Volume 52 Issue 3
Sep.  2022
Turn off MathJax
Article Contents
Yin J F, Cai L, Fang X, Xiao Y, Yang H B, Zhang H J, Zhong J, Zhao H G, Yu D L, Wen J H. Review on research progress of mechanical metamaterials and their applications in vibration and noise control . Advances in Mechanics, 2022, 52(3): 508-586 doi: 10.6052/1000-0992-22-005
Citation: Yin J F, Cai L, Fang X, Xiao Y, Yang H B, Zhang H J, Zhong J, Zhao H G, Yu D L, Wen J H. Review on research progress of mechanical metamaterials and their applications in vibration and noise control . Advances in Mechanics, 2022, 52(3): 508-586 doi: 10.6052/1000-0992-22-005

Review on research progress of mechanical metamaterials and their applications in vibration and noise control

doi: 10.6052/1000-0992-22-005
More Information
  • Mechanical metamaterials are man-made composite structures or materials constructed from artificial microstructural units with extraordinary static/dynamic properties not found in natural materials. Since these properties mainly depend on the microstructural units rather than the material components, this provides new design schemes for functional materials that allow us to manipulate mechanical properties to a larger extent. This paper first gives a brief introduction to the history, development, and main categories of mechanical materials, followed by their extraordinary mechanical properties. Then we mainly review the research progress and future trends on applications of mechanical metamaterials in underwater sound control, air-borne sound absorption/insulation, structural vibration, and impact control. Last but not least, several types of novel mechanical metamaterials are introduced to provide some reference for scientific researchers and engineers in related fields.

     

  • loading
  • 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: 383-434 (Chen Y, Liu X, Xiang P, Hu G. 2016. Pentamode material for underwater acoustic wave control. Advances in Mechanics, 46: 383-434). doi: 10.6052/1000-0992-16-010
    陈毅, 张泉, 张亚飞, 夏百战, 刘晓宁, 周萧明, 陈常青, 胡更开. 2021. 弹性拓扑材料研究进展. 力学进展, 51: 68 (Chen Y, Zhang Q, Xia B, Liu X, Zhou M, Chen C, Hu G. 2021. Research progress of elastic topological materials. Advances in Mechanics, 51: 68).
    丁昌林, 董仪宝, 赵晓鹏. 2018. 声学超材料与超表面研究进展. 物理学报, 67: 194301 (Ding C L, Dong Y B, Zhao X P. 2018. Research advances in acoustic metamaterials and metasurface. Acta Physica Sinica, 67: 194301). doi: 10.7498/aps.67.20180963
    黄凌志, 肖勇, 温激鸿, 杨海滨, 温熙森. 2015. 一种含横向圆柱形空腔的声学覆盖层的去耦机理分析. 物理学报, 64: 154301 (Huang L Z, Xiao Y, Wen J H, Yang H B, Wen X S. 2015. Analysis of decoupling mechanism of an acoustic coating layer with horizontal cylindrical cavities. Acta Physica Sinica, 64: 154301).
    季宏丽, 黄薇, 裘进浩, 成利. 2017. 声学黑洞结构应用中的力学问题. 力学进展, 47: 333-384 (Ji H L, Huang W, Qiu J H, Cheng L. 2017. Mechanics problems in application of acoustic black hole structures. Advances in Mechanics, 47: 333-384).
    季振林. 2016. 消声器声学理论与设计. 北京: 科学出版社

    Ji Z L. 2016. Theories and Design of the Acoustic Muffler. Beijing: Science Press
    吕林梅, 温激鸿, 赵宏刚, 孟浩, 温熙森. 2012. 内嵌不同形状散射子的局域共振型黏弹性覆盖层低频吸声性能研究. 物理学报, 61: 293-300 (Lü L M, Wen J H, Zhao H G, Meng H, Wen X S. 2012. Low-frequency acoustic absorption of viscoelastic coating with various shapes of scatterers. Acta Physica Sinica, 61: 293-300).
    钱德进, 贾地, 缪旭弘, 王雪仁. 2011. 隔声去耦瓦力学及声学性能研究//第十三届船舶水下噪声学术讨论会, 江西鹰潭

    Qian D J, Jia D, Miao X H, Wang X R. 2011. Research on mechanical and acoustic properties of sound insulation decoupling tile//The 13th Symposium on Navel Underwater Noise, Yingtan, Jiangxi, China.
    任晨辉, 杨德庆. 2020. 二维负刚度负泊松比超材料及其力学性能. 哈尔滨工程大学学报, 41: 1129-1135 (Ren C H, Yang D Q. 2020. Mechanical properties of a 2D metamaterial with negative stiffness and negative Poisson's ratio. Journal of Harbin Engineering University, 41: 1129-1135).
    王刚, 温激鸿, 温熙森, 郁殿龙, 刘耀宗. 2005. 细直梁弯曲振动中的局域共振带隙. 机械工程学报, 41: 107-110 (Wang G, Wen J H, Wen X S, Yu D L, Liu Y Z. 2005. Locally resonant elastic wave band gaps in flexural vibration of slender beam. Journal of Mechanical Engineering, 41: 107-110).
    王艳林, 王自东, 宋卓斐, 王强松. 2008. 潜艇管路系统振动噪声控制技术的现状与发展. 舰船科学技术, 30: 34-38 (Wang Y L, Wang Z D, Song Z F, Wang Q S. 2008. Review of vibration and noise control technology in piping system for submarnes. Ship Science and Technology, 30: 34-38).
    王育人, 缪旭弘, 姜恒, 陈猛, 刘宇, 徐文帅, 蒙丹. 2017. 水下吸声机理与吸声材料. 力学进展, 47: 121 (Wang Y R, Miao X H, Chen M, Liu Y, Xu W S, Huang D. 2017. Review on underwater sound absorption materials and mechanisms. Advances in Mechanics, 47: 121).
    温激鸿, 蔡力, 郁殿龙, 肖勇, 赵宏刚, 尹剑飞, 杨海滨. 2018. 声学超材料基础理论与应用. 北京: 科学出版社

    Wen J H, Cai L, Yu D L, Xiao Y, Zhao H G, Yin J F, Yang H B. 2018. Fundamental Theories and Applications of Acoustic Metamaterials. Beijing: Science Press
    吴九汇, 马富银, 张思文, 沈礼. 2016. 声学超材料在低频减振降噪中的应用评述. 机械工程学报, 52: 68-78 (Wu J H, Ma F Y, Zhang S W, Shen L. 2016. Application of acoustic metamaterials in low-frequency vibration and noise reduction. Journal Of Mechanical Engineering, 52: 68-78).
    夏进军, 李洁, 张雨萌, 张育新. 2021. 折纸结构及其特性的工程应用策略. 材料导报, 35: 11197-11208 (Xia J J, Li J, Zhang Y M, Zhang Y X. 2021. A tactical review of the engineering application of origami structure and its characteristics. Materials Reports, 35: 11197-11208).
    许浩, 李邦华. 2018. 舱室通风系统设计中的噪声控制. 船海工程, 47: 98-101 (Xu H, Li B H. 2018. Noise Control in Design of Cabin Ventilation System. Ship & Ocean Engineering, 47: 98-101).
    姚熊亮, 计方, 庞福振, 钱德进. 2009. 隔声去耦瓦声学性能研究//第十二届船舶水下噪声学术讨论会, 湖南长沙

    Yao X L, Ji F, Pang F Z, Qian D J. 2009. Research on acoustic performance of sound insulation decoupling tile. The 12th Symposium on Navel Underwater Noise, Changsha, Hunan, China.
    于靖军, 谢岩, 裴旭. 2018. 负泊松比超材料研究进展. 机械工程学报, 54: 1-14 (Yu J J, Xie Y, Pei X. 2018. State-of-art of Metamaterials with Negative Poisson’s Ratio. Journal of Mechanical Engineering, 54: 1-14).
    于相龙, 周济. 2016. 智能超材料研究与进展. 材料工程, 44: 119-128 (Yu X L, Zhou J. 2016. Research Advance in Smartmaterials. Journal of Materials Engineering, 44: 119-128).
    于相龙, 周济. 2019. 力学超材料的构筑及其超常新功能. 中国材料进展, 38: 14-21 (Yu X L, Zhou J. 2019. Mechanical metamaterials: architected materials and unexplored properties. Materials China, 38: 14-21).
    张燕妮, 陈克安, 郝夏影, 程营. 2020. 水声超材料研究进展. 科学通报, 65: 1396-1410 (Zhang Y N, Chen K A, Hao X Y, Cheng Y. 2020. A review of underwater acoustic metamaterials. Chinese Science Bulletin, 65: 1396-1410).
    张印, 尹剑飞, 温激鸿, 郁殿龙. 2016. 基于质量放大局域共振型声子晶体的低频减振设计. 振动与冲击, 35: 26-32 (Zhang Y, Yin J F, Wen J H, Yu D L. 2016. Low frequency vibration reduction design for inertial local resonance phononic crystals based on inertial amplification. Journal of Vibration and shock, 35: 26-32).
    赵宏刚. 2008. 基于声子晶体理论的水声吸声材料吸声特性研究[博士论文]. 长沙: 国防科技大学

