y 2016 J. Vib. Shock 35 29 (in Chinese) [方智, 季振林, 刘成洋 2016 振动与冲击 35 29]
[6] Guo R, Wang L T, Tang W B, Han S 2017 Appl. Acoust 127 105
[7] Wen X S, Wen J H, Yu D L, Wang G, Liu Y Z, Han X Y 2009 Phononic Crystals (Beijing: National Defence Industry Press) pp1-6 (in Chinese) [温熙森, 温激鸿, 郁殿龙, 王刚, 刘耀宗, 韩小云 2009 声子晶体 (北京: 国防工业出版社) 第1–6页]
[8] Wang G, Yu D L, Wen J H, Liu Y Z, Wen X S 2004 Phys. Lett. A 327 512
[9] Zhang Y F 2014 M. S. Dissertation (Changsha: National University of Defense Technology) (in Chinese) [张亚峰 2014 硕士学位论文 (长沙: 国防科学技术大学)]
[10] Xiao Y, Wen J H, Wen X S 2012 J. Sound Vib. 331 5408
[11] Yu D L, Wen J H, Zhao H G 2011 J. Sound Vib. 133 014502
[12] Liu Y Z, Meng H, Li L, Wen J H 2008 J. Vib. Shock 27 47 (in Chinese) [刘耀宗, 孟浩, 李黎, 温激鸿 2008 振动与冲击 27 47]
[13] Cao Y J, Hou Z L, Liu Y Y 2004 Phys. Lett. A 327 247
[14] Wang G, Wen J H, Han X Y, Zhao H G 2003 Acta Phys. Sin. 52 1943 (in Chinese) [王刚, 温激鸿, 韩小云, 赵宏刚 2003 52 1943]
[15] Liu J W, Yu D L, Wen J H, Shen H J, Zhang Y F 2016 J. Vib. Shock 35 141 (in Chinese) [刘江伟, 郁殿龙, 温激鸿, 沈惠杰, 张亚峰 2016 振动与冲击 35 141]
[16] Wen J H, Wang G, Liu Y Z, Yu D L 2004 Acta Phys. Sin. 53 3384 (in Chinese) [温激鸿, 王刚, 刘耀宗, 郁殿龙 2004 53 3384]
[17] Hou Z L, Fu X J, Liu Y Y 2004 Phys. Rev. B 70 2199
[18] Xiao Y 2012 Ph. D. Dissertation (Changsha: National University of Defense Technology) (in Chinese) [肖勇 2012博士学位论文 (长沙: 国防科学技术大学)]
[19] Wu J, Bai X C, Xiao Y, Geng M X, Yu D L, Wen J H 2016 Acta Phys. Sin. 65 064602 (in Chinese) [吴健, 白晓春, 肖勇, 耿明昕, 郁殿龙, 温激鸿 2016 65 064602]
[20] Fang X, Wen J H, Bonello B, Yin J F, Yu D L 2017 Nat. Commun. 8 1288
[21] Wang X N, Choy Y S, Cheng L, N X 2012 J. Acoust. Soc. Am. 132 3778
[22] Wang X N, Zhu W Y, Zhou Y D 2016 J. Acoust. Soc Am. 139 202
[23] Wu D Z, Zhang N, Mak C M, Cai C Z 2017 Sensors 17 1029
[24] Cai C Z, Mak C M 2016 J. Acoust. Soc Am. 140 471
[25] Yu D L, Du C Y, Shen H J, Liu J W, Wen J H 2017 Chin. Phys. Lett. 34 190
[26] Shen H J 2015 Ph. D. Dissertation (Changsha: National University of Defense Technology) (in Chinese) [沈惠杰 2015博士学位论文 (长沙: 国防科学技术大学)]
[27] Shi X F, Mak C M 2017 Appl. Acoust 1 15
[28] Cao X F, Yu D L, Liu J W, Wen J H 2016 J. Vib. Shock 35 20 (in Chinese) [曹晓丰, 郁殿龙, 刘江伟, 温激鸿 2016 振动与冲击 35 20]
[29] Li Y F, Shen H J, Zhang L K, Su Y S, Yu D L 2016 Phys. Lett. A 380 2322
[30] Selamet A, Ji Z L 1999 J. Sound Vib. 223 197
[31] Selamet A, Xu M, Lee I, Huff N 2005 J. Acoust. Soc Am. 117 2078
[32] Selamet A, Lee I J 2003 J. Acoust. Soc Am. 113 1975
[33] Cao X F 2016 M. S. Dissertation (Changsha: National University of Defense Technology) (in Chinese) [曹晓丰 2016硕士学位论文 (长沙: 国防科学技术大学)]
[34] Fang Z 2014 Ph. D. Dissertation (Harbin: Harbin Engineering University) (in Chinese) [方智 2014 博士学位论文 (哈尔滨: 哈尔滨工程大学)]
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