Review on underwater sound absorption materials and mechanisms

WANG Yuren; MIAO Xuhong; JIANG Heng; CHEN Meng; LIU Yu; XU Wenshuai; MENG Dan

doi:10.6052/1000-0992-16-008

Volume 47 Issue 1

Feb. 2017

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Article Navigation > Advances in Mechanics > 2017 > 47(1): 92-121

WANG Yuren, MIAO Xuhong, JIANG Heng, CHEN Meng, LIU Yu, XU Wenshuai, MENG Dan. Review on underwater sound absorption materials and mechanisms[J]. Advances in Mechanics, 2017, 47(1): 92-121. doi: 10.6052/1000-0992-16-008

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WANG Yuren, MIAO Xuhong, JIANG Heng, CHEN Meng, LIU Yu, XU Wenshuai, MENG Dan. Review on underwater sound absorption materials and mechanisms[J]. Advances in Mechanics, 2017, 47(1): 92-121. doi: 10.6052/1000-0992-16-008

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Review on underwater sound absorption materials and mechanisms

doi: 10.6052/1000-0992-16-008

WANG Yuren^{1
,
,},
MIAO Xuhong^{2
,
,},
JIANG Heng¹,
CHEN Meng¹,
LIU Yu¹,
XU Wenshuai¹,
MENG Dan¹

1.
Key Laboratory of Microgravity, Institute of Mechanics, Chinese Academy of Sciences, Beijing 100190, China
2.
Naval Academy of Armament, Beijing 100016, China

More Information

Corresponding author: WANG Yuren; MIAO Xuhong
Received Date: 2016-02-25
Available Online: 2016-11-11
Publish Date: 2017-02-24

Abstract

Abstract

As China accelerates the implementation of the marine power strategy, the demand for advanced underwater sound-absorbing materials has become increasingly urgent. Unlike air absorption, the high hydrostatic pressure and complex marine environment impose more stringent requirements regarding underwater sound-absorbing materials. The essence of the sound absorption problem is how to efficiently transform elastic energy into heat or other forms of energy. This paper reviews the traditional underwater sound absorbing materials based on both the intramolecular friction and the energy dissipation mechanisms. The main problem of traditional underwater sound-absorbing material is attributable to its poor sound absorption performance under low frequency and high hydrostatic pressure. On the one hand, this is because the underwater sound-absorbing material is of limited thickness. Besides, due to the limitation of the mass density law, it cannot effectively absorb the low-frequency sound waves from the water. On the other hand, elastic material, such as polymer, becomes "hard" under high hydrostatic pressure, thus the conversion efficiency of acoustic elastic energy is greatly reduced. With the development of local resonance theory and the concept of metamaterials, a series of new underwater sound absorbing materials have been produced, which provide new ways to solve the problems encountered in developing underwater sound absorbing materials. The local resonance theory states that a small-scale structure can control the spread of long sound waves. Therefore, it can solve the problem of sound absorption at low-frequencies. This paper focuses on the theory of local resonance, the development of new sonar wood and phonon glass, and other novel underwater sound absorbing materials. Based on the local resonance theory, the phonon glass material can improve the compression performance by introducing the porous metal skeleton structure, and solve the problem of poor sound absorption performance under high hydrostatic pressure. At the end of this paper, the future development of underwater sound-absorbing materials is explored.
- underwater sound absorption materials,
- underwater sound absorbing,
- local resonance,
- phononic glass

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References(154)