    Zhao H G. 2008. Research on sound absorption characteristics of underwater sound absorbing materials based on phononic crystal theory[PhD Thesis]. Chang Sha: National University of Defense Technology
    赵伟佳, 王倚天, 朱睿, 胡更开, 胡海岩. 2020. 轻质嵌入式超结构的低频抑振研究. 中国科学:物理学 力学 天文学, 50: 162-175 (Zhao W J, Wang Y T, Zhu R Hu G K, Hu H Y. 2020. Isolating low-frequency vibration via lightweight embedded metastructures. Scientia Sinica Physica:Mechanica & Astronomica, 50: 162-175).
    郑周甫, 尹剑飞, 温激鸿, 郁殿龙. 2020. 基于声子晶体板的弹性波拓扑保护边界态. 物理学报, 69: 285-294 (Zheng Z F, Yin J F, Wen J H, Yu D L. 2020. Topologically protected edge states of elastic waves in phononic crystal plates. Acta Physica Sinica, 69: 285-294).
    Achilleos V, Richoux O, Theocharis G. 2016. Coherent perfect absorption induced by the nonlinearity of a Helmholtz resonator. The Journal of the Acoustical Society of America, 140: EL94. doi: 10.1121/1.4954869
    Akl W, Baz A. 2010. Multi-cell active acoustic metamaterial with programmable bulk modulus. Journal of Intelligent Material Systems and Structures, 21: 541-556. doi: 10.1177/1045389X09359434
    Alderson A. 1999. A triumph of lateral thought. Chemistry & Industry, 17: 384-391.
    Allard J F, Atalla N. 2009. Propagation of Sound in Porous Media: Modelling Sound Absorbing Materials. John Wiley & Sons.
    Ambati M, Fang N, Sun C, Zhang X. 2007. Surface resonant states and superlensing in acoustic metamaterials. Physical Review B, 75: 195447. doi: 10.1103/PhysRevB.75.195447
    An B H, Lee J W. 2021. Metamaterial-based muffler with broadband tunability in a limited space: Optimal design, theoretical investigation and experiment. International Journal of Mechanical Sciences, 205: 106594. doi: 10.1016/j.ijmecsci.2021.106594
    Ang L Y L, Koh Y K, Lee H P. 2017. Broadband sound transmission loss of a large-scale membrane-type acoustic metamaterial for low-frequency noise control. Applied Physics Letters, 111: 041903. doi: 10.1063/1.4995405
    Antoniadis I, Chronopoulos D, Spitas V, Koulocheris D. 2015. Hyper-damping properties of a stiff and stable linear oscillator with a negative stiffness element. Journal of Sound and Vibration, 346: 37-52. doi: 10.1016/j.jsv.2015.02.028
    Ashman R B, Rho J Y. 1988. Elastic modulus of trabecular bone material. Journal of Biomechanics, 21: 177-181. doi: 10.1016/0021-9290(88)90167-4
    Babaee S, Overvelde J T, Chen E R, Tournat V, Bertoldi K. 2016. Reconfigurable origami-inspired acoustic waveguides. Science Advances, 2: e1601019. doi: 10.1126/sciadv.1601019
    Bacquet C L, Al Ba Ba A H, Frazier M J, Nouh M, Hussein M I. 2018. Metadamping: dissipation emergence in elastic metamaterials. Advances in Applied Mechanics, 51: 115-164.
    Bae M H, Oh J H. 2020. Amplitude-induced bandgap: New type of bandgap for nonlinear elastic metamaterials. Journal of the Mechanics and Physics of Solids, 139: 103930. doi: 10.1016/j.jmps.2020.103930
    Baravelli E, Ruzzene M. 2013. Internally resonating lattices for bandgap generation and low-frequency vibration control. Journal of Sound and Vibration, 332: 6562-6579. doi: 10.1016/j.jsv.2013.08.014
    Battaglia P W, Hamrick J B, Bapst V, Sanchez-Gonzalez A, Zambaldi V, Malinowski M, Tacchetti A, Raposo D, Santoro A, Faulkner R. 2018. Relational inductive biases, deep learning, and graph networks. arXiv preprint, arXiv: 1806.01261.
    Bender C M, Boettcher S. 1998. Real spectra in non-Hermitan Hamiltonians having PT-symmetric. Physical Review Letters, 80: 5243-5246. doi: 10.1103/PhysRevLett.80.5243
    Bernard B P, Mazzoleni M J, Garraud N. 2014. Experimental investigation of bifurcation induced bandgap reconfiguration. Journal of Applied Physics, 116: 084904. doi: 10.1063/1.4894249
    Bertoldi K, Boyce M C. 2008. Mechanically triggered transformations of phononic band gaps in periodic elastomeric structures. Physical Review B, 77: 052105. doi: 10.1103/PhysRevB.77.052105
    Bertoldi K, Vitelli V, Christensen J, Van Hecke M. 2017. Flexible mechanical metamaterials. Nature Reviews Materials, 2: 17066. doi: 10.1038/natrevmats.2017.66
    Bi Y, Jia H, Sun Z, Yang Y, Zhao H, Yang J. 2018. Experimental demonstration of three-dimensional broadband underwater acoustic carpet cloak. Applied Physics Letters, 112: 223505. doi: 10.1063/1.5026199
    Boechler N, Theocharis G, Daraio C. 2011. Bifurcation-based acoustic switching and rectification. Nature Materials, 10: 665-658. doi: 10.1038/nmat3072
    Brillouin L. 1946. Wave Propagation in Periodic Structures. Dover.
    Bückmann T, Thiel M, Kadic M, Schittny R, Wegener M. 2014. An elasto-mechanical unfeelability cloak made of pentamode metamaterials. Nature Communications, 5: 4130. doi: 10.1038/ncomms5130
    Cabras L, Brun M. 2014. Auxetic two-dimensional lattices with Poisson's ratio arbitrarily close to -1. Proceedings of the Royal Society A:Mathematical, Physical and Engineering Sciences, 470: 20140538. doi: 10.1098/rspa.2014.0538
    Caddock B D, Evans K E. 1989. Microporous materials with negative Poisson's ratios. I. Microstructure and mechanical properties. Journal of Physics D:Applied Physics, 22: 1877.
    Cai C, Zhou J, Wu L, Wang K, Xu D, Ouyang H. 2020. Design and numerical validation of quasi-zero-stiffness metamaterials for very low-frequency band gaps. Composite Structures, 236: 111862. doi: 10.1016/j.compstruct.2020.111862
    Cai L, Wen J, Yu D, Lu Z, Chen X, Zhao X. 2017. Beam steering of the acoustic metasurface under a subwavelength periodic modulation. Applied Physics Letters, 110: 201902. doi: 10.1063/1.4983643
    Cai L, Wen J, Yu D, Lu Z, Chen X, Zhao X. 2018. Anomalous wavefront manipulation and broadband sound absorption by metasurfaces with periodic subwavelength modulation. AIP Advances, 8: 095214. doi: 10.1063/1.5020378
    Cai X, Guo Q, Hu G, Yang J. 2014. Ultrathin low-frequency sound absorbing panels based on coplanar spiral tubes or coplanar Helmholtz resonators. Applied Physics Letters, 105: 121901. doi: 10.1063/1.4895617
    Carrella A, Brennan M J, Waters T P. 2007. Static analysis of a passive vibration isolator with quasi-zero-stiffness characteristic. Journal of Sound and Vibration, 301: 678-689. doi: 10.1016/j.jsv.2006.10.011
    Challapalli A, Patel D, Li G. 2021. Inverse machine learning framework for optimizing lightweight metamaterials. Materials & Design, 208: 109937.
    Chang H, Liu L, Zhang C, Hu X. 2018. Broadband high sound absorption from labyrinthine metasurfaces. AIP Advances, 8: 045115. doi: 10.1063/1.5024303
    Chaplain G J, De Ponti J M, Aguzzi G, Colombi A, Craster R V. 2020. Topological rainbow trapping for elastic energy harvesting in graded Su-Schrieffer-Heeger systems. Physical Review Applied, 14: 054035.
    Chen G, Cheng Y, Zhang P, Cai S, Liu J. 2021. Blast resistance of metallic double arrowhead honeycomb sandwich panels with different core configurations under the paper tube-guided air blast loading. International Journal of Mechanical Sciences, 201: 106457. doi: 10.1016/j.ijmecsci.2021.106457
    Chen H, Chan C T. 2007. Acoustic cloaking in three dimensions using acoustic metamaterials. Applied Physics Letters, 91: 183518. doi: 10.1063/1.2803315
    Chen H, Li X P, Chen Y Y, Huang G L. 2017b. Wave propagation and absorption of sandwich beams containing interior dissipative multi-resonators. Ultrasonics, 76: 99-108. doi: 10.1016/j.ultras.2016.12.014
    Chen M, Meng D, Zhang H, Jiang H, Wang Y. 2016a. 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
    Chen S, Wang G, Wen J, Wen X. 2013. Wave propagation and attenuation in plates with periodic arrays of shunted piezo-patches. Journal of Sound and Vibration, 332: 1520-1532. doi: 10.1016/j.jsv.2012.11.005
    Chen Y, Zheng M, Liu X, Bi Y, Sun Z, Xiang P, Yang J, Hu G. 2017a. Broadband solid cloak for underwater acoustics. Physical Review B, 95: 180104. doi: 10.1103/PhysRevB.95.180104
    Chen Y, Zhao B, Liu X, Hu G. 2020. Highly anisotropic hexagonal lattice material for low frequency water sound insulation. Extreme Mechanics Letters, 40: 100916. doi: 10.1016/j.eml.2020.100916
    Chen Y Y, Barnhart M V, Chen J K, Hu G K, Sun C T, Huang G L. 2016b. Dissipative elastic metamaterials for broadband wave mitigation at subwavelength scale. Composite Structures, 136: 358-371. doi: 10.1016/j.compstruct.2015.09.048
    Cheng Y, Fan Y, Jian Y X, Xiao J L. 2008. A multilayer structured acoustic cloak with homogeneous isotropic materials. Applied Physics Letters, 92: 151913. doi: 10.1063/1.2903500
    Chong Y D, Ge L, Stone A D. 2011. Pt-symmetry breaking and laser-absorber modes in optical scattering systems. Physical Review Letters, 106: 093902. doi: 10.1103/PhysRevLett.106.093902
    Christensen J, Martin-Moreno L, Garcia-Vidal F J. 2008. Theory of resonant acoustic transmission through subwavelength apertures. Physical Review Letters, 101: 014301. doi: 10.1103/PhysRevLett.101.014301
    Christensen J, Marti M L, Garci V F. 2010. Enhanced acoustical transmission and beaming effect through a single aperture. Physical Review B, 81: 174104. doi: 10.1103/PhysRevB.81.174104
    Christensen J, de Abajo F J G I. 2012. Negative refraction and backward waves in layered acoustic metamaterials. Physical Review B, 86: 024301. doi: 10.1103/PhysRevB.86.024301
    Christensen R M. 2012. Mechanics of Composite Materials. Massachusetts: Courier Corporation.
    Cohen N, Shashua A. 2016. Inductive bias of deep convolutional networks through pooling geometry. arXiv preprint, arXiv: 1605.06743, 2016.
    Correa D M, Klatt T, Cortes S, Haberman M, Kovar D, Seepersad C. 2015. Negative stiffness honeycombs for recoverable shock isolation. Rapid Prototyping Journal, 21: 193-200. doi: 10.1108/RPJ-12-2014-0182
    Correa-Baena J, Hippalgaonkar K, van Duren J, Jaffer S, Chandrasekhar V R, Stevanovic V, Wadia C, Guha S, Buonassisi T. 2018. Accelerating materials development via automation, machine learning, and high-performance computing. Joule, 2: 1410-1420. doi: 10.1016/j.joule.2018.05.009
    Coulais C, Teomy E, De Reus K, Shokef Y, Van Hecke M. 2016. Combinatorial design of textured mechanical metamaterials. Nature, 535: 529-532. doi: 10.1038/nature18960
