面向减振降噪应用的声学超构材料研究进展

doi:10.3901/JME.2023.19.277

摘要/Abstract

摘要： 声学超构材料是由阵列化的人工微结构单元构筑的复合声学材料/结构。通过对声学超构材料中的微结构单元及其排布方式进行调控设计，可以实现对声波/弹性波(可视为固体中的声波)的人为高效操控，使其表现出超常的减振降噪性能及优势。当前，声学超构材料研究已成为机械工程、声学、力学、材料学、物理学等多学科交叉领域关注的热点方向。针对机械工程领域关注的装备振动与噪声控制技术背景，重点综述面向减振降噪应用的声学超构材料研究进展，分别从减振、隔声、吸声等功能应用需求出发，回顾国内外相关声学超构材料的研究进展，并指出当前研究不足，展望未来发展趋势，为推动声学超构材料在减振降噪领域的应用提供借鉴和参考。

关键词: 声学超构材料, 减振, 隔声, 吸声, 低频

Abstract: Acoustic metamaterials are composite acoustic materials/structures constructed by arrays of artificial microstructure units. By designing the microstructure units and their arrangement in acoustic metamaterials, it is possible to efficiently manipulate acoustic waves and elastic waves that can be regarded as acoustic waves in solids, and achieve extraordinary vibration and noise reduction performance and advantages. Currently, the study on acoustic metamaterials has become a hot topic in the interdisciplinary fields of mechanical engineering, acoustics, mechanics, materials science, and physics. Focusing on the background of vibration and noise control technology in the field of mechanical engineering, the research progress of acoustic metamaterials for vibration reduction and noise reduction applications is reviewed. Starting from the functional application requirements of low-frequency vibration reduction, sound insulation, and sound absorption, it provides a survey of the recent studies of acoustic metamaterials, points out the current research shortcomings, and looks forward to future development trends. The review can provide reference and guidance for promoting the application of acoustic metamaterials in the field of vibration and noise reduction.

Key words: acoustic metamaterial, vibration reduction, sound insulation, sound absorption, low frequency

中图分类号:

TB535

肖勇, 王洋, 赵宏刚, 郁殿龙, 温激鸿. 面向减振降噪应用的声学超构材料研究进展[J]. 机械工程学报, 2023, 59(19): 277-298.

XIAO Yong, WANG Yang, ZHAO Honggang, YU Dianlong, WEN Jihong. Research Progress of Acoustic Metamaterials for Vibration and Noise Reduction Applications[J]. Journal of Mechanical Engineering, 2023, 59(19): 277-298.

