EI、Scopus 收录
中文核心期刊

留言板

尊敬的读者、作者、审稿人, 关于本刊的投稿、审稿、编辑和出版的任何问题, 您可以本页添加留言。我们将尽快给您答复。谢谢您的支持!

姓名
邮箱
手机号码
标题
留言内容
验证码

低频弹性波超材料的若干进展

王凯 周加喜 蔡昌琦 徐道临 文桂林

王凯, 周加喜, 蔡昌琦, 徐道临, 文桂林. 低频弹性波超材料的若干进展. 力学学报, 2022, 54(10): 2678-2694 doi: 10.6052/0459-1879-22-108
引用本文: 王凯, 周加喜, 蔡昌琦, 徐道临, 文桂林. 低频弹性波超材料的若干进展. 力学学报, 2022, 54(10): 2678-2694 doi: 10.6052/0459-1879-22-108
Wang Kai, Zhou Jiaxi, Cai Changqi, Xu Daolin, Wen Guilin. Review of low-frequency elastic wave metamaterials. Chinese Journal of Theoretical and Applied Mechanics, 2022, 54(10): 2678-2694 doi: 10.6052/0459-1879-22-108
Citation: Wang Kai, Zhou Jiaxi, Cai Changqi, Xu Daolin, Wen Guilin. Review of low-frequency elastic wave metamaterials. Chinese Journal of Theoretical and Applied Mechanics, 2022, 54(10): 2678-2694 doi: 10.6052/0459-1879-22-108

低频弹性波超材料的若干进展

doi: 10.6052/0459-1879-22-108
基金项目: 国家自然科学基金(12002122, 12122206, 11972152, 11832009)和重庆市自然科学基金(cstc2021jcyj-msxmX0461)资助项目
详细信息
    作者简介:

    周加喜, 教授, 主要研究方向: 特种装备低频减振隔振. E-mail: jxizhou@hnu.edu.cn

  • 中图分类号: O327

REVIEW OF LOW-FREQUENCY ELASTIC WAVE METAMATERIALS

  • 摘要: 超材料是一类新兴的具有超常物理性质的人造周期/拟周期材料, 能够改变电磁波、声波以及弹性波等在介质中的传播特性. 因在航天、国防以及民用科学等方面的巨大应用潜力, 超材料自被提出后便受到极大的关注并引发研究热潮. 弹性波超材料是超材料的一种, 能够基于弹性波与超材料结构的相互耦合作用实现对弹性波的操控. 带隙是评估弹性波超材料实现弹性波操控的重要工具, 其性质与超材料的材料参数、晶格常数以及局域振子的固有频率相关. 受制于超材料的承载能力、外观尺寸以及局域振子结构等因素, 利用传统超材料开启低频(约100 Hz)弹性波带隙依然存在较大困难. 文章首先简要介绍超材料开启弹性波带隙的基本原理, 然后从低频弹性波超材料基本结构与低频带隙实现方法、低频带隙优化与调控策略、低频带隙潜在应用等三个方面详细总结低频弹性波超材料的研究工作. 其中, 低频带隙超材料的基本结构主要包括布拉格散射型超材料、传统局域共振型超材料以及准零刚度局域共振超材料. 文章通过总结低频弹性波超材料的研究进展, 分析了目前研究中的不足并对未来低频弹性波的研究方向进行了展望.

     

  • 图  1  无支撑能力超材料[40-41, 43]

    Figure  1.  Supportless metamaterials[40-41, 43]

    图  2  低刚度链式超材料及其带隙结构[57]

    Figure  2.  Low-stiffness metamaterial and corresponding band structures[57]

    图  3  不同类型的局域振子结构[73, 79-80, 85-87]

    Figure  3.  Schematic diagrams of different types of local resonators[73, 79-80, 85-87]

    图  4  准零刚度系统的静力学特性[92]

    Figure  4.  Static characters of quasi-zero-stiffness system[92]

    图  5  准零刚度局域振子基本构型[57, 92, 94, 98-103]

    Figure  5.  Schematic diagrams of different types of quasi-zero-stiffness local resonators[57, 92, 94, 98-103]