    Cretegny T, Dauxois T, Ruffo S, Torcini A. 1998. Localization and equipartition of energy in the β-fpu chain: chaotic breathers. Physica D-Nonlinear Phenomena, 121: 109-126. doi: 10.1016/S0167-2789(98)00107-9
    Cummer S A, Schurig D. 2007. One path to acoustic cloaking. New Journal of Physics, 9: 45. doi: 10.1088/1367-2630/9/3/045
    Cummer S A, Popa B I, Schurig D, Smith D R, Pendry J, Rahm M, Starr A. 2008. Scattering theory derivation of a 3d acoustic cloaking shell. Physical Review Letters, 2: 024301.
    Daraio C, Nesterenko V F, Herbold E B, Jin S. 2005. Strongly nonlinear waves in a chain of teflon beads. Physical Review E, 72: 016603. doi: 10.1103/PhysRevE.72.016603
    Daraio C, Nesterenko V, Herbold E, Jin S. 2006. Tunability of solitary wave properties in one-dimensional strongly nonlinear phononic crystals. Physical Review E, 73: 026610. doi: 10.1103/PhysRevE.73.026610
    De Espinosa F M, Jimenez E, Torres M. 1998. Ultrasonic band gap in a periodic two-dimensional composite. Physical Review Letters, 6: 1208.
    de Melo Filho N G R, Van Belle L, Claeys C, Deckers E, Desmet W. 2019. Dynamic mass based sound transmission loss prediction of vibro-acoustic metamaterial double panels applied to the mass-air-mass resonance. Journal of Sound and Vibration, 442: 28-44. doi: 10.1016/j.jsv.2018.10.047
    Depauw D, Al Ba Ba A H, Nouh M. 2018. Metadamping and energy dissipation enhancement via hybrid phononic resonators. Extreme Mechanics Letters, 18: 36-44. doi: 10.1016/j.eml.2017.11.002
    Ding Y, Liu Z, Qiu C, Shi J. 2007. Metamaterial with simultaneously negative bulk modulus and mass density. Physical Review Letters, 9: 093904.
    Donda K, Zhu Y, Merkel A, Fan S, Cao L, Wan S, Assouar B. 2021. Ultrathin acoustic absorbing metasurface based on deep learning approach. Smart Materials and Structures, 30: 085003. doi: 10.1088/1361-665X/ac0675
    Dong Z, Li Y, Zhao T, Wu W, Xiao D, Liang J. 2019. Experimental and numerical studies on the compressive mechanical properties of the metallic auxetic reentrant honeycomb. Materials & Design, 182: 108036.
    Duan M, Yu C, Xin F, Lu T J. 2021. Tunable underwater acoustic metamaterials via quasi-Helmholtz resonance: from low-frequency to ultra-broadband. Applied Physics Letters, 118: 071904. doi: 10.1063/5.0028135
    Duan Y, Luo J, Wang G, Hang Z H, Hou B, Li J, Sheng P, Lai Y. 2015. Theoretical requirements for broadband perfect absorption of acoustic waves by ultra-thin elastic meta-films. Scientific Reports, 5: 12139. doi: 10.1038/srep12139
    Evans K E, Caddock B D. 1989. Microporous materials with negative poisson's ratios. Ii. Mechanisms and interpretation. Journal of Physics D:Applied Physics, 12: 1883.
    Fan H, Xia B, Tong L, Zheng S, Yu D. 2019. Elastic higher-order topological insulator with topologically protected corner states. Physical Review Letters, 122: 204301. doi: 10.1103/PhysRevLett.122.204301
    Fan H, Yang L, Tian Y, Wang Z. 2020. Design of metastructures with quasi-zero dynamic stiffness for vibration isolation. Composite Structures, 243: 112244. doi: 10.1016/j.compstruct.2020.112244
    Fang N, Lee H, Sun C, Zhang X. 2005. Sub-diffraction-limited optical imaging with a silver superlens. Science, 308: 534. doi: 10.1126/science.1108759
    Fang N, Xi D, Xu J, Ambati M, Strituravanich W, Sun C, Zhang X. 2006. Ultrasonic metamaterials with negative modulus. Nature Materials, 5: 452-456. doi: 10.1038/nmat1644
    Fang X, Wen J, Yin J, Yu D, Xiao Y. 2016. Broadband and tunable one-dimensional strongly nonlinear acoustic metamaterials: theoretical study. Physical Review E, 95: 052206. doi: 10.1103/PhysRevE.94.052206
    Fang X, Wen J, Bonello B, Yin J, Yu D. 2017a. Wave propagation in one-dimensional nonlinear acoustic metamaterials. New Journal of Physics, 19: 053007. doi: 10.1088/1367-2630/aa6d49
    Fang X, Wen J, Bonello B, Yin J, Yu D. 2017b. Ultra-low and ultra-broad-band nonlinear acoustic metamaterials. Nature Communications, 8: 1288.
    Fang X, Wen J, Yu D, Yin J. 2018a. Bridging-coupling band gaps in nonlinear acoustic metamaterials. Physical Review Applied, 10: 054049.
    Fang X, Wen J, Yu D, Huang G, Yin J. 2018b. Wave propagation in a nonlinear acoustic metamaterial beam considering third harmonic generation. New Journal of Physics, 20: 123028.
    Fang X, Wen J, Benisty H, Yu D. 2020. Ultrabroad acoustical limiting in nonlinear metamaterials due to adaptive-broadening band-gap effect. Physical Review B, 101: 104304.
    Fang X, Wen J, Cheng L, Li B. 2021. Bidirectional elastic diode with frequency-preserved nonreciprocity. Physical Review Applied, 15: 054022.
    Fedus W, Rosca M, Lakshminarayanan B, Dai A M, Mohamed S and Goodfellow I. 2017. Many paths to equilibrium: gans do not need to decrease a divergence at every step. arXiv preprint, arXiv: 1710.08446.
    Fermi E, Pasta J, Ulam S. 1955. Studies of the nonlinear problems. Los Alamos National Lab (LANL), Los Alamos, NM (United States).
    Fleury R, Sounas D, Alu A. 2015. An invisible acoustic sensor based on parity-time symmetry. Nature Communications, 6: 5905. doi: 10.1038/ncomms6905
    Flores-Méndez J, Pérez-Rodríguez F. 2013. Metasolid with anisotropic mass density. Europhysics Letters, 103: 54001.
    Florijn B, Coulais C, van Hecke M. 2014. Programmable mechanical metamaterials. Physical Review Letters, 113: 175503.
    Frenzel T, Kadic M, Wegener M. 2017. Three-dimensional mechanical metamaterials with a twist. Science, 358: 1072-1074.
    Gallavotti G. 2008. The Fermi-pasta-ulam Problem: A Status Report. Springer.
    Ganesh R, Gonella S. 2015. From modal mixing to tunable functional switches in nonlinear phononic crystals. Physical Review Letters, 114: 054302. doi: 10.1103/PhysRevLett.114.054302
    Gao N, Zhang Y. 2018. A low frequency underwater metastructure composed by helix metal and viscoelastic damping rubber. Joural of Vibration and Control, 25: 538-548.
    Gao N, Wei Z, Zhang R, Hou H. 2019. Low-frequency elastic wave attenuation in a composite acoustic black hole beam. Applied Acoustics, 154: 68-76. doi: 10.1016/j.apacoust.2019.04.029
    Gao N, Lu K. 2020. An underwater metamaterial for broadband acoustic absorption at low frequency. Applied Acoustics, 169: 107500.
    Gao N, Zhang Z, Tang L, Hou H, Chen K. 2021. Optimal design of broadband quasi-perfect sound absorption of composite hybrid porous metamaterial using tlbo algorithm. Applied Acoustics, 183: 108296.
    Garcia-Chocano V M, Cabrera S, Sanchez-Dehesa J. 2012. Broadband sound absorption by lattices of microperforated cylindrical shells. Applied Physics Letters, 101: 184101.
    Garcia-Vidal F J, Pitarke J M, Pendry J B. 1998. Silver-filled carbon nanotubes used as spectroscopic enhancers. Physical Review B, 58: 6783.
    Gatt R, Wood M V, Gatt A, Zarb F, Formosa C, Azzopardi K M, Casha A, Agius T P, Schembri-Wismayer P, Attard L, et al. 2015. Negative Poisson’s ratios in tendons: an unexpected mechanical response. Acta Biomaterialia, 24: 201-208. doi: 10.1016/j.actbio.2015.06.018
    Geniet F, Leon J. 2002. Energy transmission in the forbidden band gap of a nonlinear chain. Physical Review Letters, 89: 134102. doi: 10.1103/PhysRevLett.89.134102
    Ghaffarivardavagh R, Nikolajczyk J, Anderson S, Zhang X. 2019. Ultra-open acoustic metamaterial silencer based on fano-like interference. Physical Review B, 99: 024302.
    Gibson L J, Ashby M F. 1999. Cellular Solids: Structure and Properties. Cambridge University Press.
    Gonella S, Ruzzene M. 2008. Analysis of in-plane wave propagation in hexagonal and re-entrant lattices. Journal of Sound and Vibration, 312: 125-139.
    Gong J, Wang Q. 2010. Geometric phase in pt-symmetric quantum mechanics. Physical Review a, 82: 012103.
    Goodfellow I, Pouget-Abadie J, Mirza M, Xu B, Warde-Farley D, Ozair S, Courville A, Bengio Y. 2014. Generative adversarial nets. Advances in Neural Information Processing Systems, 27: 2672-2680.
    Greaves G N, Greer A L, Lakes R S and Rouxel T. 2011. Poisson's ratio and modern materials. Nature Materials, 823-837.
    Groby J P, Dazel O, Duclos A, Boeckx L, Kelders L. 2011. Enhancing the absorption coefficient of a backed rigid frame porous layer by embedding circular periodic inclusions. The Journal of the Acoustical Society of America, 130: 3771-3780.
    Gu Y, Zhong H, Bao B, Wang Q and Wu J. 2021. Experimental investigation of underwater locally multi-resonant metamaterials under high hydrostatic pressure for low frequency sound absorption. Applied Acoustics, 172: 107605. doi: 10.1016/j.apacoust.2020.107605
    Guenneau S, Movchan A, Pétursson G, Ramakrishna S A. 2007. Acoustic metamaterials for sound focusing and confinement. New Journal of Physics, 9: 399.
    Guo Z, Hu G, Sorokin V, Tang L, Yang X, Zhang J. 2021. Low-frequency flexural wave attenuation in metamaterial sandwich beam with hourglass lattice truss core. Wave Motion, 104: 102750. doi: 10.1016/j.wavemoti.2021.102750
    Gupta G S. 1970. Natural flexural waves and the normal modes of periodically-supported beams and plates. Journal of Sound and Vibration, 13: 89-101.
    Gupta G S. 1971. Natural frequencies of periodic skin-stringer structures using a wave approach. Journal of Sound and Vibration, 16: 567-580.
    Gupta G S. 1972. Propagation of flexural waves in doubly-periodic structures. Journal of Sound and Vibration, 20: 39-49.
    Harne R L, Lynd D T. 2016. Origami acoustics: using principles of folding structural acoustics for simple and large focusing of sound energy. Smart Materials and Structures, 25: 085031.
    Hashimoto N, Katsura M, Yasuoka M, Fujii H. 1991. Sound insulation of a rectangular thin membrane with additional weights. Applied Acoustics, 33: 21-43.
    He C, Ni X, Ge H, Sun X, Chen Y, Lu M, Liu X, Chen Y. 2016b. Acoustic topological insulator and robust one-way sound transport. Nature Physics, 12: 1124-1129. doi: 10.1038/nphys3867
    He K, Zhang X, Ren S, Sun J. 2016a. Deep residual learning for image recognition//Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, 770-778.
