二维含多孔介质周期复合结构声传播分析
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摘要
为取得理想的隔声性能,本文结合多孔介质和周期结构两类声振调控方案,讨论了一种新型含多孔介质周期复合结构;采用等效模型描述振子系统,利用薄板理论和Biot理论建立了相应的声振耦合理论模型.利用此模型计算得出的结果与文献中数据吻合良好.研究结果表明,采用简单振子系统或组合振子系统都可以在其特征频率决定的频域提升复合结构的声传递损失(STL);然而,在越过相应频域后,STL会急剧下降,选取合适的振子参数,可以拓展隔声带宽而又保持其STL水平.对比振子系统结果发现,相对简单振子系统,组合振子系统能在获得更宽STL提升频域同时减弱特征频率域后的STL下降趋势.这些结果可以为宽频减振降噪提供思路,为中低频域隔声应用设计提供理论参考.
To obtain excellent sound reduction performance, in this paper we introduce a novel periodic poroelastic composite structure, which combines poroelastic material and periodic structure and aims at using the remarkable acoustic performance of these two. This periodic composite structure comprises three parts, i.e. the poroelastic domain, the elastic domain(thin plate), and the periodic resonators, which can be simple singledegree-of-freedom resonators(SRs) or composite two-degree-of-freedom resonators(CRs). A theoretical model is established by using Biot theory for the poroelastic domain, and by using the effective medium method for the resonator-plate coupling system, which is considered as an isotropic plate with an equivalent dynamic density.This method is validated with degenerated model in the literature; the results obtained by this method are in excellent consistence with the results in the literature. Parameter analyses are performed to test the influences of poroelastic addition and periodic resonator on the sound transmission loss(STL) of this periodic composite structure under two kinds of boundary conditions. The poroelastic addition is found to increase the STL while the influences of resonators are complicated. The STL increases notably in the frequency range bounded by the characteristic frequencies of these resonators, however, a decrease just follows when it exceeds these frequencies,which can be observed in both SR case and CR case under the two boundary conditions. In the meantime, when multiple SR is placed in a periodic lattice, it is found that different resonators with ascending mass and characteristic frequencies have superior STL to those with ascending characteristic frequencies but have equal mass. The case with CR, which is more complicated as expected, shows less STL decrease than the case with SR, but wider frequency range where the STL increases than a poroelastic composite structure without resonators. This results from the fact that the frequency band of vibration suppression in the CR case is wider than in the SR case. As a result, to achieve the desired STL performance in a frequency range, the proposed composite structure using SR with tuned characteristic frequencies is enough; however, if a wider frequency band is expected even if there is a slight STL tradeoff, the CR case is a better option. Though the method proposed is only valid in the low-to-medium frequency range, the results obtained can benefit theoretical development of low-to-medium sound modulation applications, they are also valuable and illuminating for investigating the broadband sound modulation.
To obtain excellent sound reduction performance, in this paper we introduce a novel periodic poroelastic composite structure, which combines poroelastic material and periodic structure and aims at using the remarkable acoustic performance of these two. This periodic composite structure comprises three parts, i.e. the poroelastic domain, the elastic domain(thin plate), and the periodic resonators, which can be simple singledegree-of-freedom resonators(SRs) or composite two-degree-of-freedom resonators(CRs). A theoretical model is established by using Biot theory for the poroelastic domain, and by using the effective medium method for the resonator-plate coupling system, which is considered as an isotropic plate with an equivalent dynamic density.This method is validated with degenerated model in the literature; the results obtained by this method are in excellent consistence with the results in the literature. Parameter analyses are performed to test the influences of poroelastic addition and periodic resonator on the sound transmission loss(STL) of this periodic composite structure under two kinds of boundary conditions. The poroelastic addition is found to increase the STL while the influences of resonators are complicated. The STL increases notably in the frequency range bounded by the characteristic frequencies of these resonators, however, a decrease just follows when it exceeds these frequencies,which can be observed in both SR case and CR case under the two boundary conditions. In the meantime, when multiple SR is placed in a periodic lattice, it is found that different resonators with ascending mass and characteristic frequencies have superior STL to those with ascending characteristic frequencies but have equal mass. The case with CR, which is more complicated as expected, shows less STL decrease than the case with SR, but wider frequency range where the STL increases than a poroelastic composite structure without resonators. This results from the fact that the frequency band of vibration suppression in the CR case is wider than in the SR case. As a result, to achieve the desired STL performance in a frequency range, the proposed composite structure using SR with tuned characteristic frequencies is enough; however, if a wider frequency band is expected even if there is a slight STL tradeoff, the CR case is a better option. Though the method proposed is only valid in the low-to-medium frequency range, the results obtained can benefit theoretical development of low-to-medium sound modulation applications, they are also valuable and illuminating for investigating the broadband sound modulation.