    图  6  准零刚度超材料的带隙结构图[95, 103]

    Figure  6.  Band structures of quasi-zero-stiffness metamaterials[95, 103]

    图  7  惯性放大机构示意图及其带隙结构[95, 138-141]

    Figure  7.  Schematic diagrams of inertial amplification and corresponding band structure[95, 138-141]

    图  8  基于局域振子刚度调控低频带隙的超材料[14, 151, 153]

    Figure  8.  Metamaterials capable of opening tunable band structure which adjusted by resonator stiffness[14, 151, 153]

    图  9  超材料的部分应用[83, 93, 168-169, 175]

    Figure  9.  The application of metamaterials[83, 93, 168-169, 175]

  • [1] Martínez-Sala R, Sancho J, Sánchez JV, et al. Sound attenuation by sculpture. Nature, 1995, 378(6554): 241-241
    [2] Nadkarni N, Arrieta AF, Chong C, et al. Unidirectional transition waves in bistable lattices. Physical Review Letters, 2016, 116(24): 244501 doi: 10.1103/PhysRevLett.116.244501
    [3] 秦浩星, 杨德庆, 张相闻. 负泊松比声学超材料基座的减振性能研究. 振动工程学报, 2017, 30(6): 1012-1021 (Qin Haoxing, Yang Deqing, Zhang Xiangwen. Vibration reduction of auxetic acoustic metamaterial mount. Journal of Vibration Engineering, 2017, 30(6): 1012-1021 (in Chinese) doi: 10.16385/j.cnki.issn.1004-4523.2017.06.015
    [4] Cubukcu E, Aydin K, Ozbay E, et al. Electromagnetic waves: Negative refraction by photonic crystals. Nature, 2003, 423: 604-605 doi: 10.1038/423604b
    [5] Miller W, Smith CW, MacKenzie DS, et al. Negative thermal expansion: A review. Journal of Materials Science, 2009, 44: 5441-5451 doi: 10.1007/s10853-009-3692-4
    [6] Dwivedi A, Banerjee A, Adhikari S, et al. Optimal electromechanical bandgaps in piezo-embedded mechanical metamaterials. International Journal of Mechanics and Materials in Design, 2021, 17(2): 419-439 doi: 10.1007/s10999-021-09534-0
    [7] Zhu X, Liang B, Kan W, et al. Acoustic cloaking by a superlens with single-negative materials. Physical Review Letters, 2011, 106: 014301 doi: 10.1103/PhysRevLett.106.014301
    [8] Ball P. New lessons for stealth technology. Nature Materials, 2021, 20: 4 doi: 10.1038/s41563-020-00885-1
    [9] Yan M, Lu J, Li F, et al. On-chip valley topological materials for elastic wave manipulation. Nature Materials, 2018, 17(11): 993-998 doi: 10.1038/s41563-018-0191-5
    [10] 马天雪, 苏晓星, 董浩文等. 声光子晶体带隙特性与声光耦合作用研究综述. 力学学报, 2017, 49(4): 743-757 (Ma Tianxue, Su Xiaoxing, Dong Haowen, et al. Review of bandgap characteristics and acousto-optical coupling in phoxonic crystals. Chinese Journal of Theoretical and Applied Mechanics, 2017, 49(4): 743-757 (in Chinese) doi: 10.6052/0459-1879-17-130
    [11] 侯秀慧, 吕游, 周世奇等. 新型负刚度吸能结构力学特性分析. 力学学报, 2021, 53(7): 1940-1950 (Hou Xiuhui, Lü You, Zhou Shiqi, et al. Mechanical properties analysis of a new energy absorbing structure with negative stiffness. Chinese Journal of Theoretical and Applied Mechanics, 2021, 53(7): 1940-1950 (in Chinese) doi: 10.6052/0459-1879-21-083