    He Z, Wang Y, Wang Y. 2019. Active feedback control on sound radiation of elastic wave metamaterials. International Journal of Mechanical Sciences, 195: 106221.
    He Z, Wang Y, Wang Y. 2020a. External mean flow on sound radiation of active mechanical metamaterials. Aiaa Journal, 58: 4751-4763.
    He Z, Wang Y, Wang Y. 2021. Sound transmission tuned by active feedback control attached to elastic wave metamaterials immersed in water. Journal of Applied Mechanics, 88: 1-28.
    Hewage T A, Alderson K L, Alderson A, Scarpa F. 2016. Double-negative mechanical metamaterials displaying simultaneous negative stiffness and negative Poisson's ratio properties. Advanced Materials, 28: 10323-10332. doi: 10.1002/adma.201603959
    Hou X, Deng Z, Zhang K. 2016. Dynamic crushing strength analysis of auxetic honeycombs. Acta Mechanica Solida Sinica, 5: 490-501.
    Hu X, Shen Y, Liu X, Fu R, Zi J. 2004. Superlensing effect in liquid surface waves. Physical Review E, 69: 30201.
    Huang G L, Sun C T. 2010. Band gaps in a multiresonator acoustic metamaterial. Journal of Vibration and Acoustics, 132: 031003.
    Huang H H, Sun C T. 2011. Locally resonant acoustic metamaterials with 2d anisotropic effective mass density. Philosophical Magazine, 91: 981-996.
    Huang L, Xiao Y, Wen J, Yang H, Wen X. 2016. Analysis of underwater decoupling properties of a locally resonant acoustic metamaterial coating. Chinese Physics B, 25: 024302.
    Huang S, Fang X, Wang X, Assouar B, Cheng Q, Li Y. 2019a. Acoustic perfect absorbers via Helmholtz resonators with embedded apertures. The Journal of the Acoustical Society of America, 145: 254-262.
    Huang S, Zhou Z, Li D, Liu T, Wang X, Zhu J, Li Y. 2019b. Compact broadband acoustic sink with coherently coupled weak resonances. Science Bulletin, 65: 373-379.
    Hussein M I, Frazier M J. 2013. Metadamping: an emergent phenomenon in dissipative metamaterials. Journal of Sound and Vibration, 332: 4767-4774.
    Hussein M I, Leamy M J, Ruzzene M. 2014. Dynamics of phononic materials and structures: historical origins, recent progress, and future outlook. Applied Mechanics Reviews, 66: 040802. doi: 10.1115/1.4026911
    Imbalzano G, Tran P, Ngo T D, Lee P V S. 2017. Three-dimensional modelling of auxetic sandwich panels for localised impact resistance. Journal of Sandwich Structures & Materials, 19: 291-316.
    Imbalzano G, Linforth S, Ngo T D, Lee P V S, Tran P. 2018. Blast resistance of auxetic and honeycomb sandwich panels: comparisons and parametric designs. Composite Structures, 183: 242-261. doi: 10.1016/j.compstruct.2017.03.018
    Ivansson S M. 2012. Anechoic coatings obtained from two- and three-dimensional monopole resonance diffraction gratings. Journal of the Acoustical Society of America, 131: 2622-2637.
    Ji J C, Luo Q, Ye K. 2021. Vibration control based metamaterials and origami structures: a state-of-the-art review. Mechanical Systems and Signal Processing, 161: 107945. doi: 10.1016/j.ymssp.2021.107945
    Jiang H, Wang Y, Milin Z, 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
    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
    Jiao P, Alavi A H. 2021. Artificial intelligence-enabled smart mechanical metamaterials: advent and future trends. International Materials Reviews, 66: 1-29.
    Jiao W, Gonella S. 2019. Doubly nonlinear waveguides with self-switching functionality selection capabilities. Physical Review E, 99: 042206.
    Jiménez N, Huang W, Romero-García V, Pagneux V, Groby J P. 2016. Ultra-thin metamaterial for perfect and quasi-omnidirectional sound absorption. Applied Physics Letters, 109: 121902.
    Jin G, Shi K, Ye T, Zhou J, Yin Y. 2020. Sound absorption behaviors of metamaterials with periodic multi-resonator and voids in water. Applied Acoustics, 166: 107351. doi: 10.1016/j.apacoust.2020.107351
    Jin X, Wang Z, Ning J, Xiao G, Liu E, Shu X. 2016. Dynamic response of sandwich structures with graded auxetic honeycomb cores under blast loading. Composites Part B:Engineering, 106: 206-217. doi: 10.1016/j.compositesb.2016.09.037
    Jones R M. 2014. Mechanics of Composite Materials. CRC Press.
    Junca S, Lombard B. 2020. Analysis of a sugimoto model of nonlinear acoustics in an array of helmholtz resonators. Siam Journal on Applied Mathematics, 80: 1704-1722.
    Kadic M, Bückmann T, Schittny R, Gumbsch P, Wegener M. 2014. Pentamode metamaterials with independently tailored bulk modulus and mass density. Physical Review Applied, 2: 054007.
    Kafesaki M, Penciu R S, Economou E N. 2000. Air bubbles in water: a strongly multiple scattering medium for acoustic waves. Physical Review Letters, 84: 6050.
    Kamrava S, Mousanezhad D, Ebrahimi H, Ghosh R, Vaziri A. 2017. Origami-based cellular metamaterial with auxetic, bistable, and self-locking properties. Scientific Reports, 7: 46046. doi: 10.1038/srep46046
    Ke M, Liu Z, Qiu C, Wang W, Shi J, Wen W, Sheng P. 2005. Negative-refraction imaging with two-dimensional phononic crystals. Physical Review B, 72: 064306.
    Keskar N R, Chelikowsky J R. 1992. Negative Poisson ratios in crystalline SiO2 from first-principles calculations. Nature, 358: 222-224.
    Kim H, Ma P, Kim B, Kim S and Lee S. 2019. Low-frequency sound absorption of elastic micro-perforated plates in a parallel arrangement. Journal of Sound and Vibration, 460: 114884. doi: 10.1016/j.jsv.2019.114884
    Kim S, Kim Y, Jang J. 2006. A theoretical model to predict the low-frequency sound absorption of a Helmholtz resonator array. The Journal of the Acoustical Society of America, 119: 1933-1936.
    Klatt T, Haberman M R. 2013. A nonlinear negative stiffness metamaterial unit cell and small-on-large multiscale material model. Journal of Applied Physics, 114: 167-207.
    Kolken H M, Zadpoor A A. 2017. Auxetic mechanical metamaterials. RSC Advances, 9: 5111-5129.
    Krizhevsky A, Sutskever I and Hinton G E. 2017. Imagenet classification with deep convolutional neural networks. Advances in Neural Information Processing Systems, 60: 84-90.
    Kumar S, Lee H P. 2020. Labyrinthine acoustic metastructures enabling broadband sound absorption and ventilation. Applied Physics Letters, 116: 134103. doi: 10.1063/5.0004520
    Kumar S, Xiang T B, Lee H P. 2020. Ventilated acoustic metamaterial window panels for simultaneous noise shielding and air circulation. Applied Acoustics, 159: 107088. doi: 10.1016/j.apacoust.2019.107088
    Kushwaha M S, Halevi P, Dobrzynski L and Djafari-Rouhani B. 1993. Acoustic band structure of periodic elastic composites. Physical Review Letters, 71: 2022-2025.
    Kushwaha M S, Halevi P. 1996. Giant acoustic stop bands in two-dimensional periodic arrays of liquid cylinders. Applied Physics Letters, 69: 31-33.
    Kushwaha M S. 1997. Stop-bands for periodic metallic rods: sculptures that can filter the noise. Applied Physics Letters, 70: 3218-3220.
    Lagarrigue C, Groby J P, Tournat V, Dazel O, Umnova O. 2013. Absorption of sound by porous layers with embedded periodic arrays of resonant inclusions. The Journal of the Acoustical Society of America, 134: 4670-4680.
    Lagarrigue C, Groby J P, Daze O, Tournat V. 2016. Design of metaporous supercells by genetic algorithm for absorption optimization on a wide frequency band. Applied Acoustics, 102: 49-54. doi: 10.1016/j.apacoust.2015.09.011
    Lakes R. 1987. Foam structures with a negative Poisson's ratio. Science, 235: 1038-1041. doi: 10.1126/science.235.4792.1038
    Lakes R, Wojciechowski K W. 2008. Negative compressibility, negative Poisson's ratio, and stability. Physica Status Solidi (B), 245: 545-551.
    Lakes R S, Lee T, Bersie A, Wang Y. 2001a. Extreme damping in composite materials with negative-stiffness inclusions. Nature, 410: 565-567.
    Lakes R S. 2001b. Extreme damping in composite materials with a negative stiffness phase. Physical Review Letters, 86: 2897-2900.
    Langfeldt F, Hoppen H and Gleine W. 2020. Broadband low-frequency sound transmission loss improvement of double walls with Helmholtz resonators. Journal of Sound and Vibration, 476: 115309. doi: 10.1016/j.jsv.2020.115309
    Lau S, Zhu X and Lu Z. 2021. Enhancing the acoustic absorption of vegetation with embedded periodic metamaterials. Applied Acoustics, 171: 107576.
    Lee E H, Yang W H. 1973. On waves in composite materials with periodic structure. Siam Journal on Applied Mathematics, 25: 492-499.
    Lee J B, Peng S, Yang D, Roh Y H, Funabashi H, Park N, Rice E J, Chen L, Long R, Wu M, Luo D. 2012. A mechanical metamaterial made from a dna hydrogel. Nature Nanotechnology, 7: 816-820.
    Lee S H, Park C M, Seo Y M, Wang Z G, Kim C K. 2009a. Acoustic metamaterial with negative density. Physics Letters A, 373: 4464-4469.
    Lee S H, Park C M, Seo Y M, Wang Z G, Kim C K. 2009b. Acoustic metamaterial with negative modulus. Journal of Physics:Condensed Matter, 21: 175704.
    Lee S H, Park C M, Seo Y M, Wang Z G, Kim C K. 2010. Composite acoustic medium with simultaneously negative density and modulus. Physical Review Letters, 104: 054301. doi: 10.1103/PhysRevLett.104.054301
    Lee T, Nomura T, Dede E M, Iizuka H. 2020. Asymmetric loss-induced perfect sound absorption in duct silencers. Applied Physics Letters, 116: 214101.
    Lees C, Vincent J F, Hillerton J E. 1991. Poisson's ratio in skin. Bio-Medical Materials and Engineering, 1: 19-23. doi: 10.3233/BME-1991-1104
    Li H, Li Y, Li J. 2020. Negative stiffness devices for vibration isolation applications: a review. Advances in Structural Engineering, 23: 1739-1755.
    Li H, Hu Y, Huang H, Chen J, Zhao M, Li B. 2021b. Broadband low-frequency vibration attenuation in 3d printed composite meta-lattice sandwich structures. Composites Part B:Engineering, 215: 108772. doi: 10.1016/j.compositesb.2021.108772
    Li J, Chan C T. 2004. Double-negative acoustic metamaterial. Physical Review E, 70: 055602(R). doi: 10.1103/PhysRevE.70.055602
    Li J, Wang W, Xie Y, Popa B, Cummer S A. 2016. A sound absorbing metasurface with coupled resonators. Applied Physics Letters, 109: 091908.