参考文献

[1] 温激鸿,蔡力,郁殿龙,等. 声学超材料基础理论与应用[M]. 北京:科学出版社,2018. WEN Jihong,CAI Li,YU Dianlong,et al. Basic theory and application of acoustic metamaterials[M]. Beijing:Science Press,2018.
[2] 肖勇. 局域共振型结构的带隙调控与减振降噪特性研究[D]. 长沙:国防科学技术大学,2012. XIAO Yong. Locally resonant structures:band gap tuning and properties of vibration and noise reduction[D]. Changsha:National University of Defense Technology,2012.
[3] LIU Zhengyou,ZHANG Xixiang,MAO Yiwei,et al. Locally resonant sonic materials[J]. Science, 2000,289(5485):1734-1736.
[4] LI J,CHAN C T. Double-negative acoustic metamaterial[J]. Physical Review E, 2004,7:055602(R).
[5] SIGALAS M M,ECONOMOU E N. Elastic and acoustic wave band structure[J]. Journal of Sound and Vibration,1992,158(2):377-382.
[6] KUSHWAHA M S,HALEVI P,DOBRZYNSKI L,et al. Acoustic band structure of periodic elastic composites[J]. Physical Review Letters,1993,71(13):2022-2025.
[7] 温熙森,温激鸿,郁殿龙,等. 声子晶体[M]. 北京:国防工业出版社,2009. WEN Xisen,WEN Jihong,YU Dianlong,et al. Phononic crystals[M]. Beijing:National Defence Industry Press,2009.
[8] WANG Gang,WEN Xisen,WEN Jihong,et al. Quasi-one-dimensional periodic structure with locally resonant band gap[J]. Journal of Applied Mechanics,2006,73(1):167-170.
[9] WANG Gang,WEN Jihong,WEN Xisen. Quasi-one-dimensional phononic crystals studied using the improved lumped-mass method:application to locally resonant beams with flexural wave band gap[J]. Physical Review B,2005,71(10):104302.
[10] YU Dianlong,LIU Yaozong,WANG Gang, et al. Flexural vibration band gaps in Timoshenko beams with locally resonant structures[J]. Journal of Applied Physics,2006,100(12):124901.
[11] YU Dianlong,LIU Yaozong,ZHAO Honggang,et al. Flexural vibration band gaps in Euler-Bernoulli beams with locally resonant structures with two degrees of freedom[J]. Physical Review B, 2006,73(6):064301.
[12] 王刚. 声子晶体局域共振带隙机理及减振特性研究[D]. 长沙:国防科学技术大学,2005. WANG Gang. Research on the mechanism and the vibration attenuation characteristic of locally resonant band gap in phononic crystals[D]. Changsha:National University of Defense Technology,2005.
[13] YU Dianlong,WANG Gang,LIU Yaozong,et al. Flexural vibration band gaps in thin plates with two-dimensional binary locally resonant structures.[J]. Chinese Physics,2006,15(2):266-271.
[14] YU Dianlong,LIU Yaozong,QIU Jing,et al. Experimental and theoretical research on the vibrational gaps in two-dimensional three-component composite thin plates[J]. Chinese Physics Letters,2005,22(8):1958-1960.
[15] WU T,HUANG Zigui,TSAI T,et al. Evidence of complete band gap and resonances in a plate with periodic stubbed surface[J]. Applied Physics Letters,2008,93(11):111902.
[16] PENNEC Y,DJAFARI-ROUHANI B,LARABI H,et al. Low-frequency gaps in a phononic crystal constituted of cylindrical dots deposited on a thin homogeneous plate[J]. Physical Review B,2008,78(10):104105.
[17] OUDICH M,LI Y,ASSOUAR B M,et al. A sonic band gap based on the locally resonant phononic plates with stubs[J]. New Journal of Physics,2010,12(8):083049.
[18] ASSOUAR M B,OUDICH M. Enlargement of a locally resonant sonic band gap by using double-sides stubbed phononic plates[J]. Applied Physics Letters,2012,100(12):123506.
[19] ASSOUAR M B,SENESI M,OUDICH M,et al. Broadband plate-type acoustic metamaterial for low-frequency sound attenuation[J]. Applied Physics Letters,2012,101(17):173505.
[20] WANG Gang,WEN Xisen,WEN Jihong,et al. Two-dimensional locally resonant phononic crystals with binary structures[J]. Physical Review Letters,2004,93(15):154302.
[21] XIAO Yong,WEN Jihong,WEN Xisen. Broadband locally resonant beams containing multiple periodic arrays of attached resonators[J]. Physics Letters A,2012,376(16):1384-1390.
[22] XIAO Yong,WEN Jihong,WEN Xisen. Longitudinal wave band gaps in metamaterial-based elastic rods containing multi-degree-of-freedom resonators[J]. New Journal of Physics,2012,14(3):033042.
[23] ZHU Rui,LIU Xiaoning HU Gengkai,et al. A chiral elastic metamaterial beam for broadband vibration suppression[J]. Journal of Sound and Vibration,2014,333(10):2759-2773.