References

[1]	白国锋. 2003.水下消声覆盖层吸声机理研究.[硕士论文].哈尔滨:哈尔滨工程大学
[2]	Bai G F. 2003.Research of the absorboing mechanism of the underwater anechoic coatings.[Master Thesis]. Haerbin:Harerbin Engineering University
[3]	蔡俊, 李亚红, 蔡伟民. 2007. PZT/CB/PVC压电导电高分子复合材料的吸声机理.高分子材料科学与工程, 23:215-218 http://www.cnki.com.cn/Article/CJFDTOTAL-GFZC200704057.htm
[4]	Cai J, Li Y H, Cai W M. 2007. Study on acoustic absorption mechanism of piezoelectric and electrical conductive polymeric composite PZT/CB/PVC. Polymer Materials Science And Engerning, 23:215-218. https://www.researchgate.net/publication/288555585_Study_on_acoustic_absorption_mechanism_of_piezoelectric_and_electrical_conductive_polymeric_composite_PZTCBPVC
[5]	陈建平. 2007.消声瓦声学性能计算方法研究.噪声与振动控制, 4:123-126 http://www.cnki.com.cn/Article/CJFDTOTAL-ZSZK200704036.htm
[6]	Chen J P. 2007. Study on the computation method of anechoic tile acoustical characteristic. Noise and Vibration Control, 4:123-126.
[7]	陈毅, 刘晓宁, 向平, 胡更开. 2016.五模材料及其水声调控研究.力学进展, 46:201609 http://lxjz.m.koryoan.com/CN/abstract/abstract145825.shtml
[8]	Chen Y, Liu X N, Xiang P, Hu G K. 2016. Pentamode material for underwater acoustic wave control. Advances in Mechanics, 46:201609. http://en.cnki.com.cn/Article_en/CJFDTotal-LXJZ201600009.htm
[9]	陈月辉. 2004.声学功能橡胶.特种橡胶制品, 25:55-62 http://www.cnki.com.cn/Article/CJFDTOTAL-TZXJ200401016.htm
[10]	Chen Y H. 2004. Acoustics functional rubber.Special Purpose Rubber Products, 25:55-62.
[11]	傅明源, 孙酣经. 1994.聚氨脂弹性体及其应用.北京:化学工业出版社
[12]	Fu M Y, Sun H J. 1994.Polyurethane Elastomers and Application. Beijing:Chemical Industry Press.
[13]	高玲, 尚福亮. 2007.吸声材料的研究与应用.化工时刊, 21:63-69 http://www.cnki.com.cn/Article/CJFDTOTAL-HGJS200702021.htm
[14]	Gao L, Shang F L. 2007. Development and applications of sound-absorbing materials. Chemical Industry Times, 21:63-69. http://en.cnki.com.cn/Article_en/CJFDTOTAL-HGJS200702021.htm
[15]	顾金海, 叶学千. 1981.水声学基础.北京:国防工业出版社
[16]	Gu J H, Ye X Q. 1981. Underwater Acoustics Foundation. Beijing:National Defense Industry Press.
[17]	何世平, 汤渭霖, 何琳, 汤智胤. 2006.变截面圆柱形空腔覆盖层吸声系数的二维近似解.船舶力学, 10:120-127 http://www.cnki.com.cn/Article/CJFDTOTAL-CBLX200601015.htm
[18]	He S P, Tang W L, He L, Tang Z Y. 2006. Analysis of acoustic characteristics of anechoic coating containing varying sectional cylindrical cavity. Journal of Ship Mechanics, 10:120-127.
[19]	刘颖. 2002.冲击载荷作用下含液饱和多孔介质中应力波传播问题的研究.[博士论文].大连:大连理工大学.
[20]	Liu Y. 2002. Stress wave propagation in fluid-saturated porous media under impact loading.[PhD Thesis]. Dalian:Dalian University of Technology.
[21]	马大猷. 2004.现代声学理论基础.北京:科学出版社, 241-245
[22]	Ma D Y. 2004. Modern Acoustic Theory Foundation. Beijing:Science Press, 241-245.
[23]	缪旭弘, 王振全. 2005.舰艇水下噪声控制技术现状及发展对策//第十届船舶水下噪声学术讨论会
[24]	Miao X H, Wang Z Q. 2005. Ship underwater noise control technology present situation and development countermeasures//Proceedings of the 10th Symposium on Ship Underwater Noise.
[25]	谭红波, 赵洪, 徐海亭. 2003.有限元法分析空腔周期分布黏弹性层的声特性.声学学报, 28:277-282 http://www.cnki.com.cn/Article/CJFDTOTAL-XIBA200303014.htm
[26]	Tan H B, Zhao H, Xu H T. 2003. Sound characteristics of the viscoelastic layer containing Periodic cvaities by the finite element method. Acta Acustica, 28:277-282. http://en.cnki.com.cn/Article_en/CJFDTOTAL-SXXW200401004.htm
[27]	汤渭霖, 何世平, 范军. 2005.含圆柱形空腔吸声覆盖层的二维理论.声学学报, 30:289-295 http://www.cnki.com.cn/Article/CJFDTOTAL-XIBA200504003.htm
[28]	Tang W L, He S P, Fan J. 2005. Two-dimensional model for acoustic absorption of viscoelastic coating containing cylindrical holes. Acta Acustica, 30:289-295.
[29]	唐劲松, 张春华. 1999.水声工程的新进展--欧洲UDT 99观感.应用声学, 18:5-10 http://www.cnki.com.cn/Article/CJFDTOTAL-YYSN199905001.htm
[30]	Tang J S, Zhang C H. 1999. Development in underwater acoustic engineering-a survey of UDT Europe'99. Applied Acoustics, 18:5-10. http://en.cnki.com.cn/Article_en/CJFDTOTAL-YYSN199905001.htm
[31]	汪越胜. 2006.声带隙功能材料的科学问题及力学思考.固体力学若干新进展//第一届全国固体力学青年学者研讨会论文集, 北京:清华大学出版社, 323-342
[32]	Wang Y S. 2006. Scientific problems and mechanical thinking of acoustic band gap material. Some new progress in solid mechanics//Proceedings of the first national seminar for young scholars of solid mechanics. Beijing:Tsinghua University Press, 323-342.