    Li L, Zheng B, Zhong L, Yang J, Liang B, Cheng J. 2018. Broadband compact acoustic absorber with high-efficiency ventilation performance. Applied Physics Letters, 113: 103501.
    Li Y, Liang B, Gu Z M, Zou X Y, Cheng J C. 2013. Reflected wavefront manipulation based on ultrathin planar acoustic metasurfaces. Scientific Reports, 3: 1-6.
    Li Z, Wang Z, Guo Z, Wang X, Liang X. 2021a. Ultra-broadband sound absorption of a hierarchical acoustic metamaterial at high temperatures. Applied Physics Letters, 118: 161903.
    Liang Z, Li J. 2012. Extreme acoustic metamaterial by coiling up space. Physical Review Letters, 108: 114301.
    Lin Z, Ramezani H, Eichelkraut T, Kottos T, Cao H and Christodoulides D N. 2011. Unidirectional invisibility induced by PT-symmetric periodic structures. Physical Review Letters, 106: 213901. doi: 10.1103/PhysRevLett.106.213901
    Liu B, Jiang Y. 2018. Controllable asymmetric transmission via gap-tunable acoustic metasurface. Applied Physics Letters, 112: 173503.
    Liu C, Bai Y, Zhou J, Zhao Q, Yang Y, Chen H, Qiao L. 2019. High-performance bifunctional polarization switch chiral metamaterials by inverse design method. npj Computational Materials, 5: 1-8.
    Liu C, Shi J, Zhao W, Zhou X, Ma C, Peng R, Wang M, Hang Z H, Liu X, Christensen J, Fang N X, Lai Y. 2021a. Three-dimensional soundproof acoustic metacage. Physical Review Letters, 127: 084301. doi: 10.1103/PhysRevLett.127.084301
    Liu E, Fang X, Wen J. 2021b. Harmonic and shock wave propagation in bistable periodic structure: regularity, randomness, and tunability. Journal of Vibration and Control, 107754632110310.
    Liu J, Yu D, Yang H, Shen H, Wen J. 2020b. Effect of mean flow on acoustic wave propagation in a duct with a periodic array of Helmholtz resonators. Chinese Physics Letters, 37: 034301.
    Liu L, Chang H, Zhang C, Hu X. 2017. Single-channel labyrinthine metasurfaces as perfect sound absorbers with tunable bandwidth. Applied Physics Letters, 111: 083503.
    Liu C R, Wu J H, Yang Z, Ma F Y. 2020. Ultra-broadband acoustic absorption of a thin microperforated panel metamaterial with multi-order resonance. Composite Structures, 246: 112366. doi: 10.1016/j.compstruct.2020.112366
    Liu X, Hu G, Huang G, Sun C. 2011a. An elastic metamaterial with simultaneously negative mass density and bulk modulus. Applied Physics Letters, 98: 251907.
    Liu X N, Hu G K, Sun C T, Huang G L. 2011b. Wave propagation characterization and design of two-dimensional elastic chiral metacomposite. Journal of Sound and Vibration, 330: 2536-2553.
    Liu Y, Du J, Cheng L. 2020a. Bandgap formation under temperature-induced quasi-periodicity in an acoustic duct with flexible walls. Journal of Sound and Vibration, 486: 115615. doi: 10.1016/j.jsv.2020.115615
    Liu Z Y, Zhang X X, Mao Y W, Zhu Y Y, Yang Z Y, Chan C T, Sheng P. 2000. Locally resonant sonic materials. Science, 289: 1734-1736.
    Long H, Liu C, Shao C, Cheng Y, Tao J, Qiu X, Liu X. 2020. Tunable and broadband asymmetric sound absorptions with coupling of acoustic bright and dark modes. Journal of Sound and Vibration, 479: 115371. doi: 10.1016/j.jsv.2020.115371
    Lu H, Wang X, Chen T. 2021. In-plane dynamics crushing of a combined auxetic honeycomb with negative Poisson's ratio and enhanced energy absorption. Thin-Walled Structures, 160: 107366. doi: 10.1016/j.tws.2020.107366
    Lu Z, Yu X, Lau S, Khoo B C, Cui F. 2020. Membrane-type acoustic metamaterial with eccentric masses for broadband sound isolation. Applied Acoustics, 157: 107003. doi: 10.1016/j.apacoust.2019.107003
    Luo C, Johnson S G, Joannopoulos J D, Pendry J B. 2003. Subwavelength imaging in photonic crystals. Physical Review B, 68: 045115.
    Ma G, Yang M, Xiao S, Yang Z, Sheng P. 2014. Acoustic metasurface with hybrid resonances. Nature Materials, 13: 873-878.
    Maa D. 1998. Potential of microperforated panel absorber. The Journal of the Acoustical Society of America, 104: 2861-2866.
    Mao D, Wang X, Li Y and, Dong R. 2021. Ultrabroadband acoustic ventilation barriers via hybrid-functional metasurfaces. Physical Review Applied, 15: 024044.
    Mao Y, He Q, Zhao X. 2020. Designing complex architectured materials with generative adversarial networks. Science Advances, 6: eaaz4169.
    Martin A, Kadic M, Schittny R, Bückmann T, Wegener M. 2012. Phonon band structures of three-dimensional pentamode metamaterials. Physical Review B, 86: 155116.
    Martinez-Sala R, Sancho J, Sanchez J V, Gomez V, Llinares J, Meseguer F. 1995. Sound attenuation by sculpture. Nature, 378: 241-241.
    Mead D J. 1971. Vibration response and wave propagation in periodic structures. Journal of Engineering for Industry, 93: 783-792. doi: 10.1115/1.3428014
    Mead D M. 1996. Wave propagation in continuous periodic structures: research contributions from Southampton, 1964-1995. Journal of Sound and Vibration, 190: 495-524.
    Meaud J, Che K. 2017. Tuning elastic wave propagation in multistable architected materials. International Journal of Solids and Structures, 122: 69-80.
    Mei J, Ma G, Yang M, Yang Z, Wen W, Sheng P. 2012. Dark acoustic metamaterials as super absorbers for low-frequency sound. Nature Communications, 1: 1-7. doi: 10.1038/ncomms1758
    Meloni M, Cai J, Zhang Q, Sang-Hoon Lee D, Li M, Ma R, Parashkevov T E, Feng J. 2021. Engineering origami: a comprehensive review of recent applications, design methods, and tools. Advanced Science, 8: 2000636. doi: 10.1002/advs.202000636
    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.
    Milton G W. 1992. Composite materials with Poisson's ratios close to−1. Journal of the Mechanics and Physics of Solids, 40: 1105-1137.
    Milton G W, Cherkaev A V. 1995. Which elasticity tensors are realizable. Journal of Engineering Materials & Technology, 117: 483-493.
    Milton G W. 2004. The Theory of Composites. Cambridge University Press.
    Milton G W, Briane M, Willis J R. 2006. On cloaking for elasticity and physical equations with a transformation invariant form. New Journal of Physics., 8: 248.
    Milton G W. 2013. Complete characterization of the macroscopic deformations of periodic unimode metamaterials of rigid bars and pivots. Journal of the Mechanics and Physics of Solids, 61: 1543-1560.
    Milton G W. 2015. New examples of three-dimensional dilational materials. Physica Status Solidi (B), 252: 1426-1430.
    Min H, Guo W. 2019. Sound absorbers with a micro-perforated panel backed by an array of parallel-arranged sub-cavities at different depths. Applied Acoustics, 149: 123-128. doi: 10.1016/j.apacoust.2019.01.013
    Miranda Jr E, Dos Santos J. 2019. Flexural wave band gaps in multi-resonator elastic metamaterial Timoshenko beams. Wave Motion, 91: 102391. doi: 10.1016/j.wavemoti.2019.102391
    Miranda Jr E, Nobrega E D, Ferreira A, Dos Santos J. 2019. Flexural wave band gaps in a multi-resonator elastic metamaterial plate using Kirchhoff-love theory. Mechanical Systems and Signal Processing, 116: 480-504. doi: 10.1016/j.ymssp.2018.06.059
    Muhammad S, Wang S, Li F, Zhang C. 2020. Bandgap enhancement of periodic nonuniform metamaterial beams with inertial amplification mechanisms. Journal of Vibration and Control, 26: 1309-1318.
    Nadkarni N, Daraio C, Kochmann D M. 2014. Dynamics of periodic mechanical structures containing bistable elastic elements: from elastic to solitary wave propagation. Physical Review E, 90: 023204. doi: 10.1103/PhysRevE.90.023204
    Naify C J, Chang C, Mcknight G, Nutt S. 2011. Transmission loss of membrane-type acoustic metamaterials with coaxial ring masses. Journal of Applied Physics, 110: 124903.
    Nesterenko V F. 1983. Propagation of nonlinear compression pulses in granular media. Journal of Applied Mechanics and Technical Physics, 24: 733-743.
    Nesterenko V F. 2001. Dynamics of Heterogeneous Materials. New York: Springer.
    Nguyen H, Wu Q, Xu X, Chen H, Tracy S and Huang G. 2020. Broadband acoustic silencer with ventilation based on slit-type Helmholtz resonators. Applied Physics Letters, 117: 134103.
    Ni X, Weiner M, Alu A, Khanikaev A B. 2019. Observation of higher-order topological acoustic states protected by generalized chiral symmetry. Nature Materials, 18: 113-120.
    Ning L, Wang Y, Wang Y. 2021. Broadband square cloak in elastic wave metamaterial plate with active control. The Journal of the Acoustical Society of America, 150: 4343-4352.
    Ning L, Wang Y, Wang Y. 2020a. Active control cloak of the elastic wave metamaterial. International Journal of Solids and Structures, 202: 126-135.
    Ning L, Wang Y, Wang Y. 2020b. Active control of a black hole or concentrator for flexural waves in an elastic metamaterial plate. Mechanics of Materials, 142: 103300. doi: 10.1016/j.mechmat.2019.103300
    Nobrega E D, Gautier F, Pelat A, Dos Santos J. 2016. Vibration band gaps for elastic metamaterial rods using wave finite element method. Mechanical Systems and Signal Processing, 79: 192-202. doi: 10.1016/j.ymssp.2016.02.059
    Norris A N. 2008. Acoustic cloaking theory. Physical and Engineering Sciences, 464: 2411-2434.
    Norris A N. 2009. Acoustic metafluids. The Journal of the Acoustical Society of America, 125: 839-849.
    Norris A N, Hladky-Hennion A C. 2013. Negative refraction of acoustic waves using a foam-like metallic structure. Applied Physics Letters, 102: 144103. doi: 10.1063/1.4801642
    Oliveri G, Overvelde J T. 2020. Inverse design of mechanical metamaterials that undergo buckling. Advanced Functional Materials, 30: 1909033.
    Olson G B. 2000. Designing a new material world. Science, 228: 993-998.
    Orta A H, Yilmaz C. 2019. Inertial amplification induced phononic band gaps generated by a compliant axial to rotary motion conversion mechanism. Journal of Sound and Vibration, 439: 329-343. doi: 10.1016/j.jsv.2018.10.014
    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: 193503. doi: 10.1063/1.3513218
    Overvelde J T B, Shan S, Bertoldi K. 2012. Compaction through buckling in 2d periodic, soft, and porous structures: effect of pore shape. Advanced Materials, 24: 2337-2342.