    [12] 邱海, 方虹斌, 徐鉴. 多稳态串联折纸结构的非线性动力学特性. 力学学报, 2019, 51(4): 1110-1121 (Qiu Hai, Fang Hongbin, Xu Jian. Nonlinear dynamical characteristics of a multi-stable series origami structure. Chinese Journal of Theoretical and Applied Mechanics, 2019, 51(4): 1110-1121 (in Chinese) doi: 10.6052/0459-1879-19-115
    [13] 陈焱. 基于机构运动的大变形超材料. 机械工程学报, 2020, 56(19): 2-13 (Chen Yan. Review on kinematic metamaterials. Journal of Vibration Engineering, 2020, 56(19): 2-13 (in Chinese) doi: 10.3901/JME.2020.19.002
    [14] 袁毅, 游镇宇, 陈伟球. 压电超构材料及其波动控制研究: 现状与展望. 力学学报, 2021, 53(8): 2101-2116 (Yuan Yi, You Zhenyu, Chen Weiqiu. Piezoelectric metamaterials and wave control: status quo and prospects. Chinese Journal of Theoretical and Applied Mechanics, 2021, 53(8): 2101-2116 (in Chinese) doi: 10.6052/0459-1879-21-198
    [15] Liu Z, Zhang X, Mao Y, et al. Locally resonant sonic materials. Science, 2000, 289(5485): 1734-1736 doi: 10.1126/science.289.5485.1734
    [16] Yang Z, Mei J, Yang M, et al. Membrane-type acoustic metamaterial with negative dynamic mass. Physical Review Letters, 2008, 101: 204301 doi: 10.1103/PhysRevLett.101.204301
    [17] Wu R, Cui T. Microwave metamaterials: from exotic physics to novel information systems. Frontiers of Information Technology and Electronic Engineering, 2020, 21(1): 4-26 doi: 10.1631/FITEE.1900465
    [18] Shanshan Y, Xiaoming Z, Gengkai H. Experimental study on negative effective mass in a 1D mass-spring system. New Journal of Physics, 2008, 10: 043020 doi: 10.1088/1367-2630/10/4/043020
    [19] Zhu R, Liu XN, Hu GK, et al. Negative refraction of elastic waves at the deep-subwavelength scale in a single-phase metamaterial. Nature Communications, 2014, 5: 5510 doi: 10.1038/ncomms6510
    [20] Wang G, Wen X, Wen J, et al. Two-dimensional locally resonant phononic crystals with binary structures. Physical Review Letters, 2004, 93: 154302 doi: 10.1103/PhysRevLett.93.154302
    [21] Fang X, Wen J, Bonello B, et al. Ultra-low and ultra-broad-band nonlinear acoustic metamaterials. Nature Communications, 2017, 8(1): 1288 doi: 10.1038/s41467-017-00671-9
    [22] 于靖军, 谢岩, 裴旭. 负泊松比超材料研究进展. 机械工程学报, 2018, 54(13): 1-14 (Yu Jingjun, Xie Yan, Pei Xu. State-of-art of metamaterials with negative Poisson’s ratio. Journal of Vibration Engineering, 2018, 54(13): 1-14 (in Chinese) doi: 10.3901/JME.2018.13.001
    [23] 刘敏, 张斌珍, 段俊萍. 一种基于超材料的宽频带定向性微带天线. 机械工程学报, 2018, 54(9): 64-68 (Liu Min, Zhang Binzhen, Duan Junping. Broadband and directional microstrip antenna based on metamaterials. Journal of Vibration Engineering, 2018, 54(9): 64-68 (in Chinese) doi: 10.3901/JME.2018.09.064
    [24] Ma G, Sheng P. Acoustic metamaterials : From local resonances to broad horizons. Science Advances, 2016, 2: e1501595 doi: 10.1126/sciadv.1501595
    [25] 温熙森, 温激鸿, 郁殿龙等. 声子晶体. 北京: 国防工业出版社, 2009