[33]	王光荣, 游蕾. 2001.潜艇隐身衣--消声瓦.现代舰船, 24-25 http://www.cnki.com.cn/Article/CJFDTOTAL-XDJC200105013.htm
[34]	Wang G R, You L. 2001. Submarine invisibility cloak-anechoic tile. Modem Ships, 24-25.
[35]	王仁乾, 马黎黎. 2004.吸声材料的物理参数对消声瓦吸声性能的影响.哈尔滨工程大学学报, 25:288-294. http://www.cnki.com.cn/Article/CJFDTOTAL-HEBG200403006.htm
[36]	Wang R Q, Ma L L. 2004. Effects of physical parameters of the absorption material on absorption capability of anechoic tiles. Journal of Harbin Engineering University, 25:288-294. https://www.researchgate.net/publication/293239583_Effects_of_physical_parameters_of_the_absorption_material_on_absorption_capability_of_anechoic_tiles
[37]	王晓林. 2007.金属多孔材料吸声板的优化模型.声学学报, 32:116-121 http://www.cnki.com.cn/Article/CJFDTOTAL-XIBA200702004.htm
[38]	Wang X L. 2007. An optimized model for porous metal sound absorbers. Acta Acustica, 32:116-121.
[39]	温激鸿, 王刚, 刘耀宗, 郁殿龙. 2005.基于集中质量法的一维声子晶体弹性波带隙计算.物理学报, 53:3384-3388 http://www.cnki.com.cn/Article/CJFDTOTAL-WLXB200410026.htm
[40]	Wen J H, Wang G, Liu Y Z, Yu D L. 2005. Lumped-mass method on calculation of elastic band gaps of one-dimensional phononic crystals. Acta Physica Sinica, 53:3384-3388. http://en.cnki.com.cn/Article_en/CJFDTOTAL-WLXB200410026.htm
[41]	吴福根, 刘有延. 2002.二维周期性复合介质中声波带隙结构及其缺陷态.物理学报, 51:1434-1438 http://www.cnki.com.cn/Article/CJFDTOTAL-WLXB200207005.htm
[42]	Wu F G, Liu Y Y. 2002. Acoustic band gaps and defect states in two-dimensional composite materials. Acta Physica Sinica, 51:1434-1438. http://en.cnki.com.cn/Article_en/CJFDTOTAL-WLXB200207005.htm
[43]	杨雪, 王源升, 余红伟. 2007.多层高分子复合结构斜入射声波吸声性能.复合材料学报, 23:21-28 http://www.cnki.com.cn/Article/CJFDTOTAL-FUHE200606003.htm
[44]	Yang X, Wang Y S, Yu H W. 2007. Sound absorption properties of multilayered polymer composites for obl ique incidence. Acta Materiae Compositae Sinica, 23:21-28. https://www.researchgate.net/publication/288808183_Sound_absorption_properties_of_multilayered_polymer_composites_for_oblique_incidence
[45]	姚耀中, 林立. 2007.潜艇机械噪声控制技术综述.舰船科学技术, 29:21-26 http://www.cnki.com.cn/Article/CJFDTOTAL-JCKX200701009.htm
[46]	Yao Y Z, Lin L. 2007. A review of control ofmechanical no ise for submarines. Ship Science and Technology, 29:21-26.
[47]	张海澜. 2007.理论声学.北京:高等教育出版社, 199-201
[48]	Zhang H L. 2007. Theoretical Acoustics.Beijing:China Higher Education Press, 199-201.
[49]	张文毓. 2010.国外消声瓦的研究与应用进展.船舶, 21:1-4 http://www.cnki.com.cn/Article/CJFDTOTAL-CBZZ201006002.htm
[50]	Zhang W Y. 2010. Overseas research and application of the silence tile. Ship and Boat, 21:1-4. http://en.cnki.com.cn/Article_en/CJFDTOTAL-CBZZ201006002.htm
[51]	赵敏兰, 朱蓓丽. 1996.用等效参数法研究含球形空腔弹性体的吸声性能.噪声与振动控制, 5:11-14 http://www.cnki.com.cn/Article/CJFDTOTAL-ZSZK605.002.htm
[52]	Zhao M L, Zhu B L. 1996. Acoustic properties analysis of elasticity with a spherical cavity using equivalent parametric method. Noise and Vibration Control, 5:11-14.
[53]	周成飞. 2005.聚氨酯水声材料研究进展.聚氨酯工业, 19:1-4 http://www.cnki.com.cn/Article/CJFDTOTAL-JAZG200406001.htm
[54]	Zhou C F. 2005. Recent development in the underwater acoustic materials of polyurethane. Polyurethane Industry, 19:1-4.
[55]	周洪, 黄光速, 陈喜荣, 何显儒. 2004.高分子吸声材料.化学进展, 16:450-455 http://www.cnki.com.cn/Article/CJFDTOTAL-HXJZ200403018.htm
[56]	Zhou H, Huang G S, Chen X R, He X R. 2004. Advances in sound absorption polymers. Progress in Chemistry, 16:450-455. http://en.cnki.com.cn/Article_en/CJFDTOTAL-HXJZ200403018.htm
[57]	周萧明, 蔡小兵, 胡更开. 2007.左手材料设计及透明现象研究进展.力学进展, 37:517-536 http://lxjz.m.koryoan.com/CN/abstract/abstract132920.shtml
[58]	Zhou X M, Cai X B, Hu G K. 2007. Advances in left-handed material design and transparency phenomenon.Advances in Mechanics, 37:517-536.
[59]	朱世成, 钟爱升. 2006.橡胶材料和结构在低频耐压吸声上的一些认识与设想.橡塑资源利用, 1:10-18 http://www.cnki.com.cn/Article/CJFDTOTAL-TJXJ200601002.htm
[60]	Zhu S C, Zhong A S. 2006. Some understanding and ideas on sound absorption and proof pressure under low frequency of rubber material and structure. Rubber and Plastics Resources Utilization, 1:10-18.