[24] ZHOU Jiaxi,WANG Kai,XU Daolin,et al. Multi-low-frequency flexural wave attenuation in Euler-Bernoulli beams using local resonators containing negative-stiffness mechanisms[J]. Physics Letters A,2017,381(37):3141-3148.
[25] MENG H,CHRONOPOULOS D,FABRO A T,et al. Rainbow metamaterials for broadband multi-frequency vibration attenuation:numerical analysis and experimental validation[J]. Journal of Sound and Vibration,2020,465:115005.
[26] HU Guobiao,AUSTIN A C M,SOROKIN V,et al. Metamaterial beam with graded local resonators for broadband vibration suppression[J]. Mechanical Systems and Signal Processing,2021,146:106982.
[27] MIRANDA JR E J P,DOS SANTOS J M C. Flexural wave band gaps in multi-resonator elastic metamaterial Timoshenko beams[J]. Wave Motion,2019,91:102391.
[28] MIRANDA JR E J P,NOBREGA E D,FERREIRA A H R,et al. Flexural wave band gaps in a multi-resonator elastic metamaterial plate using Kirchhoff-Love theory[J]. Mechanical Systems and Signal Processing,2019,116:480-504.
[29] XIAO Yong,MACE B R,WEN Jihong,et al. Formation and coupling of band gaps in a locally resonant elastic system comprising a string with attached resonators[J]. Physics Letters A,2011,375(12):1485-1491.
[30] XIAO Yong,WEN Jihong,YU Dianlong,et al. Flexural wave propagation in beams with periodically attached vibration absorbers:band-gap behavior and band formation mechanisms[J]. Journal of Sound and Vibration,2013,332(4):867-893.
[31] XIAO Yong,WEN Jihong,WANG Gang,et al. Theoretical and experimental study of locally resonant and bragg band gaps in flexural beams carrying periodic arrays of beam-like resonators[J]. Journal of Vibration and Acoustics,2013,135:041006.
[32] LI Yongqiang,XIAO Yong,GUO Jiajia,et al. Single-phase metabeam for three-directional broadband vibration suppression[J]. International Journal of Mechanical Sciences,2022,234:107683.
[33] XIAO Yong,WEN Jihong,WEN Xisen. Flexural wave band gaps in locally resonant thin plates with periodically attached spring-mass resonators[J]. Journal of Physics D:Applied Physics,2012,45(19):195401.
[34] 朱席席,肖勇,温激鸿,等. 局域共振型加筋板的弯曲波带隙与减振特性[J]. 物理学报,2016,65(17) 176202. ZHU Xixi,XIAO Yong,WEN Jihong,et al. Flexural wave band gaps and vibration reduction properties of a locally resonant stiffened plate[J]. Acta Physica Sinica,2016,65(17):76202.
[35] XIAO Yong,WEN Jihong,HUANG Lingzhi, et al. Analysis and experimental realization of locally resonant phononic plates carrying a periodic array of beam-like resonators[J]. Journal of Physics D:Applied Physics,2014,47(4):045307.
[36] KRUSHYNSKA A O,MINIACI M,BOSIA F,et al. Coupling local resonance with Bragg band gaps in single-phase mechanical metamaterials[J]. Extreme Mechanics Letters,2017,12:30-36.
[37] XIAO Yong,WEN Jihong. Closed-form formulas for bandgap estimation and design of metastructures undergoing longitudinal or torsional vibration[J]. Journal of Sound and Vibration,2020,485:115578.
[38] XIAO Yong,WANG Shuaixing,LI Yongqiang,et al. Closed-form bandgap design formulas for beam-type metastructures[J]. Mechanical Systems and Signal Processing,2021,159:107777.
[39] GUO Jiajia,LI Yongqiang,XIAO Yong,et al. Multiscale modeling and design of lattice truss core sandwich metastructures for broadband low-frequency vibration reduction[J]. Composite Structures,2022,289:115463.
[40] YILMAZ C,HULBERT G M,KIKUCHI N. Phononic band gaps induced by inertial amplification in periodic media[J]. Physical Review B,2007,76(5):054309.
[41] ACAR G,YILMAZ C. Experimental and numerical evidence for the existence of wide and deep phononic gaps induced by inertial amplification in two-dimensional solid structures[J]. Journal of Sound and Vibration,2013,332(24):6389-6404.
[42] TANIKER S,YILMAZ C. Design,analysis and experimental investigation of three-dimensional structures with inertial amplification induced vibration stop bands[J]. International Journal of Solids and Structures,2015,72:88-97.
[43] YUKSEL O,YILMAZ C. Realization of an ultrawide stop band in a 2-D elastic metamaterial with topologically optimized inertial amplification mechanisms[J]. International Journal of Solids and Structures,2020,203:138-150.