    Wen Xisen, Wen Jihong, Yu Dianlong, et al. Phononic Crystals. Beijing: National Defence Industry Press, 2009 (in Chinese)
    [26] Zouhdi S, Sihvola A, Vinogradov AP. Metamaterials and Plasmonics: Fundamentals, Modelling, Applications. Dordrecht: Springer Science & Business Media, 2008
    [27] Kadic M, Schittny R, Bückmann T, et al. Hall-effect sign inversion in a realizable 3D metamaterial. Physical Review X, 2015, 5: 021030 doi: 10.1103/PhysRevX.5.021030
    [28] Wang Y, Zhao W, Rimoli JJ, et al. Prestress-controlled asymmetric wave propagation and reciprocity-breaking in tensegrity metastructure. Extreme Mechanics Letters, 2020, 37: 100724 doi: 10.1016/j.eml.2020.100724
    [29] Ji JC, Luo Q, Ye K. Vibration control based metamaterials and origami structures: A state-of-the-art review. Mechanical Systems and Signal Processing, 2021, 161: 107945 doi: 10.1016/j.ymssp.2021.107945
    [30] Tang L, Cheng L. Impaired sound radiation in plates with periodic tunneled acoustic black holes. Mechanical Systems and Signal Processing, 2020, 135: 106410 doi: 10.1016/j.ymssp.2019.106410
    [31] Askari M, Hutchins DA, Thomas PJ, et al. Additive manufacturing of metamaterials: A review. Additive Manufacturing, 2020, 36: 101562 doi: 10.1016/j.addma.2020.101562
    [32] Jia Z, Chen Y, Yang H, et al. Designing phononic crystals with wide and robust Band gaps. Physical Review Applied, 2018, 9: 044021 doi: 10.1103/PhysRevApplied.9.044021
    [33] 肖庆雨, 周加喜, 徐道临等. 一种六自由度准零刚度隔振平台. 振 动 与 冲 击, 2019, 38(1): 258-264 (Xiao Qingyu, Zhou Jiaxi, Xu Daolin, et al. A 6-DOF quasi-zero stiffness vibration isolation platform. Journal of Vibration and Shock, 2019, 38(1): 258-264 (in Chinese)
    [34] Zhou J, Wang K, Xu D, et al. Local resonator with high-static-low-dynamic stiffness for lowering band gaps of flexural wave in beams. Journal of Applied Physics, 2017, 121: 044902 doi: 10.1063/1.4974299
    [35] 冯青松, 杨舟, 梁玉雄等. 双周期声子晶体梁弯曲振动带隙特性分析. 噪声与振动控制, 2020, 40(3): 1-8 (Feng Qingsong, Yang Zhou, Liang Yuxiong, et al. Study on bending vibration band gap characteristics of a double periodic phononic crystal beam. Noise and Vibration Control, 2020, 40(3): 1-8 (in Chinese) doi: 10.3969/j.issn.1006-1355.2020.03.001
    [36] Maslov K, Kinra VK, Henderson BK. Elastodynamic response of a coplanar periodic layer of elastic spherical inclusions. Mechanics of Materials, 2000, 32(12): 785-795 doi: 10.1016/S0167-6636(00)00046-6
    [37] Jensen JS. Phononic band gaps and vibrations in one- and two-dimensional mass-spring structures. Journal of Sound and Vibration, 2003, 266(5): 1053-1078 doi: 10.1016/S0022-460X(02)01629-2
    [38] 邱学云, 胡家光, 唐启祥. 填充率对一维二元声子晶体杆带隙的影响. 重庆师范大学学报(自然科学版), 2016, 33(2): 113-117 (Qiu Xueyun, Hu Jiaguang, Tang Qiqiang, et al. Influences of filling ratio on the rod-shaped structure of one-dimensional two-component phononic crystals. Journal of Chongqing Normal University (Natural Science), 2016, 33(2): 113-117 (in Chinese)
    [39] Zheng B, Xu J. Mechanical logic switches based on DNA-inspired acoustic metamaterials with ultrabroad low-frequency band gaps. Journal of Physics D: Applied Physics, 2017, 50: 465601 doi: 10.1088/1361-6463/aa8b08
    [40] Oh JH, Choi SJ, Lee JK, et al. Zero-frequency Bragg gap by spin-harnessed metamaterial. New Journal of Physics, 2018, 20: 083035 doi: 10.1088/1367-2630/aada38