[61]	Achenbach J D, Kitahara M. 1986. Reflection and transmission of an obliquely incident wave by an array of spherical cavities. The Journal of the Acoustical Society of America, 80:1209-1214. doi: 10.1121/1.393812
[62]	Achenbach J D, Kitahara M. 1987. Harmonic waves in a solid with a periodic distribution of spherical cavities. The Journal of the Acoustical Society of America, 81:595-598. doi: 10.1121/1.394825
[63]	Arenas J P, Crocker M J. 2010. Recent trends in porous sound-absorbing materials. Sound & vibration, 44:12-18. https://www.researchgate.net/publication/272151761_Recent_Trends_in_Porous_Sound-Absorbing_Materials
[64]	Audoly C, Dumery G. 1990. Modeling of compliant tube underwater reflectors. The Journal of the Acoustical Society of America, 87:1841-1846. doi: 10.1121/1.399310
[65]	Boulanger P, Hayes M. 1997. Wave propagation in sheared rubber. Acta mechanica, 122:75-87. doi: 10.1007/BF01181991
[66]	Brigham G A, Libuha J J, Radlinski R P. 1977. Analysis of scattering from large planar gratings of compliant cylindrical shells. The Journal of the Acoustical Society of America, 61:48-59. doi: 10.1121/1.381267
[67]	Burke J, Twersky V. 1966. On scattering of waves by the infinite grating of elliptic cylinders. Antennas and Propagation, IEEE Transactions on Antenna & Propagation, 14:465-480. https://www.researchgate.net/publication/3012274_On_Scattering_of_Waves_by_the_Infinite_Grating_of_Elliptic_Cylinders
[68]	Cai L W, Williams J H. 1999. Large-scale multiple scattering problems. Ultrasonics, 37:453-462. doi: 10.1016/S0041-624X(99)00029-3
[69]	Cao Y, Hou Z, Liu Y. 2004. Finite difference time domain method for band-structure calculations of twodimensional phononic crystals. Solid State Communications, 132:539-543. doi: 10.1016/j.ssc.2004.09.003
[70]	Cervenka P, Challande P. 1991. A new efficient algorithm to compute the exact reflection and transmission factors for plane waves in layered absorbing media (liquids and solids). The Journal of the Acoustical Society of America, 89:1579-1589. doi: 10.1121/1.400993
[71]	Chen G P, He D P, Shu G J. 2001. Underwater sound absorption property of porous aluminum. Colloids and Surfaces A:Physicochemical and Engineering Aspects, 179:191-194. https://www.researchgate.net/publication/244139064_Underwater_sound_absorption_property_of_porous_aluminum
[72]	Chen M, Jiang H, Feng Y, Wang Y. 2014. Investigation of locally resonant absorption and factors affecting the absorption band of a phononic glass. Applied Physics A, 117:2067-2072. doi: 10.1007/s00339-014-8620-z
[73]	Chen M, Meng D, Zhang H, Jiang H, Wang Y. 2016. Resonance-coupling effect on broad band gap formation in locally resonant sonic metamaterials. Wave Motion, 63:111-119. doi: 10.1016/j.wavemoti.2016.02.003
[74]	Climente A, Torrent D, Sanchez-Dehesa J. 2012. Omnidirectional broadband acoustic absorber based on metamaterials. Applied Physics Letters, 100:144103-144103-4. doi: 10.1063/1.3701611
[75]	Ding C L, Zhao X D, Hao L M, Zhu W R. 2011. Acoustic metamaterial with split hollow spheres. Acta Physica Sinica, 4:044301.
[76]	Dowling J P. 1992. Sonic band structure in fluids with periodic density variations. The Journal of the Acoustical Society of America, 91:2539-2543. doi: 10.1121/1.402990
[77]	Easwaran V, Munjal M L. 1993. Analysis of reflection characteristics of a normal incidence plane wave on resonant sound absorbers:A finite element approach. The Journal of the Acoustical Society of America, 93:1308-1318. doi: 10.1121/1.405416
[78]	Emery P A. 1995. New cladding material. UDT, 527-531.
[79]	Esquivel-Sirvent R, Cocoletzi G H. 1994. Band structure for the propagation of elastic waves in superlattices.The Journal of the Acoustical Society of America, 95:86-90. doi: 10.1121/1.408301
[80]	Gaunaurd G C, Callen E, Barlow J. 1984. Pressure effects on the dynamic effective properties of resonating perforated elastomers. The Journal of the Acoustical Society of America, 76:173-177. doi: 10.1121/1.391090
[81]	Gaunaurd G C, Uberall H. 1978. Theory of resonant scattering from spherical cavities in elastic and vis-coelastic media. The Journal of the Acoustical Society of America, 63:1699-1712. doi: 10.1121/1.381908