[44] FRANDSEN N M M,BILAL O R,JENSEN J S,et al. Inertial amplification of continuous structures:Large band gaps from small masses[J]. Journal of Applied Physics,2016,119(12):124902.
[45] LI Jingru,LI Sheng. Generating ultra wide low-frequency gap for transverse wave isolation via inertial amplification effects[J]. Physics Letters A,2018,382(5):241-247.
[46] BARYS M,JENSEN J S,FRANDSEN N M M. Efficient attenuation of beam vibrations by inertial amplification[J]. European Journal of Mechanics-A/Solids,2018,71:245-257.
[47] LI Jingru,YANG Peng,LI Sheng. Phononic band gaps by inertial amplification mechanisms in periodic composite sandwich beam with lattice truss cores[J]. Composite Structures,2020,231:111458.
[48] XI Chenyang,DOU Lingling,MI Yongzhen,et al. Inertial amplification induced band gaps in corrugated-core sandwich panels[J]. Composite Structures,2021,267:113918.
[49] NESTERENKO V F. Propagation of nonlinear compression pulses in granular media[J]. Journal of Applied Mechanics and Technical Physics,1983,24:733-743.
[50] DARAIO C,NESTERENKO V F,HERBOLD E B,et al. Tunability of solitary wave properties in one-dimensional strongly nonlinear phononic crystals[J]. Physical Review E,2006,73:026610.
[51] DARAIO C,NESTERENKO V F,HERBOLD E B,et al. Strongly nonlinear waves in a chain of Teflon beads[J]. Physical Review. E,72:016603.
[52] FANG Xin,WEN Jihong,BONELLO B,et al. Ultra-low and ultra-broad-band nonlinear acoustic metamaterials[J]. Nature Communications,2017,8(1):1288.
[53] FANG Xin,WEN Jihong,YU Dianlong,et al. Bridging-coupling band gaps in nonlinear acoustic metamaterials[J]. Physical Review Applied,2018,10(5):054049.
[54] SHENG Peng,FANG Xin,WEN Jihong,et al. Vibration properties and optimized design of a nonlinear acoustic metamaterial beam[J]. Journal of Sound and Vibration,2021,492:115739.
[55] YANG Z,DAI H M,CHAN N H,et al. Acoustic metamaterial panels for sound attenuation in the 50-1000 Hz regime[J]. Applied Physics Letters,2010,96(4):041906.
[56] YANG Z,MEI Jun,YANG Min,et al. Membrane-type acoustic metamaterial with negative dynamic mass[J]. Physical Review Letters,2008,101(20):204301.
[57] XIAO Yong,WEN Jihong,WEN Xisen. Sound transmission loss of metamaterial-based thin plates with multiple subwavelength arrays of attached resonators[J]. Journal of Sound and Vibration,2012,331(25):5408-5423.
[58] HASHIMOTO N,KATSURA M,YASUOKA M,et al. Sound insulation of a rectangular thin membrane with additional weights[J]. Applied Acoustics,1991,33(1):21-43.
[59] VARANASI S,BOLTON J S,SIEGMUND T H,et al. The low frequency performance of metamaterial barriers based on cellular structures[J]. Applied Acoustics,2013,74(4):485-495.
[60] VARANASI S,BOLTON J S,SIEGMUND T. Experiments on the low frequency barrier characteristics of cellular metamaterial panels in a diffuse sound field[J]. The Journal of the Acoustical Society of America,2017,141(1):602-610.
[61] WANG Xiaoloe,ZHAO Hui,LUO Xudong,et al. Membrane-constrained acoustic metamaterials for low frequency sound insulation[J]. Applied Physics Letters,2016,108:041905.
[62] XIAO Yong,CAO Jianzhi,WANG Shuaixing,et al. Sound transmission loss of plate-type metastructures:semi-analytical modeling,elaborate analysis,and experimental validation[J]. Mechanical Systems and Signal Processing,2021,153:107487.
[63] 王帅星,肖勇,汤晏宁,等. 轻质超材料板结构的隔声机理及调控规律[J]. 机械工程学报,2023,59(15):94-109. WANG Shuaixing,XIAO Yong,TANG Yanning,et al. Sound insulation mechanisms and behavior of lightweight metamaterial plate[J]. Journal of Mechanical Engineering,2023,59(15):94-109.
[64] LANGFELDT F,GLEINE W. Plate-type acoustic metamaterials with strip masses[J]. The Journal of the Acoustical Society of America,2021,149(6):3727-3738.
[65] SONG Yubao,FENG Leping,WEN Jihong,et al. Reduction of the sound transmission of a periodic sandwich plate using the stop band concept[J]. Composite Structures,2015,128:428-436.
[66] Van BELLE L,CLAEYS C,DECKERS E,et al. The impact of damping on the sound transmission loss of locally resonant metamaterial plates[J]. Journal of Sound and Vibration,2019,461:114909.