    [41] Oh JH, Assouar B. Quasi-static stop band with flexural metamaterial having zero rotational stiffness. Scientific Reports, 2016, 6: 33410 doi: 10.1038/srep33410
    [42] Zhang YY, Wu JH, Hu GZ, et al. Flexural wave suppression by an elastic metamaterial beam with zero bending stiffness. Journal of Applied Physics, 2017, 121: 134902 doi: 10.1063/1.4979686
    [43] Park S, Jeon W. Ultra-wide low-frequency band gap in a tapered phononic beam. Journal of Sound and Vibration, 2021, 499: 115977 doi: 10.1016/j.jsv.2021.115977
    [44] 王倚天, 赵建雷, 张铭凯等. 含机构位移模式的超材料低频宽带波动控制. 科学通报, 2021, 66: 1-11 (Wang Yitian, Zhao Jianlei, Zhang Mingkai, et al. Mechanism-based metamaterials for low-frequency broadband wave control. Chinese Science Bulletin, 2021, 66: 1-11 (in Chinese) doi: 10.1360/tb-2021-0518
    [45] Bae MH, Oh JH. Nonlinear elastic metamaterial for tunable bandgap at quasi-static frequency. Mechanical Systems and Signal Processing, 2022, 170: 108832 doi: 10.1016/j.ymssp.2022.108832
    [46] Ghavanloo E, El-Borgi S, Fazelzadeh SA. Formation of quasi-static stop band in a new one-dimensional metamaterial. Archive of Applied Mechanics, 2022, https: //doi.org/10.1007/s00419-022-02146-w
    [47] Wang Z, Chu Y, Cai C, et al. Composite pentamode metamaterials with low frequency locally resonant characteristics. Journal of Applied Physics, 2017, 122: 025114 doi: 10.1063/1.4993904
    [48] Kadic M, Bückmann T, Stenger N, et al. On the practicability of pentamode mechanical metamaterials. Applied Physics Letters, 2012, 100: 191901 doi: 10.1063/1.4709436
    [49] 陈毅, 刘晓宁, 向平等. 五模材料及其水声调控研究. 力学进展, 2016, 46: 201609 (Chen Yi, Liu Xiaoning, Xiang Ping, et al. Pentamode material for underwater acoustic wave control. Advances in Mechanics, 2016, 46: 201609 (in Chinese) doi: 10.6052/1000-0992-16-010
    [50] Chen Y, Zheng M, Liu X, et al. Broadband solid cloak for underwater acoustics. Physical Review B, 2017, 95: 180104(R doi: 10.1103/PhysRevB.95.180104
    [51] Zheng M, Liu X, Chen Y, et al. Theory and realization of nonresonant anisotropic singly polarized solids carrying only shear waves. Physical Review Applied, 2019, 12: 014027 doi: 10.1103/PhysRevApplied.12.014027
    [52] Zheng M, Park C Il, Liu X, et al. Non-resonant metasurface for broadband elastic wave mode splitting. Applied Physics Letters, 2020, 116(17): 171903 doi: 10.1063/5.0005408
    [53] Huang Y, Zhang X. Pentamode metamaterials with ultra-low-frequency single-mode band gap based on constituent materials. Journal of Physics Condensed Matter, 2021, 33: 185703 doi: 10.1088/1361-648X/abeebd
    [54] 王兆宏, 李青蔚, 蔡成欣等. 可用于隔声和带隙调控的五模式超材料. 声学学报, 2017, 42(5): 610-618 (Wang Zhaohong, Li Qingwei, Cai Chengxin, et al. Pentamode metamaterials used for sound insulation and band gap controlling consisting of double-cones. Acta Acustica, 2017, 42(5): 610-618 (in Chinese)
    [55] Cai C, Wang Z, Chu Y, et al. The phononic band gaps of Bragg scattering and locally resonant pentamode metamaterials. Journal of Physics D: Applied Physics, 2017, 50: 415105 doi: 10.1088/1361-6463/aa83ec
    [56] Cai C, Han C, Wu J, et al. Tuning method of phononic band gaps of locally resonant pentamode metamaterials. Journal of Physics D: Applied Physics, 2019, 52: 045601 doi: 10.1088/1361-6463/aaebdc