[82]	Gaunaurd G C. 1977. Sonar cross section of a coated hollow cylinder in water. The Journal of the Acoustical Society of America, 61:360-368. doi: 10.1121/1.381313
[83]	Gaunaurd G C. 1989. Elastic and acoustic resonance wave scattering. Applied Mechanics Reviews, 42:143-192. doi: 10.1115/1.3152427
[84]	Gaunaurd G. 1977. One-dimensional model for acoustic absorption in a viscoelastic medium containing short cylindrical cavities. The Journal of the Acoustical Society of America, 62:298-307. doi: 10.1121/1.381528
[85]	Gaunaurd G. 1985. Comments on absorption mechanisms for waterborne sound in Alberich anechoic layers.Ultrasonics, 23:90-91. doi: 10.1016/0041-624X(85)90038-1
[86]	Goffaux C, Sánchez-Dehesa J, Lambin P. 2004. Comparison of the sound attenuation efficiency of locally resonant materials and elastic band-gap structures. Physical Review B, 70:1-6. https://www.researchgate.net/publication/235461091_Comparison_of_the_sound_attenuation_efficiency_of_locally_resonant_materials_and_elastic_band-gap_structures
[87]	Goffaux C, Sánchez-Dehesa J, Yeyati A L. 2002. Evidence of fano-like interference phenomena in locally resonant materials. Physical Review Letters, 88:1-4. https://www.ncbi.nlm.nih.gov/pubmed/12059426
[88]	Guenneau S, Movchan A, Pétursson G, Ramakrishna S A. 2007. Acoustic metamaterials for sound focusing and confinement. New Journal of physics, 9:1-18. doi: 10.1088/1367-2630/9/1/001
[89]	Han F, Seiffert G, Zhao Y, Gibbs B. 2003. Acoustic absorption behaviour of an open-celled aluminium foam.Journal of Physics D:Applied Physics, 36:294. doi: 10.1088/0022-3727/36/3/312
[90]	Heinemann M, Larraza A, Smith K B. 2003. Experimental studies of applications of time-reversal acoustics to noncoherent underwater communications. The Journal of the Acoustical Society of America, 113:3111-3116. doi: 10.1121/1.1570832
[91]	Hinders M K, Rhodes B A, Fang T. M. 1995. Particle-loaded composites for acoustic anechoic coatings.Journal of Sound and Vibration, 185:219-246. doi: 10.1006/jsvi.1995.0377
[92]	Hladky-Hennion A C, Decarpigny J N. 1991. Analysis of the scattering of a plane acoustic wave by a doubly periodic structure using the finite element method:Application to Alberich anechoic coatings. Journal of the Acoustical Society of America, 90:3556-3367. https://www.researchgate.net/publication/238990438_Analysis_of_the_scattering_of_a_plane_acoustic_wave_by_a_doubly_periodic_structure_using_the_finite_element_method_Application_to_Alberich_anechoic_coatings
[93]	Hsu J C, Wu T T. 2007. Lamb waves in binary locally resonant phononic plates with two-dimensional lattices. Applied Physics Letters, 90:1-3. doi: 10.1063/1.2739369
[94]	Huang H H, Sun C T. 2012. Anomalous wave propagation in a one-dimensional acoustic metamaterial having simultaneously negative mass density and Young's modulus. The Journal of the Acoustical Society of America, 132:2887-2895. doi: 10.1121/1.4744977
[95]	Jensen J S. 2003. Phononic band gaps and vibrations in one-and two-dimensional mass-spring structures.Journal of Sound and Vibration, 266:1053-1078.
[96]	Jiang H, Wang Y, Zhang M, Hu Y, Lan D, Zhang Y, Wei B. 2009. Locally resonant phononic woodpile:A wide band anomalous underwater acoustic absorbing material. Applied Physics Letters, 95:104101. doi: 10.1063/1.3216805
[97]	Jiang H, Wang Y. 2012. Phononic glass:a robust acoustic-absorption material. The Journal of the Acoustical Society of America 132:694-699. doi: 10.1121/1.4730922
[98]	Jiang H, Zhang M, Wang Y, Hu Y, Lan D, Wei B. 2009. A wide band strong acoustic absorption in a locally network anechoic coating. Chinese Physics Letters, 26:1-4. http://cpl.iphy.ac.cn/fileup/PDF/2009-1003.pdf
[99]	Jiang H, Wang Y, Zhang M, Hu Y, Lan D, Wu Q, Lu H. 2010. Wide-band underwater acoustic absorption based on locally resonant unit and interpenetrating network structure. Chinese Physics B, 19:1-6. http://mall.cnki.net/magazine/article/ZGWL201002058.htm