    Pelat A, Gautier F C C O, Conlon S C, Semperlotti F. 2020. The acoustic black hole: a review of theory and applications. Journal of Sound and Vibration, 476: 115316. doi: 10.1016/j.jsv.2020.115316
    Pendry J B. 2000. Negative refraction makes a perfect lens. Physical Review Letters, 85: 3966.
    Pendry J B. 2006. Controlling electromagnetic fields. Science, 312: 1780.
    Pendry J B, Li J. 2008. An acoustic metafluid: realizing a broadband acoustic cloak. New Journal of Physics, 10: 115032.
    Pilania G, Wang C, Jiang X, Rajasekaran S, Ramprasad R. 2013. Accelerating materials property predictions using machine learning. Scientific Reports, 3: 2810.
    Popa B, Zigoneanu L, Cummer S A. 2013. Tunable active acoustic metamaterials. Physical Review B, 88: 024303.
    Popa B, Cummer S A. 2014. Non-reciprocal and highly nonlinear active acoustic metamaterials. Nature Communications, 5: 3398. doi: 10.1038/ncomms4398
    Popa B, Wang W, Konneker A, Cummer S A, Rohde C A, Martin T P, Orris G J, Guild M D. 2016. Anisotropic acoustic metafluid for underwater operation. The Journal of the Acoustical Society of America, 139: 3325-3331.
    Pratapa P P, Suryanarayana P, Paulino G H. 2018. Bloch wave framework for structures with nonlocal interactions: application to the design of origami acoustic metamaterials. Journal of the Mechanics and Physics of Solids, 118: 115-132. doi: 10.1016/j.jmps.2018.05.012
    Qi D, Yu H, Hu W, He C, Wu W, Ma Y. 2019. Bandgap and wave attenuation mechanisms of innovative reentrant and anti-chiral hybrid auxetic metastructure. Extreme Mechanics Letters, 28: 58-68. doi: 10.1016/j.eml.2019.02.005
    Qi J, Chen Z, Jiang P, Hu W, Wang Y, Zhao Z, Cao X, Zhang S, Tao R, Li Y, Others. 2021. Recent progress in active mechanical metamaterials and construction principles. Advanced Science, 2102662.
    Qiu C, Liu Z, Mei J, Shi J. 2005a. Mode-selecting acoustic filter by using resonant tunneling of two-dimensional double phononic crystals. Applied Physics Letters, 87: 104101. doi: 10.1063/1.2037853
    Qiu C, Zhang X, Liu Z. 2005b. Far-field imaging of acoustic waves by a two-dimensional sonic crystal. Physical Review B, 5: 054302. doi: 10.1103/PhysRevB.71.054302
    Qiu C, Liu Z. 2006. Acoustic directional radiation and enhancement caused by band-edge states of two-dimensional phononic crystals. Applied Physics Letters, 89: 063106.
    Rafsanjani A, Akbarzadeh A, Pasini D. 2015. Snapping mechanical metamaterials under tension. Advanced Materials, 27: 5931-5935.
    Rayleigh J W S B. 1896. The Theory of Sound. Macmillan.
    Ren X, Das R, Tran P, Ngo T D, Xie Y M. 2018. Auxetic metamaterials and structures: a review. Smart Materials and Structures, 27: 023001.
    Richards D, Pines D J. 2003. Passive reduction of gear mesh vibration using a periodic drive shaft. Journal of Sound and Vibration, 264: 317-342.
    Richoux O, Tournat V, Van S L. 2007. Acoustic wave dispersion in a one-dimensional lattice of nonlinear resonant scatterers. Physical Review E, 75: 026615. doi: 10.1103/PhysRevE.75.026615
    Romeo F, Luongo A. 2003. Vibration reduction in piecewise bi-coupled periodic structures. Journal of Sound and Vibration, 268: 601-615. doi: 10.1016/S0022-460X(03)00375-4
    Ronellenfitsch H, Stoop N, Yu J, Forrow A, Dunkel J. 2019. Inverse design of discrete mechanical metamaterials. Physical Review Materials, 3: 095201.
    Ruzzene M, Mazzarella L, Tsopelas P, Scarpa F. 2002. Wave propagation in sandwich plates with periodic auxetic core. Journal of Intelligent Material Systems and Structures, 13: 587-597.
    Ruzzene M, Scarpa F, Soranna F. 2003. Wave beaming effects in two-dimensional cellular structures. Smart Materials and Structures, 12: 363-372.
    Ruzzene M, Scarpa F. 2003. Control of wave propagation in sandwich beams with auxetic core. Journal of Intelligent Material Systems and Structures, 14: 443-453.
    Rybin M V, Khanikaev A B, Inoue M, Samusev K B, Steel M J, Yushin G, Limonov M F. 2009. Fano resonance between mie and Bragg scattering in photonic crystals. Physical Review Letters, 103: 023901.
    Sánchez-Dehesa J, Garcia-Chocano V M, Torrent D, Cervera F, Cabrera S, Simon F. 2011. Noise control by sonic crystal barriers made of recycled materials. Journal of the Acoustical Society of America, 129: 1173-1183.
    Sanchez-Lengeling B, Aspuru-Guzik A. 2018. Inverse molecular design using machine learning: Generative models for matter engineering. Science, 361: 360-365.
    Sanchez-Perez J V, Caballero D, Martinez-Sala R, Rubio C, Sanchez-Dehesa J, Meseguer F, Llinares J, Galvez F. 1998. Sound attenuation by a two-dimensional array of rigid cylinders. Physical Review Letters, 80: 5325-5328.
    Saxena K K, Das R, Calius E P. 2016. Three decades of auxetics research- materials with negative Poisson's ratio: a review. Advanced Engineering Materials, 18: 1847-1870.
    Schaedler T A, Jacobsen A J, Torrents A, Sorensen A E, Lian J, Greer J R, Valdevit L, Carter W B. 2011. Ultralight metallic microlattices. Science, 334: 962-965.
    Schumacher C, Bickel B, Rys J, Marschner S, Daraio C, Gross M. 2015. Microstructures to control elasticity in 3d printing. ACM Transactions on Graphics (Tog), 34: 1-13.
    Schütt K T, Glawe H, Brockherde F, Sanna A, Müller K, Gross E K. 2014. How to represent crystal structures for machine learning: towards fast prediction of electronic properties. Physical Review B, 89: 205118.
    Seo S, Kim Y, Kim K. 2018. Design of silencer using resonator arrays with high sound pressure and grazing flow. Applied Acoustics, 138: 188-198. doi: 10.1016/j.apacoust.2018.04.001
    Serra-Garcia M, Peri V, Süsstrunk R, Bilal O R, Larsen T, Villanueva L G, Huber S D. 2018. Observation of a phononic quadrupole topological insulator. Nature, 555: 342-345.
    Shan S, Kang S H, Raney J R, Wang P, Fang L, Candido F, Lewis J A, Bertoldi K. 2015. Multistable architected materials for trapping elastic strain energy. Advanced Materials, 27: 4296-4301.
    Shelby R A, Smith D R, Schultz S. 2001. Experimental verification of a negative index of refraction. Science, 292: 77-79. doi: 10.1126/science.1058847
    Shen C, Xie Y, Li J, Cummer S A, Jing Y. 2018. Acoustic metacages for sound shielding with steady air flow. Journal of Applied Physics, 123: 124501.
    Shen H, Païdoussis M P, Wen J, Yu D, Cai L, Wen X. 2012. Acoustic cloak/anti-cloak device with realizable passive/active metamaterials. Journal of Physics D:Applied Physics, 45: 285401.
    Shen Y, Yang Y, Guo X, Shen Y, Zhang D. 2019. Low-frequency anechoic metasurface based on coiled channel of gradient cross-section. Applied Physics Letters, 114: 083501.
    Sheng P, Fang X, Wen J, Yu D. 2021. Vibration properties and optimized design of a nonlinear acoustic metamaterial beam. Journal of Sound and Vibration, 492: 115739. doi: 10.1016/j.jsv.2020.115739
    Shi K, Jin G, Liu R, Ye T, Xue Y. 2019. Underwater sound absorption performance of acoustic metamaterials with multilayered locally resonant scatterers. Results in Physics, 12: 132-142. doi: 10.1016/j.rinp.2018.11.060
    Sigalas M M, Economou E N. 1992. Elastic and acoustic wave band structure. Journal of Sound and Vibration, 158: 377-382.
    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.
    Sigalas M M. 1998. Defect states of acoustic waves in a two-dimensional lattice of solid cylinders. Journal of Applied Physics, 84: 3026-3030.
    Song Y, Wen J, Yu D, Wen X. 2013. Analysis and enhancement of torsional vibration stopbands in a periodic shaft system. Journal of Physics D:Applied Physics, 46: 145306. doi: 10.1088/0022-3727/46/14/145306
    Song Y, Feng L, Wen J, Yu D, Wen X. 2015. Reduction of the sound transmission of a periodic sandwich plate using the stop band concept. Composite Structures, 128: 428-436. doi: 10.1016/j.compstruct.2015.02.053
    Song Y, Feng L, Liu Z, Wen J, Yu D. 2019. Suppression of the vibration and sound radiation of a sandwich plate via periodic design. International Journal of Mechanical Sciences, 150: 744-754. doi: 10.1016/j.ijmecsci.2018.10.055
    Song Y, Wen J, Tian H, Lu X, Li Z, Feng L. 2020. Vibration and sound properties of metamaterial sandwich panels with periodically attached resonators: simulation and experiment study. Journal of Sound and Vibration, 489: 115644. doi: 10.1016/j.jsv.2020.115644
    Spadoni A, Ruzzene M. 2007. Numerical and experimental analysis of the static compliance of chiral truss-core airfoils. Journal of Mechanics of Materials and Structures, 2: 965-981.
    Spadoni A, Ruzzene M, Gonella S, Scarpa F. 2009. Phononic properties of hexagonal chiral lattices. Wave Motion, 64: 435-450.
    Sugimoto M. 1992. Propagation of nonlinear acoustic waves in a tunnel with an array of Helmholtz resonators. Journal of Fluid Mechanics, 244: 55-78. doi: 10.1017/S0022112092002969
    Sugino C, Leadenham S, Ruzzene M, Erturk A. 2016. On the mechanism of bandgap formation in locally resonant finite elastic metamaterials. Journal of Applied Physics, 120: 134501.
    Sugino C, Xia Y, Leadenham S, Ruzzene M, Erturk A. 2017. A general theory for bandgap estimation in locally resonant metastructures. Journal of Sound and Vibration, 406: 104-123. doi: 10.1016/j.jsv.2017.06.004
    Sun Z, Sun X, Jia H, Bi Y, Yang J. 2019. Quasi-isotropic underwater acoustic carpet cloak based on latticed pentamode metafluid. Applied Physics Letters, 114: 094101. doi: 10.1063/1.5085568
    Szefi J T. 2003. Helicopter gearbox isolation using periodically layered fluidic isolators. The Pennsylvania State University.
    Tang K, Qiu C, Lu J, Ke M, Liu Z. 2015. Focusing and directional beaming effects of airborne sound through a planar lens with zigzag slits. Journal of Applied Physics, 117: 024503.
    Tang L, Cheng L. 2017a. Broadband locally resonant band gaps in periodic beam structures with embedded acoustic black holes. Journal of Applied Physics, 19: 194901.
    Tang L, Cheng L. 2017b. Ultrawide band gaps in beams with double-leaf acoustic black hole indentations. The Journal of the Acoustical Society of America, 142: 2802-2807.