引文
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[2] Deckers E, Jonckheere S, Vandepitte D, Desmet W 2015Arch. Comput. Methods Eng. 22 183
[3] Bolton J S, Shiau N M, Kang Y J 1996 J. Sound Vib. 191 317
[4] Zhou J, Bhaskar A, Zhang X 2013 J. Sound Vib. 332 3724
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[8] Deresiewicz H 1961 Bull. Seismol. Soc. Am. 51 51
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[11] Talebitooti R, Daneshjou K, Kornokar M 2016 J. Sound Vib.363 380
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[13] Schanz M 2009 Appl. Mech. Rev. 62 030803
[14] Panneton R, Atalla N 1997 J. Acoust. Soc. Am. 101 3287
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[20] Wen X S 2006 Photonic/Phononic Theory and Technology(Beijing:Science Press)pp38-104(in Chinese)[温熙森2006光子/声子晶体理论与技术(北京:科学出版社)第38—341页]
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[22] Lin G C, Sun H W, Tan H F, Du X W 2011 Acta Phys. Sin.60 034302(in Chinese)[林国昌,孙宏伟,谭惠丰,杜星文2011物理学报60 034302]
[23] Ding C L, Zhao X P 2009 Acta Phys. Sin. 58 6351(in Chinese)[丁昌林,赵晓鹏2009物理学报58 6351]
[24] Yu D L, Shen H J, Liu J W, Yin J F, Zhang Z F, Wen J H2018 Chin. Phys. B 27 064301
[25] Zhang F H, Tang Y F, Xin F X, Lu T J 2018 Acta Phys. Sin.67 234302(in Chinese)[张丰辉,唐宇帆,辛锋先,卢天健2018物理学报67 234302]
[26] Zhu X X, Xiao Y, Wen J H, Yu D L 2016 Acta Phys. Sin. 65176202(in Chinese)[朱席席,肖勇,温激鸿,郁殿龙2016物理学报65 176202]
[27] Chen X, Cai L, Wen J H 2018 Chin. Phys. B 27 057803
[28] Song Y B, Wen J H, Yu D L, Shen H J 2018 Chin. J. Mech.Eng.54 60(in Chinese)[宋玉宝,温激鸿,郁殿龙,沈惠杰2018机械工程学报54 60]
[29] Kidner M R F, Fuller C R, Gardner B 2006 J. Sound Vib.294 466
[30] Idrisi K, Johnson M E, Toso A, Carneal J P 2009 J. Sound Vib. 323 51
[31] Cui S, Harne R L 2017 J. Acoust. Soc. Am. 141 4715
[32] Harne R L, Song Y, Dai Q 2017 Extrem. Mech. Lett. 12 41
[33] Bishop J, Harne R L 2018 Appl. Acoust. 130 222
[34] Wen J H, Yu D L, Zhao H G, Cai L, Xiao Y, Wang G, Yin J F 2016 Propagation of Elastic Waves in Artificial Periodic Structures:Vibrational and Acoustical Properties(Beijing:Science Press)pp272-290(in Chinese)[温激鸿,郁殿龙,赵宏刚,蔡力,肖勇,王刚,尹剑飞2015人工周期结构中弹性波的传播:振动与声学特性(北京:科学出版社)第272-290页]
[35] Xiao Y, Wen J, Wen X 2012 J. Sound Vib. 331 5408
[36] Li P, Yao S, Zhou X, Huang G, Hu G 2014 J. Acoust. Soc.Am. 135 1844
[37] Xiao Y, Wen J, Wen X 2012 J. Phys. D:Appl. Phys. 45195401
[38] Biot M A 1956 J. Acoust. Soc. Am. 28 179
[39] Junger M C, Feit D 1986 Sound, Structures, and Their Interaction(Massachusetts:MIT Press)pp235-277
[40] Cheng J C 2012 Theory of Sound(Beijing:Science Press)p51(in Chinese)[程建春2012声学原理(北京:科学出版社)第51页]
[41] Den Hartog J P 1985 Mechanical Vibrations(New York:Dover Publications)pp79-121
[42] He L, Zhu H C, Qiu X J, Du G H 2006 Theory and Engineering Applications of Acoustics(Beijing:Science Press)pp173-184(in Chinese)[何琳,朱海潮,邱小军,杜功焕2006声学理论与工程应用(北京:科学出版社)第173—184页]
[43] Peng H, Frank Pai P, Deng H 2015 Int. J. Mech. Sci. 103 104
[2] Deckers E, Jonckheere S, Vandepitte D, Desmet W 2015Arch. Comput. Methods Eng. 22 183
[3] Bolton J S, Shiau N M, Kang Y J 1996 J. Sound Vib. 191 317
[4] Zhou J, Bhaskar A, Zhang X 2013 J. Sound Vib. 332 3724
[5] Liu Y 2015 J. Sound Vib. 339 376
[6] Qiao H, He Z, Jiang W, Peng W 2019 J. Sound Vib. 440 256