[100]	Kafesaki M, Economou E N. 1999. Multiple-scattering theory for three-dimensional periodic acoustic composites. Physical Review B, 60:11993-12001. doi: 10.1103/PhysRevB.60.11993
[101]	Khelif A, Achaoui Y, Benchabane S, Laude V, Aoubiza B. 2010. Locally resonant surface acoustic wave band gaps in a two-dimensional phononic crystal of pillars on a surface. Physical Review B, 81:1-7. https://www.researchgate.net/publication/235547088_Locally_resonant_surface_acoustic_wave_band_gaps_in_a_two-dimensional_phononic_crystal_of_pillars_on_a_surface
[102]	Khelif A, Aoubiza B, Mohammadi S, Adibi A, Laude V. 2006. Complete band gaps in two-dimensional phononic crystal slabs. Physical Review E, 74:1-5. https://www.ncbi.nlm.nih.gov/pubmed/17155195
[103]	Kishi H, Kuwata M, Matsuda S, Asami T, Murakami A. 2004. Damping properties of thermoplasticelastomer interleaved carbon fiber-reinforced epoxy composites. Composites Science and Technology, 64:2517-2523. doi: 10.1016/j.compscitech.2004.05.006
[104]	Kushwaha M S, Halevi P, Dobrzynski L, Djafari-Rouhani B. 1993. Acoustic band structure of periodic elastic composites. Physical Review Letters, 71:2022. doi: 10.1103/PhysRevLett.71.2022
[105]	Lai Y, Wu Y, Sheng P, Zhang Z Q. 2011. Hybrid elastic solids. Nature materials, 10:620-624. doi: 10.1038/nmat3043
[106]	Lakhtakia A, Varadan V V, Varadan V K. 1986. Reflection characteristics of an elastic slab containing a periodic array of elastic cylinders:SH wave analysis. The Journal of the Acoustical Society of America, 80:311-316. doi: 10.1121/1.394148
[107]	Lakhtakia A, Varadan V V, Varadan V K. 1988. Reflection characteristics of an elastic slab containing a periodic array of circular elastic cylinders:P and SV wave analysis. The Journal of the Acoustical Society of America, 83:1267-1275. doi: 10.1121/1.395982
[108]	Lamb H. 1904. On group-velocity. Proc. London Math. Soc., S2-1:473-479. doi: 10.1112/plms/s2-1.1.473
[109]	Langlet P, Hladky-Hennion A C, Decarpigny J N. 1995. Analysis of the propagation of plane acoustic waves in passive periodic materials using the finite element method. The Journal of the Acoustical Society of America, 98:2792-2800. doi: 10.1121/1.413244
[110]	Lee Y Y, Lee E W M, Ng C F. 2005. Sound absorption of a finite flexible micro-perforated panel backed by an air cavity. Journal of Sound and Vibration, 287:227-243. doi: 10.1016/j.jsv.2004.11.024
[111]	Lefebvre L P, Banhart J, Dunand D. 2008. Porous metals and metallic foams:current status and recent developments. Advanced Engineering Materials, 10:775-787. doi: 10.1002/adem.v10:9
[112]	Liu X N, Hu G K, Huang G L, Sun C T. 2011. An elastic metamaterial with simultaneously negative mass density and bulk modulus. Applied Physics Letters, 98:1-3. https://www.researchgate.net/publication/224243359_An_elastic_metamaterial_with_simultaneously_negative_mass_density_and_bulk_modulus
[113]	Liu Y, Yu, Zhao H, Wen J, Wen X. 2008. Theoretical study of two-dimensional phononic crystals with viscoelasticity based on fractional derivative models. Journal of Physics D:Applied Physics, 41:1-7. doi: 10.1051/epjap:2007176
[114]	Liu Z, Zhang X, Mao Y, Zhu Y Y, Yang Z, Chan C T, Shen P. 2000. Locally resonant sonic materials.Science, 289:1734-1736. doi: 10.1126/science.289.5485.1734
[115]	Lu T J, Hess A, Ashby M F. 1999. Sound absorption in metallic foams. Journal of Applied Physics, 85:7528-7539. doi: 10.1063/1.370550
[116]	Ma G, Yang M, Xiao S, Yang Z, Shen P. 2014. Acoustic metasurface with hybrid resonances. Nature Materials, 13:873. doi: 10.1038/nmat3994
[117]	Martinezsala R, Sancho J, Sánchez J V, Gomez V, Llinares J, Meseguer F. 1995. Sound-attenuation by sculpture. Nature, 378:241. https://www.researchgate.net/publication/247593387_Sound_attenuation_by_sculpture
[118]	Mei J, Liu Z, Shi J, Tian D. 2003. Theory for elastic wave scattering by a two-dimensional periodical array of cylinders:An ideal approach for band-structure calculations. Physical Review B, 67:1-7.
[119]	Mei J, Ma G, Yang M, Weng W, Shen P. 2012. Dark acoustic metamaterials as super absorbers for lowfrequency sound. Nature Communications, 3:132-136. https://www.ncbi.nlm.nih.gov/pubmed/22453829