    [57] Zhou J, Pan H, Cai C, et al. Tunable ultralow frequency wave attenuations in one-dimensional quasi-zero-stiffness metamaterial. International Journal of Mechanics and Materials in Design, 2021, 17(2): 285-300 doi: 10.1007/s10999-020-09525-7
    [58] Zhang Q, Guo D, Hu G. Tailored mechanical metamaterials with programmable quasi-zero-stiffness features for full-band vibration isolation. Advanced Functional Materials, 2021, 31(33): 2101428 doi: 10.1002/adfm.202101428
    [59] 赵伟佳, 王倚天, 朱睿等. 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, 2020, 50(9): 090010 (Zhao Weijia, Wang Yitian, Zhu Rui, et al. Isolating low-frequency vibration via lightweight embedded metastructures. Scientia Sinica Physica, Mechanica& Astronomica, 2020, 50(9): 090010 (in Chinese) doi: 10.1360/SSPMA-2020-0153
    [60] 吴健, 白晓春, 肖勇等. 一种多频局域共振型声子晶体板的低频带隙与减振特性. 物理学报, 2016, 65(6): 0646002 (Wu Jian, Bai Xiaochun, Xiao Yong, et al. Low frequency band gaps and vibration reduction properties of a multi-frequency locally resonant phononic plate. Acta Physica Sinica, 2016, 65(6): 0646002 (in Chinese) doi: 10.7498/aps.65.064602
    [61] Nair S, Jokar M, Semperlotti F. Nonlocal acoustic black hole metastructures: Achieving broadband and low frequency passive vibration attenuation. Mechanical Systems and Signal Processing, 2022, 169: 108716 doi: 10.1016/j.ymssp.2021.108716
    [62] Lazarov BS, Jensen JS. Low-frequency band gaps in chains with attached non-linear oscillators. International Journal of Non-Linear Mechanics, 2007, 42(10): 1186-1193 doi: 10.1016/j.ijnonlinmec.2007.09.007
    [63] Yu D, Liu Y, Wang G, et al. Flexural vibration band gaps in Timoshenko beams with locally resonant structures. Journal of Applied Physics, 2006, 100: 124901 doi: 10.1063/1.2400803
    [64] Xiao Y, Wen J, Wen X. Flexural wave band gaps in locally resonant thin plates with periodically attached springmass resonators. Journal of Physics D: Applied Physics, 2012, 45: 195401 doi: 10.1088/0022-3727/45/19/195401
    [65] Hussein MI, Leamy MJ, Ruzzene M. Dynamics of phononic materials and structures: Historical origins, recent progress, and future outlook. Applied Mechanics Reviews, 2014, 66(4): 040802 doi: 10.1115/1.4026911
    [66] Ning S, Yang F, Luo C, et al. Low-frequency tunable locally resonant band gaps in acoustic metamaterials through large deformation. Extreme Mechanics Letters, 2020, 35: 100623 doi: 10.1016/j.eml.2019.100623
    [67] Muhammad F, Ket C, Ooi L, et al. Increased power output of an electromagnetic vibration energy harvester through anti-phase resonance. Mechanical Systems and Signal Processing, 2019, 116: 129-145 doi: 10.1016/j.ymssp.2018.06.012
    [68] Zhang YY, Gao NS, Wu JH. New mechanism of tunable broadband in local resonance structures. Applied Acoustics, 2020, 169: 107482 doi: 10.1016/j.apacoust.2020.107482
    [69] Fan L, He Y, Chen X, et al. Elastic metamaterial shaft with a stack-like resonator for low-frequency vibration isolation. Journal of Physics D: Applied Physics, 2020, 53: 105101 doi: 10.1088/1361-6463/ab5d59
    [70] Lu K, Zhou G, Gao N, et al. Flexural vibration bandgaps of the multiple local resonance elastic metamaterial plates with irregular resonators. Applied Acoustics, 2020, 159: 107115 doi: 10.1016/j.apacoust.2019.107115
    [71] 吕锐翔, 李丽霞, 杨继博. 单边周期环形谐振径向声子晶体结构›. 振动与冲击, 2021, 40(1): 68-72 (Lü Ruixiang, Li Lixia, Yang Jibo. Radial phononic crystal structure with unilateral periodic ring resonance. Journal of Vibration and Shock, 2021, 40(1): 68-72 (in Chinese)