[7] Allard J F, Depollier C, Rebillard P, Lauriks W, Cops A 1989J. Appl. Phys. 66 2278
[8] Deresiewicz H 1961 Bull. Seismol. Soc. Am. 51 51
[9] Zhou J, Bhaskar A, Zhang X 2013 Appl. Acoust. 74 1422
[10] Liu Y, Sebastian A 2015 J. Sound Vib. 344 399
[11] Talebitooti R, Daneshjou K, Kornokar M 2016 J. Sound Vib.363 380
[12] Shojaeifard M H, Talebitooti R, Ranjbar B, Ahmadi R 2014Appl. Math. Mech. 35 1447
[13] Schanz M 2009 Appl. Mech. Rev. 62 030803
[14] Panneton R, Atalla N 1997 J. Acoust. Soc. Am. 101 3287
[15] Verdiere K, Panneton R, Elkoun S, Dupont T, Leclaire P2013 J. Acoust. Soc. Am. 134 4648
[16] Brillouin L 2003 Wave Propagation in Periodic Structures:Electric Filters and Crystal Lattices(New York:Dover Publications)ppl-16
[17] Mead D M 1996 J. Sound Vib. 190 495
[18] Cao Y J, Zhou P Q, Dong C H 2006 Acta Phys. Sin. 55 6470(in Chinese)[曹永军,周培勤,董纯红2006物理学报55 6470]
[19] Ding C L, Dong Y B, Zhao X P 2018 Acta Phys. Sin. 67194301(in Chinese)[丁昌林,董仪宝,赵晓鹏2018物理学报67 194301]
[20] Wen X S 2006 Photonic/Phononic Theory and Technology(Beijing:Science Press)pp38-104(in Chinese)[温熙森2006光子/声子晶体理论与技术(北京:科学出版社)第38—341页]
[21] Jiang J L, Yao H, Du J, Zhao J B, Deng T 2017 Acta Phys.Sin.66 064301(in Chinese)[姜久龙,姚宏,杜军,赵静波,邓涛2017物理学报66 064301]
[22] Lin G C, Sun H W, Tan H F, Du X W 2011 Acta Phys. Sin.60 034302(in Chinese)[林国昌,孙宏伟,谭惠丰,杜星文2011物理学报60 034302]
[23] Ding C L, Zhao X P 2009 Acta Phys. Sin. 58 6351(in Chinese)[丁昌林,赵晓鹏2009物理学报58 6351]
[24] Yu D L, Shen H J, Liu J W, Yin J F, Zhang Z F, Wen J H2018 Chin. Phys. B 27 064301
[25] Zhang F H, Tang Y F, Xin F X, Lu T J 2018 Acta Phys. Sin.67 234302(in Chinese)[张丰辉,唐宇帆,辛锋先,卢天健2018物理学报67 234302]
[26] Zhu X X, Xiao Y, Wen J H, Yu D L 2016 Acta Phys. Sin. 65176202(in Chinese)[朱席席,肖勇,温激鸿,郁殿龙2016物理学报65 176202]
[27] Chen X, Cai L, Wen J H 2018 Chin. Phys. B 27 057803
[28] Song Y B, Wen J H, Yu D L, Shen H J 2018 Chin. J. Mech.Eng.54 60(in Chinese)[宋玉宝,温激鸿,郁殿龙,沈惠杰2018机械工程学报54 60]
[29] Kidner M R F, Fuller C R, Gardner B 2006 J. Sound Vib.294 466
[30] Idrisi K, Johnson M E, Toso A, Carneal J P 2009 J. Sound Vib. 323 51
[31] Cui S, Harne R L 2017 J. Acoust. Soc. Am. 141 4715
[32] Harne R L, Song Y, Dai Q 2017 Extrem. Mech. Lett. 12 41
[33] Bishop J, Harne R L 2018 Appl. Acoust. 130 222
[34] Wen J H, Yu D L, Zhao H G, Cai L, Xiao Y, Wang G, Yin J F 2016 Propagation of Elastic Waves in Artificial Periodic Structures:Vibrational and Acoustical Properties(Beijing:Science Press)pp272-290(in Chinese)[温激鸿,郁殿龙,赵宏刚,蔡力,肖勇,王刚,尹剑飞2015人工周期结构中弹性波的传播:振动与声学特性(北京:科学出版社)第272-290页]
[35] Xiao Y, Wen J, Wen X 2012 J. Sound Vib. 331 5408
[36] Li P, Yao S, Zhou X, Huang G, Hu G 2014 J. Acoust. Soc.Am. 135 1844
[37] Xiao Y, Wen J, Wen X 2012 J. Phys. D:Appl. Phys. 45195401
[38] Biot M A 1956 J. Acoust. Soc. Am. 28 179
[39] Junger M C, Feit D 1986 Sound, Structures, and Their Interaction(Massachusetts:MIT Press)pp235-277
[40] Cheng J C 2012 Theory of Sound(Beijing:Science Press)p51(in Chinese)[程建春2012声学原理(北京:科学出版社)第51页]
[41] Den Hartog J P 1985 Mechanical Vibrations(New York:Dover Publications)pp79-121
[42] He L, Zhu H C, Qiu X J, Du G H 2006 Theory and Engineering Applications of Acoustics(Beijing:Science Press)pp173-184(in Chinese)[何琳,朱海潮,邱小军,杜功焕2006声学理论与工程应用(北京:科学出版社)第173—184页]
[43] Peng H, Frank Pai P, Deng H 2015 Int. J. Mech. Sci. 103 104