[120]	Meng H, Wen J, Zhao H, Wen X. 2012. Optimization of locally resonant acoustic metamaterials on underwater sound absorption characteristics. Journal of Sound and Vibration, 331:4406-4416. doi: 10.1016/j.jsv.2012.05.027
[121]	Mikata Y, Achenbach J D. 1988. Interaction of harmonic waves with a periodic array of inclined cracks.Wave Motion, 10:59-72. doi: 10.1016/0165-2125(88)90006-6
[122]	Modinos A, Stefanou N, Psarobas I E, Yannopapas V. 2001. On wave propagation in inhomogeneous systems.Physica B:Condensed Matter, 296:167-173. doi: 10.1016/S0921-4526(00)00795-X
[123]	Odell D, Hertel K, Nelson C. 2002. New acoustic systems for AUV tracking, communications, and noise measurements at NSWCCD-ARD, lake pend oreille, Idaho. Oceans Conference Record (IEEE), 1:266-271. https://www.researchgate.net/publication/4006818_New_acoustic_systems_for_AUV_tracking_communications_and_noise_measurement_at_NSWCCD-ARD_Lake_Pend_Oreille_Idaho
[124]	Oh J H, Kim Y J, Kim Y Y. 2013. Wave attenuation and dissipation mechanisms in viscoelastic phononic crystals. Journal of Applied Physics, 113:1-3. http://adsabs.harvard.edu/abs/2013JAP...113j6101H
[125]	Oudich M, Assouar M B, Hou Z. 2010. Propagation of acoustic waves and waveguiding in a two-dimensional locally resonant phononic crystal plate. Applied Physics Letters, 97:1-3. https://www.researchgate.net/profile/Badreddine_Assouar/publication/224192953_Propagation_of_acoustic_waves_and_waveguiding_in_a_two-dimensional_locally_resonant_phononic_crystal_plate/links/570e074708ae2b772e433bed.pdf?origin=publication_detail
[126]	Pedersen P C, Tretiak O, He P. 1982. Impedance-matching properties of an inhomogeneous matching layer with continuously changing acoustic impedance. The Journal of the Acoustical Society of America, 72:327-336. doi: 10.1121/1.388085
[127]	Pennec Y, Djafari-Rouhani B, Larabi H, Vasseur J O, Hladky-Hennion A C. 2008. Low-frequency gaps in a phononic crystal constituted of cylindrical dots deposited on a thin homogeneous plate. Physical Review B, 78:1-8. https://www.researchgate.net/publication/235574044_Low-frequency_gaps_in_a_phononic_crystal_constituted_of_cylindrical_dots_deposited_on_a_thin_homogeneous_plate
[128]	Philip B, Abrahaham J K, Varadan V K, Natarajan V, Jayakuman V G. 2004. Passive underwater acoustic damping materials with Rho-C rubber-carbon fiber and molecular sieves. Smart Materials and Structures, 13:99-104. doi: 10.1088/0964-1726/13/6/N01
[129]	Pocklington H C. 1905. Growth of a wave-group when the group-velocity is negative. Nature, 71:607-608. http://www.nature.com/nature/journal/v71/n1852/abs/071607b0.html
[130]	Psarobas I E, Stefanou N, Modinos A. 2000. Scattering of elastic waves by periodic arrays of spherical bodies. Physical Review B, 62:1-19. doi: 10.1103/PhysRevB.62.1
[131]	Radlinski R P, Simon M M. 1982. Scattering by multiple gratings of compliant tubes. The Journal of the Acoustical Society of America, 72:607-614. doi: 10.1121/1.388042
[132]	Radlinski R P. 1989. Scattering from multiple gratings of compliant tubes in a viscoelastic layer. The Journal of the Acoustical Society of America, 85:2301-2310. doi: 10.1121/1.397776
[133]	Sainidou R, Djafari-Rouhani B, Pennec Y, Vasseur J O. 2006. Locally resonant phononic crystals made of hollow spheres or cylinders. Physical Review B, 73:1-7. https://www.researchgate.net/publication/235481842_Locally_resonant_phononic_crystals_made_of_hollow_spheres_or_cylinders
[134]	Sergeeva L M, Skiba S I, Karabanova L V. 1996. Filler effect on formation and properties of interpenetrating polymer networks based on polyurethane and polyesteracrylate. Polymer International, 39:317-325. doi: 10.1002/(ISSN)1097-0126
[135]	Sheng P, Zhang X, Liu Z, Chan C. 2003. Locally resonant sonic materials. Physica B:Condensed Matter, 338:201-205. doi: 10.1016/S0921-4526(03)00487-3
[136]	Sigalas M M, Economou E N. 1992. Elastic and acoustic wave band structure. Journal of Sound and Vibration, 158:377-382. doi: 10.1016/0022-460X(92)90059-7