    Tang L, Cheng L. 2019. Periodic plates with tunneled acoustic-black-holes for directional band gap generation. Mechanical Systems and Signal Processing, 133: 106257. doi: 10.1016/j.ymssp.2019.106257
    Tao M, Tang W L, Fan J. 2010. Mechanism analysis of noise reduction by compliant decoupling layers. Journal of Ship Mechanics, 14: 421-429.
    Tayong R, Dupont T, Leclaire P. 2010. On the variations of acoustic absorption peak with particle velocity in micro-perforated panels at high level of excitation. The Journal of the Acoustical Society of America, 127: 2875-2882.
    Tian Y, Wei Q, Cheng Y, Xu Z, Liu X. 2015. Broadband manipulation of acoustic wavefronts by pentamode metasurface. Applied Physics Letters, 107: 221906.
    Torres M, Montero E F, Garc P D, Garc N. 1999. Sonic band gaps in finite elastic media: surface states and localization phenomena in linear and point defects. Physical Review Letters, 82: 3054-3057.
    Wang D T, Zhu D W, Huang X C. 2015. Influences of internal resonances on the vibration and sound reduction of chiral layer coating. Noise and Vibration Control, 35: 22-25.
    Wang F, Chen T, Wang X, Bao K, Wan L. 2017b. A membrane-type acoustic metamaterial muffler. International Journal of Modern Physics B, 31: 1750049.
    Wang G, Wen J and Wen X. 2005. Quasi-one-dimensional phononic crystals studied using the improved lumped-mass method: application to locally resonant beams with flexural wave band gap. Physical Review B, 71: 104302. doi: 10.1103/PhysRevB.71.104302
    Wang G, Wen X, Wen J, Liu Y. 2006. Quasi-one-dimensional periodic structure with locally resonant band gap. Journal of Applied Mechanics, 73: 167-170.
    Wang M, Ye L, Christensen J, Liu Z. 2018. Valley physics in non-Hermitian artificial acoustic boron nitride. Physical Review Letters, 120: 246601.
    Wang S, Xiao Y, Guo J, Zhang H, Wen J. 2021. Broadband diffuse field sound insulation of double layer metamaterial plates lined with porous material. Applied Physics Letters, 199: 084103.
    Wang X, Mak C. 2014. Disorder in a periodic Helmholtz resonators array. Applied Acoustics, 82: 1-5. doi: 10.1016/j.apacoust.2014.03.002
    Wang X, Chen Y, Zhou G, Chen T, Ma F. 2019a. Synergetic coupling large-scale plate-type acoustic metamaterial panel for broadband sound insulation. Journal of Sound and Vibration, 459: 114867. doi: 10.1016/j.jsv.2019.114867
    Wang X, Fang X, Mao D, Jing Y, Li Y. 2019b. Extremely asymmetrical acoustic metasurface mirror at the exceptional point. Physical Review Letters, 123: 214302.
    Wang Y, Zhao H, Yang H, Zhong J, Wen J. 2017a. A space-coiled acoustic metamaterial with tunable low-frequency sound absorption. Europhysics Letters, 120: 54001.
    Wang Z G, Lee S H, Kim C K, Park C M, Nahm K, Nikitov S A. 2008. Acoustic wave propagation in one-dimensional phononic crystals containing Helmholtz resonators. Journal of Applied Physics, 103: 064907.
    Ward L, Agrawal A, Choudhary A, Wolverton C. 2016. A general-purpose machine learning framework for predicting properties of inorganic materials. npj Computational Materials, 2: 16028.
    Wen J, Yu D, Cai L, Wen X. 2009. Acoustic directional radiation operating at the pass band frequency in two-dimensional phononic crystals. Journal of Physics D:Applied Physics, 42: 115417.
    Wen J, Chen S, Wang G, Yu D, Wen X. 2016. Directionality of wave propagation and attenuation in plates with resonant shunting arrays. Journal of Intelligent Material Systems and Structures, 27: 28-38.
    Wu D, Zhang N, Mak C M, Cai C. 2017. Noise attenuation performance of a Helmholtz resonator array consist of several periodic parts. Sensors, 17: 1029.
    Wu F, Xiao Y, Yu D, Zhao H, Wang Y, Wen J. 2019. Low-frequency sound absorption of hybrid absorber based on micro-perforated panel and coiled-up channels. Applied Physics Letters, 114: 151901.
    Wu X, Fu C, Li X, Meng Y, Gao Y, Tian J, Wang L, Huang Y, Yang Z, Wen W. 2016. Low-frequency tunable acoustic absorber based on split tube resonators. Applied Physics Letters, 109: 043501.
    Wu X, Meng Y, Hao Y, Zhang R, Li J, Zhang X. 2021. Topological corner modes induced by Dirac vortices in arbitrary geometry. Physical Review Letters, 126: 226802.
    Xi C, Dou L, Mi Y and Zheng H. 2021. Inertial amplification induced band gaps in corrugated-core sandwich panels. Composite Structures, 113918.
    Xia Y, Erturk A, Ruzzene M. 2020. Topological edge states in quasiperiodic locally resonant metastructures. Physical Review Applied, 13: 014023.
    Xiao Y, Mace B R, Wen J, Wen X. 2011. Formation and coupling of band gaps in a locally resonant elastic system comprising a string with attached resonators. Physics Letters A, 375: 1485-1491.
    Xiao Y, Wen J, Wen X. 2012a. Sound transmission loss of metamaterial-based thin plates with multiple subwavelength arrays of attached resonators. Journal of Sound and Vibration, 331: 5408-5423.
    Xiao Y, Wen J, Wen X. 2012b. Longitudinal wave band gaps in metamaterial-based elastic rods containing multi-degree-of-freedom resonators. New Journal of Physics, 14: 033042.
    Xiao Y, Wen J, Wen X. 2012c. Broadband locally resonant beams containing multiple periodic arrays of attached resonators. Physics Letters A, 376: 1384-1390.
    Xiao Y, Wen J, Wen X. 2012d. Flexural wave band gaps in locally resonant thin plates with periodically attached spring-mass resonators. Journal of Physics D:Applied Physics, 45: 195401.
    Xiao Y, Wen J, Wen X. 2012e. Sound transmission loss of metamaterial-based thin plates with multiple subwavelength arrays of attached resonators. Journal of Sound and Vibration, 331: 5408-5423.
    Xiao Y, Wen J, Yu D, Wen X. 2013a. Flexural wave propagation in beams with periodically attached vibration absorbers: band-gap behavior and band formation mechanisms. Journal of Sound and Vibration, 332: 867-893.
    Xiao Y, Wen J, Wang G, Wen X. 2013b. Theoretical and experimental study of locally resonant and Bragg band gaps in flexural beams carrying periodic arrays of beam-like resonators. Journal of Vibration and Acoustics, 135: 041006.
    Xiao Y, Wen J. 2020. Closed-form formulas for bandgap estimation and design of metastructures undergoing longitudinal or torsional vibration. Journal of Sound and Vibration, 485: 115578. doi: 10.1016/j.jsv.2020.115578
    Xiao Y, Cao J, Wang S, Guo J, Wen J, Zhang H. 2021a. Sound transmission loss of plate-type metastructures: semi-analytical modeling, elaborate analysis, and experimental validation. Mechanical Systems and Signal Processing, 153: 107487. doi: 10.1016/j.ymssp.2020.107487
    Xiao Y, Wang S, Li Y, Wen J. 2021b. Closed-form bandgap design formulas for beam-type metastructures. Mechanical Systems and Signal Processing, 159: 107777. doi: 10.1016/j.ymssp.2021.107777
    Xie B, Wang H, Zhang X, Zhan P, Jiang J, Lu M, Chen Y. 2021. Higher-order band topology. Nature Reviews Physics, 3: 520-532.
    Xu L, Shyu T C, Kotov N A. 2017. Origami and kirigami nanocomposites. Acs Nano, 11: 7587-7599.
    Xue H, Yang Y, Gao F, Chong Y, Zhang B. 2019. Acoustic higher-order topological insulator on a kagome lattice. Nature Materials, 18: 108-112.
    Yang H, Zhao H, Yin J, Wen J. 2019a. Hybrid meta-structure for broadband waterborne sound absorption. AIP Advances, 9: 125226.
    Yang H, Xiao Y, Zhao H, Zhong J, Wen J. 2019b. On wave propagation and attenuation properties of underwater acoustic screens consisting of periodically perforated rubber layers with metal plates. Journal of Sound and Vibration, 444: 21-34. doi: 10.1016/j.jsv.2018.12.031
    Yang H, Ma L. 2021. Impact resistance of additively manufactured 3D double-U auxetic structures. Thin-Walled Structures, 169: 108373. doi: 10.1016/j.tws.2021.108373
    Yang M, Meng C, Fu C, Li Y, Yang Z, Sheng P. 2015. Subwavelength total acoustic absorption with degenerate resonators. Applied Physics Letters, 107: 104104.
    Yang M, Chen S, Fu C, Sheng P. 2017. Optimal sound-absorbing structures. Materials Horizons, 4: 673-680. doi: 10.1039/C7MH00129K
    Yang S, Page J H, Liu Z, Cowan M L, Chan C T, Sheng P. 2004. Focusing of sound in a 3d phononic crystal. Physical Review Letters, 93: 024301.
    Yang Z, Mei J, Yang M, Chan N H, Sheng P. 2008. Membrane-type acoustic metamaterial with negative dynamic mass. Physical Review Letters, 101: 204301.
    Yang Z, Dai H M, Chan N H, Ma G C, Sheng P. 2010. Acoustic metamaterial panels for sound attenuation in the 50-1000 hz regime. Applied Physics Letters, 96: 041906.
    Yang Z, Yabansu Y C, Al-Bahrani R, Liao W, Choudhary A N, Kalidindi S R, Agrawal A. 2018. Deep learning approaches for mining structure-property linkages in high contrast composites from simulation datasets. Computational Materials Science, 151: 278-287. doi: 10.1016/j.commatsci.2018.05.014
    Yao S, Zhou X, Hu G. 2008. Experimental study on negative effective mass in a 1D mass-spring system. New Journal of Physics, 10: 043020.
    Yasuda H, Miyazawa Y, Charalampidis E G, Chong C, Kevrekidis P G, Yang J. 2019. Origami-based impact mitigation via rarefaction solitary wave creation. Science Advances, 5: eaau2835. doi: 10.1126/sciadv.aau2835
    Yimaz C, Hulbert G M, Kikuchi N. 2007. Phononic band gaps induced by inertial amplification in periodic media. Physical Review B, 76: 054309.
    Yilmaz C, Hulbert G M. 2010. Theory of phononic gaps induced by inertial amplification in finite structures. Physics Letters A, 374: 3576-3584.
    Yin J, Ruzzene M, Wen J, Yu D, Cai L, Yue L. 2018. Band transition and topological interface modes in 1D elastic phononic crystals. Scientific Reports, 8: 1-10.
    Yu D, Liu Y, Zhao H, Wang G, Qiu J. 2006a. Flexural vibration band gaps in Euler-Bernoulli beams with locally resonant structures with two degrees of freedom. Physical Review B, 73: 064301.
    Yu D, Wang G, Liu Y, Wen J, Qiu J. 2006b. Flexural vibration band gaps in thin plates with two-dimensional binary locally resonant structures. Chinese Physics, 15: 0266-06.
    Yu D, Wen J, Zhao H, Liu Y, Wen X. 2008. Vibration reduction by using the idea of phononic crystals in a pipe-conveying fluid. Journal of Sound and Vibration, 318: 193-205.