[67] PIRES F A,WANDEL M,THOMAS C,et al. Improve sound transmission loss of an aircraft's lining panel by the use of locally resonant metamaterials[C]//Belgium:Proceedings of ISMA-USD,2022.
[68] DROZ C,ROBIN O,ICHCHOU M,et al. Improving sound transmission loss at ring frequency of a curved panel using tunable 3D-printed small-scale resonators[J]. The Journal of the Acoustical Society of America,2019,145(1):EL72-EL78.
[69] De MELO FILHO N G R,CLAEYS C,DECKERS E, et al. Realisation of a thermoformed vibro-acoustic metamaterial for increased STL in acoustic resonance driven environments[J]. Applied Acoustics,2019,156:78-82.
[70] ZHANG Hao,WEN Jihong,XIAO Yong,et al. Sound transmission loss of metamaterial thin plates with periodic subwavelength arrays of shunted piezoelectric patches[J]. Journal of Sound and Vibration,2015,343:104-120.
[71] ZHANG Hao,XIAO Yong,WEN Jihong,et al. Ultra-thin smart acoustic metasurface for low-frequency sound insulation[J]. Applied Physics Letters,2016,108:141902.
[72] ZHANG Hao,CHEN Shengbing,LIU Zongzheng,et al. Light-weight large-scale tunable metamaterial panel for low-frequency sound insulation[J]. Applied Physics Express,2020,13(6):67003.
[73] WANG Xiaopeng,CHEN Yongyong,ZHOU Guojian,et al. Synergetic coupling large-scale plate-type acoustic metamaterial panel for broadband sound insulation[J]. Journal of Sound and Vibration,2019,459:114867.
[74] LANGFELDT F,GLEINE W. Optimizing the bandwidth of plate-type acoustic metamaterials[J]. The Journal of the Acoustical Society of America,2020,148(3):1304-1314.
[75] De MELO FILHO N G R,CLAEYS C,DECKERS E,et al. Metamaterial foam core sandwich panel designed to attenuate the mass-spring-mass resonance sound transmission loss dip[J]. Mechanical Systems and Signal Processing,2020,139:106624.
[76] LANGFELDT F,HOPPEN H,GLEINE W. Broadband low-frequency sound transmission loss improvement of double walls with Helmholtz resonators[J]. Journal of Sound and Vibration,2020,476:115309.
[77] WANG Shuaixing,XIAO Yong,GU Jintao, et al. Double-panel metastructure lined with porous material for broadband low-frequency sound insulation[J]. Applied Acoustics,2023,207:109332.
[78] WANG Shuaixing,XIAO Yong,GUO Jiajia,et al. Broadband diffuse field sound insulation of double layer metamaterial plates lined with porous material[J]. Applied Physics Letters,2021,119(8):084103.
[79] De MELO FILHO N G R,Van BELLE L,CLAEYS C,et al. Dynamic mass based sound transmission loss prediction of vibro-acoustic metamaterial double panels applied to the mass-air-mass resonance[J]. Journal of Sound and Vibration,2019,442:28-44.
[80] MEI Jun,MA Guancong,YANG Min,et al. Dark acoustic metamaterials as super absorbers for low-frequency sound[J]. Nature Communications,2012,3:756.
[81] MA Guancong,YANG Min,XIAO Songwen,et al. Acoustic metasurface with hybrid resonances[J]. Nature Materials,2014,13:873.
[82] CHEN Yangyang,HUANG Guoliang,ZHOU Xiaoming,et al. Analytical coupled vibroacoustic modeling of membrane-type acoustic metamaterials:membrane model[J]. The Journal of the Acoustical Society of America,2014,136(3):969-979.
[83] CHEN Yangyang,HUANG Guoliang,ZHOU Xiaoming,et al. Analytical coupled vibroacoustic modeling of membrane-type acoustic metamaterials:plate model[J]. The Journal of the Acoustical Society of America,2014,136(6):2926-2934.
[84] YANG Min,MA Guangcong,YANG Zhiyu,et al. Subwavelength perfect acoustic absorption in membrane-type metamaterials:a geometric perspective[J]. EPJ Applied Metamaterials,2015,2:10.
[85] CAI Xiaobing,GUO Qiuquan,HU Gengkai,et al. Ultrathin low-frequency sound absorbing panels based on coplanar spiral tubes or coplanar Helmholtz resonators[J]. Applied Physics Letters,2014,105:121901.
[86] LIU Liu,CHANG Huiting,ZHANG Chi,et al. Single-channel labyrinthine metasurfaces as perfect sound absorbers with tunable bandwidth[J]. Applied Physics Letters,2017,111(8):083503.
[87] ZHANG Chi,HU Xinhua. Three-dimensional Single-port labyrinthine acoustic metamaterial:perfect absorption with large bandwidth and tunability[J]. Physical Review Applied,2016,6(6):064025.