[137]	Sigalas M M, Soukoulis CM. 1995. Elastic-wave propagation through disordered and/or absorptive layered systems. Physical Review B, 51:2780-2789. doi: 10.1103/PhysRevB.51.2780
[138]	Sigalas M M. 1997. Elastic wave band gaps and defect states in two-dimensional composites. The Journal of the Acoustical Society of America, 101:1256-1261. doi: 10.1121/1.418156
[139]	Sigalas M M. 1998. Defect states of acoustic waves in a two-dimensional lattice of solid cylinders. Journal of Applied Physics, 84:3026-3030. doi: 10.1063/1.368456
[140]	Veselago V G, Narimanov E E. 2006. The left hand of brightness:past, present and future of negative index materials. Nature Materials, 5:759-762. doi: 10.1038/nmat1746
[141]	Vovk I V, Grinchenko V T, Kononuchenko L A. 1976. Diffraction of a sound-wave by a plane grating formed by hollow elastic bars. Soviet Physics Acoustics-ussr, 22:113-115. https://www.researchgate.net/publication/291278040_DIFFRACTION_OF_A_SOUND_WAVE_BY_A_PLANE_GRATING_FORMED_BY_HOLLOW_ELASTIC_BARS
[142]	Wang C N, Tse C C, Chen S K. 2007. On analysis of passive underwater acoustic damping materials.Journal of the Chinese Institute of Engineers, 30:251-257. doi: 10.1080/02533839.2007.9671251
[143]	Wang G, Wen J, Liu Y, Wen X. 2004. Lumped-mass method for the study of band structure in twodimensional phononic crystals. Physical Review B, 69:1-6. https://www.researchgate.net/profile/Gang_Wang50/publication/260076516_Lumped-mass_method_for_the_study_of_band_structure_in_two-dimensional_phononic_crystals/links/559344f508ae16f493ee573f.pdf?origin=publication_detail
[144]	Wang G, Wen X, Wen J, Shao L, Liu Y. 2004. Two-dimensional locally resonant phononic crystals with binary structures. Physical Review Letters, 93:1-4. https://www.researchgate.net/publication/8195468_Two-Dimensional_Locally_Resonant_Phononic_Crystals_with_Binary_Structures
[145]	Wang X. 2007. Porous metal absorbers for underwater sound. The Journal of the Acoustical Society of America, 122:2626-2635. doi: 10.1121/1.2785041
[146]	Wen J, Zhao H, Lv L, Yuan B, Wang G, Wen X. 2011. Effects of locally resonant modes on underwater sound absorption in viscoelastic materials. The Journal of the Acoustical Society of America, 130:1201-1208. doi: 10.1121/1.3621074
[147]	Wu T T, Huang Z G, Tsai T C, Wu T C. 2008. Evidence of complete band gap and resonances in a plate with periodic stubbed surface. Applied Physics Letters, 93:1-3. https://www.researchgate.net/publication/252926595_Evidence_of_complete_band_gap_and_resonances_in_a_plate_with_periodic_stubbed_surface
[148]	Yang Z, Mei J, Yang M, Chan N H, Shen P. 2008. Membrane-type acoustic metamaterial with negative dynamic mass. Physical Review letters, 101:1-4. https://www.researchgate.net/publication/23710553_Membrane-Type_Acoustic_Metamaterial_with_Negative_Dynamic_Mass
[149]	Yilmaz C, Hulbert G M, Kikuchi N. 2007. Phononic band gaps induced by inertial amplification in periodic media. Physical Review B, 76:1-9. https://www.researchgate.net/publication/259101580_Phononic_band_gaps_induced_by_inertial_amplification_in_periodic_media
[150]	Zhang S, Yin L, Fang N. 2009. Focusing ultrasound with an acoustic metamaterial network. Physical Review letters, 102:1-4. http://d.scholar.cnki.net/detail/SJPD0711_U/SJPD12102102025793
[151]	Zhao H G, Liu Y Z, Wen J H, Yu D, Wang G, Wem X. 2006. Sound absorption of locally resonant sonic materials. Chinese Physics Letters, 23:2132-2134. doi: 10.1088/0256-307X/23/8/047
[152]	Zhao H, Liu Y, Yu D, Wen J, Wen X. 2007. Absorptive properties of three-dimensional phononic crystal.Journal of sound and vibration, 303:185-194. doi: 10.1016/j.jsv.2007.01.004
[153]	Zhao H, Wen J, Yang H, Lv L, Wen X. 2014. Backing effects on the underwater acoustic absorption of a viscoelastic slab with locally resonant scatterers. Applied Acoustics, 76:48-51. doi: 10.1016/j.apacoust.2013.07.022
[154]	Zhao H, Wen J, Yu D, Wen X. 2010. Low-frequency acoustic absorption of localized resonances:Experiment and theory. Journal of Applied Physics, 107:1-5. https://www.researchgate.net/publication/224110397_Low-frequency_acoustic_absorption_of_localized_resonances_Experiment_and_theory