    Yu D, Wen J, Shen H, Xiao Y, Wen X. 2012. Propagation of flexural wave in periodic beam on elastic foundations. Physics Letters A, 376: 626-630.
    Yu M, Fang X, Yu D. 2021a. Combinational design of linear and nonlinear elastic metamaterials. International Journal of Mechanical Sciences, 199: 106422. doi: 10.1016/j.ijmecsci.2021.106422
    Yu S, He C, Sun X, Wang H, Wang J, Zhang Z, Xie B, Tian Y, Lu M, Chen Y. 2021b. Critical couplings in topological-insulator waveguide-resonator systems observed in elastic waves. National Science Review, 8: nwaa262.
    Yu X, Zhou J, Liang H, Jiang Z, Wu L. 2018a. Mechanical metamaterials associated with stiffness, rigidity and compressibility: a brief review. Progress in Materials Science, 94: 114-173. doi: 10.1016/j.pmatsci.2017.12.003
    Yuan B, Humphrey V F, Wen J, Wen X. 2013. On the coupling of resonance and Bragg scattering effects in three-dimensional locally resonant sonic materials. Ultrasonics, 53: 1332-1343.
    Yuan B, Jiang W, Jiang H, Chen M, Liu Y. 2018. Underwater acoustic properties of graphene nanoplatelet-modified rubber. Journal of Reinforced Plastics and Composites, 37: 609-616.
    Yuan X, Chen M, Yao Y, Guo X, Huang Y, Peng Z, Xu B, Lv B, Tao R, Duan S. 2021. Recent progress in the design and fabrication of multifunctional structures based on metamaterials. Current Opinion in Solid State and Materials Science, 1: 100883.
    Yuksel O, Yilmaz C. 2020. Realization of an ultrawide stop band in a 2-d elastic metamaterial with topologically optimized inertial amplification mechanisms. International Journal of Solids and Structures, 203: 138-150. doi: 10.1016/j.ijsolstr.2020.07.018
    Zangeneh-Nejad F, Fleury R. 2019. Topological analog signal processing. Nature Communications, 10: 2058. doi: 10.1038/s41467-019-10086-3
    Zhang C, Hu X. 2016. Three-dimensional single-port labyrinthine acoustic metamaterial: Perfect absorption with large bandwidth and tunability. Physical Review Applied, 6: 064025. doi: 10.1103/PhysRevApplied.6.064025
    Zhang G L, Yang D Q, Zhu J W. 2013b. Performance analysis of a novel marine honeycomb vibration isolator. Chinese Journal of Ship Research, 8: 52-58.
    Zhang H, Zhu Y, Liang B, Yang J, Yang J, Cheng J. 2017. Sound insulation in a hollow pipe with subwavelength thickness. Scientific Reports, 7: 44106.
    Zhang H, Wang Y, Zhao H, Lu K, Yu D, Wen J. 2021d. Accelerated topological design of metaporous materials of broadband sound absorption performance by generative adversarial networks. Materials & Design, 207: 109855.
    Zhang J, V R, G T, O R, V A, J F D. 2016. Second-harmonic generation in membrane-type nonlinear acoustic metamaterials. Crystals, 6: 86. doi: 10.3390/cryst6080086
    Zhang J, Romero-García V, Theocharis G, Richoux O, Achilleos V, Frantzeskakis D J. 2021b. High-amplitude sound propagation in acoustic transmission-line metamaterial. Applied Physics Letters, 118: 104102.
    Zhang S, Xia C, Fang N. 2011. Broadband acoustic cloak for ultrasound waves. Physical Review Letters, 106: 024301. doi: 10.1103/PhysRevLett.106.024301
    Zhang X, Liu Z. 2004. Negative refraction of acoustic waves in two-dimensional phononic crystals. Applied Phyics Letters, 85: 341-343.
    Zhang X, An C, Shen Z, Wu H, Yang W, Bai J. 2020. Dynamic crushing responses of bio-inspired re-entrant auxetic honeycombs under in-plane impact loading. Materials Today Communications, 23: 100918. doi: 10.1016/j.mtcomm.2020.100918
    Zhang X, Yu H, He Z, Huang G, Chen Y, Wang G. 2021c. A metamaterial beam with inverse nonlinearity for broadband micro-vibration attenuation. Mechanical Systems and Signal Processing, 159: 107826. doi: 10.1016/j.ymssp.2021.107826
    Zhang X, Liu L, Lu M, Chen Y. 2021e. Valley-selective topological corner states in sonic crystals. Physical Review Letters, 126: 156401.
    Zhang Y, Wen J, Xiao Y, Wen X, Wang J. 2012. Theoretical investigation of the sound attenuation of membrane-type acoustic metamaterials. Physics Letters A, 376: 1489-1494. doi: 10.1016/j.physleta.2012.03.010
    Zhang Y, Wen J, Zhao H, Yu D, Cai L, Wen X. 2013c. Sound insulation property of membrane-type acoustic metamaterials carrying different masses at adjacent cells. Journal of Applied Physics, 114: 063515. doi: 10.1063/1.4818435
    Zhang Y, Pan J, Chen K, Zhong J. 2018a. Subwavelength and quasi-perfect underwater sound absorber for multiple and broad frequency bands. The Journal of the Acoustical Society of America, 114: 648-659.
    Zhang Y, Fan X, Li J, Li F, Yu G, Zhang R, Yuan K. 2021a. Low-frequency vibration insulation performance of the pyramidal lattice sandwich metamaterial beam. Composite Structures, 278: 114719. doi: 10.1016/j.compstruct.2021.114719
    Zhang Y B, Ren C Y, Zhu X. 2013a. Research on vibration and sound radiation from submarine functionally graded material nonpressure cylindrical shell. Advances in Materials Research, 690: 3046-3049.
    Zhang Z, Lopez M R, Cheng Y, Liu X J, Christensen J. 2019. Non-Hermitian sonic second-order topological insulator. Physical Review Letters, 122: 195501. doi: 10.1103/PhysRevLett.122.195501
    Zhang Z, Tian Y, Wang Y, Gao S, Cheng Y, Liu X, Christensen J. 2018b. Directional acoustic antennas based on valley‐hall topological insulators. Advanced Materials, 30: 1803229.
    Zhao A, Zhao Z, Zhang X, Cai X, Wang L, Wu T, Chen H. 2017a. Design and experimental verification of a water-like pentamode material. Applied Physics Letters, 110: 011907.
    Zhao D G, Shen Y X, Zhang Y, Zhu X F, Yi L. 2016. Bound states in one-dimensional acoustic parity-time-symmetric lattices for perfect sensing. Physical Letter A, 380: 2698-2702.
    Zhao H, Liu Y, Wen J, Yu D, Wen X. 2007. Tri-component phononic crystals for underwater anechoic coatings. Physics Letters A, 367: 224-232.
    Zhao H, Wang Y, Wen J, Lam Y W, Umnova O. 2018a. A slim subwavelength absorber based on coupled microslits. Applied Acoustics, 142: 11-17. doi: 10.1016/j.apacoust.2018.08.004
    Zhao H, Wang Y, Yu D, Yang H, Zhong J, Wu F, Wen J. 2020. A double porosity material for low frequency sound absorption. Composite Structures, 239: 111978. doi: 10.1016/j.compstruct.2020.111978
    Zhao H G, Wen J H, Yang H B, Lü L M, Wen X S. 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
    Zhao X, Cai L, Yu D, Lu Z, Wen J. 2017b. A low frequency acoustic insulator by using the acoustic metasurface to a Helmholtz resonator. AIP Advances, 7: 065211.
    Zhao X, Gao Q, Wang L, Yu Q, Ma Z D. 2018b. Dynamic crushing of double-arrowed auxetic structure under impact loading. Materials & Design, 160: 527-537.
    Zheng B, Yang J, Liang B, Cheng J. 2020b. Inverse design of acoustic metamaterials based on machine learning using a Gauss–Bayesian model. Journal of Applied Physics, 128: 134902.
    Zheng M, Liu X, Chen Y, Miao H, Zhu R, Hu G. 2019. Theory and realization of nonresonant anisotropic singly polarized solids carrying only shear waves. Physical Review Applied, 12: 014027.
    Zheng M, Park C I, Liu X, Zhu R, Hu G, Kim Y Y. 2020a. Non-resonant metasurface for broadband elastic wave mode splitting. Applied Physics Letters, 116: 171903.
    Zheng S, Duan G, Xia B. 2020c. Underwater acoustic positioning based on valley-chirality locked beam of sonic system. International Journal of Mechanical Sciences, 174: 105463. doi: 10.1016/j.ijmecsci.2020.105463
    Zheng X, Lee H, Weisgraber T H, Shusteff M, Deotte J, Duoss E B, Kuntz J D, Biener M M, Ge Q, Jackson J A. 2014. Ultralight, ultrastiff mechanical metamaterials. Science, 344: 1373-1377.
    Zheng Z F, Yin J F, Wen J H, Yu D L. 2022. High-order topological states in locally resonant elastic metamaterials. Applied Physics Letters, 120: 144101.
    Zhong H, Gu Y, Bao B, Wang Q, Wu J. 2019a. 2D underwater acoustic metamaterials incorporating a combination of particle-filled polyurethane and spiral-based local resonance mechanisms. Composite Structures, 220: 1-10.
    Zhong J, Wen J, Zhao H, Yin J, Yang H. 2015. Effects of core position of locally resonant scatterers on low-frequency acoustic absorption in viscoelastic panel. Chinese Physics B, 24: 84301.
    Zhong J, Zhao H, Yang H, Wang Y, Yin J, Wen J. 2019b. Theoretical requirements and inverse design for broadband perfect absorption of low-frequency waterborne sound by ultrathin metasurface. Scientific Reports, 9: 1181. doi: 10.1038/s41598-018-37510-w
    Zhou G, Wu J H, Lu K, Tian X, Huang W, Zhu K. 2020. Broadband low-frequency membrane-type acoustic metamaterials with multi-state anti-resonances. Applied Acoustics, 159: 107078. doi: 10.1016/j.apacoust.2019.107078
    Zhou J, Dou L, Wang K, Xu D, Ouyang H. 2019. A nonlinear resonator with inertial amplification for very low-frequency flexural wave attenuations in beams. Nonlinear Dynamics, 96: 647-665.
    Zhou Y, Lu M H, Feng L, Ni X, Chen Y F, Zhu Y Y, Zhu S N, Ming N B. 2010. Acoustic surface evanescent wave and its dominant contribution to extraordinary acoustic transmission and collimation of sound. Physical Review Letters, 104: 164301.
    Zhu J, Christensen J, Jung J, Martin-Moreno L, Yin X, Fok L, Zhang X, Garcia-Vidal F J. 2011. A holey-structured metamaterial for acoustic deep-subwavelength imaging. Nature Physics, 7: 52-5. doi: 10.1038/nphys1804
    Zhu R, Liu X N, Hu G K, Sun C T, Huang G L. 2014. Negative refraction of elastic waves at the deep-subwavelength scale in a single-phase metamaterial. Nature Communications, 5: 5510. doi: 10.1038/ncomms6510
    Zhu X F, Feng L, Zhang P, Yin X, Zhang X. 2013. One-way invisible cloak using parity-time symmetric transformation optics. Optics Letters, 38: 2821-2824.
    Zhu Y, Fei F, Fan S, Cao L, Donda K, Assouar B. 2019. Reconfigurable origami-inspired metamaterials for controllable sound manipulation. Physical Review Applied, 12: 034029.
  • 加载中

Catalog

    通讯作者: 陈斌, bchen63@163.com
    • 1. 

      沈阳化工大学材料科学与工程学院 沈阳 110142

    1. 本站搜索
    2. 百度学术搜索
    3. 万方数据库搜索
    4. CNKI搜索

    Figures(54)  / Tables(1)

    Article Metrics

    Article views (6349) PDF downloads(2211) Cited by()
    Proportional views
    Related

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return