[88] CHANG Huiting,LIU Liu,ZHANG Chi,et al. Broadband high sound absorption from labyrinthine metasurfaces[J]. AIP Advances,2018,8(4):045115.
[89] YANG Min,CHEN Shuyu,FU Caixing,et al. Optimal sound-absorbing structures[J]. Materials Horizons,2017,4(4):673-680.
[90] 王洋. 空间折叠超材料低频吸声研究[D]. 长沙:国防科技大学,2018. WANG Yang. Low-frequency sound absorption of metamaterials with coiled-up space[D]. Changsha:National University of Defense Technology,2018.
[91] LI Yong,ASSOUAR B M. Acoustic metasurface-based perfect absorber with deep subwavelength thickness[J]. Applied Physics Letters,2016,108(6):063502.
[92] WANG Yang,ZHAO Honggang,YANG Haibin,et al. A space-coiled acoustic metamaterial with tunable low-frequency sound absorption[J]. Europhysics Letters,2017,120(5):54001.
[93] WANG Yang,ZHAO Honggang,YANG Haibin,et al. A tunable sound-absorbing metamaterial based on coiled-up space[J]. Journal of Applied Physics,2018,123(18):185109.
[94] RYOO H,JEON W. Dual-frequency sound-absorbing metasurface based on visco-thermal effects with frequency dependence[J]. Journal of Applied Physics,2018,123(11):115110.
[95] JIMÉNEZ N,HUANG W,ROMERO-GARCÍA V,et al. Ultra-thin metamaterial for perfect and quasi-omnidirectional sound absorption[J]. Applied Physics Letters,2016,109(12):121902.
[96] JIMÉNEZ N,ROMERO-GARCÍA V,PAGNEUX V,et al. Rainbow-trapping absorbers:broadband,perfect andasymmetric sound absorption by subwavelength panels for transmission problems[J]. Scientific Reports,2017,7(1):13595.
[97] TANG Yufan,REN Shuwei,MENG Han,et al. Hybrid acoustic metamaterial as super absorber for broadband low-frequency sound[J]. Scientific Reports,2017,7(1):43340.
[98] SHAO Chen,ZHU Yuanzhou,LONG Houyou,et al. Metasurface absorber for ultra-broadband sound via over-damped modes coupling[J]. Applied Physics Letters,2022,120(8):083504.
[99] ZHOU Zhiling,HUANG Sibo,LI Dongting,et al. Broadband impedance modulation via non-local acoustic metamaterials[J]. National Science Review,2022,9(8):nwab171.
[100] WU Fei,XIAO Yong,YU Dianlong,et al. Low-frequency sound absorption of hybrid absorber based on micro-perforated panel and coiled-up channels[J]. Applied Physics Letters,2019,114(15):151901.
[101] WU Fei,ZHANG Xiao,JU Zegang,et al. Ultra-broadband sound absorbing materials based on periodic gradient impedance matching[J]. Frontiers in Materials,2022,9:909666.
[102] ZHAO Honggang,WANG Yang,YU Dianlong,et al. A double porosity material for low frequency sound absorption[J]. Composite Structures,2020,239:111978.
[103] GROBY J P,DAZEL O,DUCLOS A,et al. Enhancing the absorption coefficient of a backed rigid frame porous layer by embedding circular periodic inclusions[J]. The Journal of the Acoustical Society of America,2011,130(6):3771-3780.
[104] GROBY J P,LAGARRIGUE C,BROUARD B,et al. Using simple shape three-dimensional rigid inclusions to enhance porous layer absorption[J]. The Journal of the Acoustical Society of America,2014,136(3):1139-1148.
[105] LAGARRIGUE C,GROBY J P,TOURNAT V,et al. Absorption of sound by porous layers with embedded periodic arrays of resonant inclusions[J]. The Journal of the Acoustical Society of America,2013,134(6):4670-4680.
[106] LAGARRIGUE C,GROBY J P,DAZEL O,et al. Design of metaporous supercells by genetic algorithm for absorption optimization on a wide frequency band[J]. Applied Acoustics,2016,102:49-54.
[107] YANG J,LEE J S,KIM Y Y. Metaporous layer to overcome the thickness constraint for broadband sound absorption[J]. Journal of Applied Physics,2015,117(17):174903.
[108] YANG J,LEE J S,KIM Y Y. Multiple slow waves in metaporous layers for broadband sound absorption[J]. Journal of Physics D:Applied Physics,2017,50:015301.
[109] GAO Nansha,ZHANG Zhicheng. Optimization design and experimental verification of composite absorber with broadband and high efficiency sound absorption[J]. Applied Acoustics,2021,183:108288.
[110] ZHANG Hongjia,WANG Yang,ZHAO Honggang,et al. Accelerated topological design of metaporous materials of broadband sound absorption performance by generative adversarial networks[J]. Materials & Design,2021,207:109855.