    [72] 刘荣强, 赵浩江, 李长洲等. 三组元栅格板的振动特性研究. 振动与冲击, 2016, 35(15): 53-57 (Liu Rongqiang, Zhao Haojiang, Li Changzhou, et al. Vibration characteristics of three-component grid plates. Journal of Vibration and Shock, 2016, 35(15): 53-57 (in Chinese)
    [73] Zhang H, Xiao Y, Wen J, et al. Flexural wave band gaps in metamaterial beams with membrane-type resonators: Theory and experiment. Journal of Physics D: Applied Physics, 2015, 48: 435305 doi: 10.1088/0022-3727/48/43/435305
    [74] Nouh M, Aldraihem O, Baz A. Metamaterial structures with periodic local resonances. Health Monitoring of Structural and Biological Systems, 2014, 9064: 90641Y doi: 10.1117/12.2046433
    [75] Li J, Fan X, Li F. Numerical and experimental study of a sandwich-like metamaterial plate for vibration suppression. Composite Structures, 2020, 238: 111969 doi: 10.1016/j.compstruct.2020.111969
    [76] Miao L, Li C, Lei L, et al. A new periodic structure composite material with quasi-phononic crystals. Physics Letters, Section A: General, Atomic and Solid State Physics, 2020, 384(25): 126594 doi: 10.1016/j.physleta.2020.126594
    [77] Xiao Y, Wen J. Closed-form formulas for bandgap estimation and design of metastructures undergoing longitudinal of torsional vibration. Journal of Sound and Vibration, 2017, 485: 115578 doi: 10.1016/j.jsv.2020.115578
    [78] Zhao L, Lu ZQ, Ding H, et al. Experimental observation of transverse and longitudinal wave propagation in a metamaterial periodically arrayed with nonlinear resonators. Mechanical Systems and Signal Processing, 2022, 170: 108836 doi: 10.1016/j.ymssp.2022.108836
    [79] Jiang T, He Q. Dual-directionally tunable metamaterial for low-frequency vibration isolation. Applied Physics Letters, 2017, 110: 021907 doi: 10.1063/1.4974034
    [80] Tian Y, Wu JH, Li H, et al. Elastic wave propagation in the elastic metamaterials containing parallel multi-resonators. Journal of Physics D: Applied Physics, 2019, 52: 395301 doi: 10.1088/1361-6463/ab2dba
    [81] 张思文, 吴九汇. 局域共振复合单元声子晶体结构的低频带隙特性研究. 物理学报, 2013, 62(13): 134302 (Zhang Siwen, Wu Jiuhui. Low-frequency band gaps in phononic crystals with composite locally resonant structures. Acta Physica Sinica, 2013, 62(13): 134302 (in Chinese) doi: 10.7498/aps.62.134302
    [82] 张思文, 吴九汇. 基于局域共振声子晶体结构的低频振动能量回收研究. 固体力学学报, 2013, 34(4): 333-341 (Zhang Siwen, Wu Jiuhui. Energy harvesting based on locally resonant phononic crystals for low frequency vibrations. Chinese Journal of Solid Mechanics, 2013, 34(4): 333-341 (in Chinese) doi: 10.19636/j.cnki.cjsm42-1250/o3.2013.04.002
    [83] Bilal OR, Foehr A'e, Daraio C. Bistable metamaterial for switching and cascading elastic vibrations. Proceedings of the National Academy of Sciences of the United States of America, 2017, 114(18): 4603-4606 doi: 10.1073/pnas.1618314114
    [84] Jin Y, Zeng S, Wen Z, et al. Deep-subwavelength lightweight metastructures for low-frequency vibration isolation. Materials and Design, 2022, 215: 110499 doi: 10.1016/j.matdes.2022.110499
    [85] 温卓群, 王鹏飞, 张雁等. 面向大尺度结构的力学超材料减振技术. 航空学报, 2018, 39: 721651 (Wen Zhuoqun, Wang Pengfei, Zhang Yan, et al. Vibration reduction technology of mechanical metamaterials presented to large scale structures. Acta Aeronautica et Astronautica Sinica, 2018, 39: 721651 (in Chinese) doi: 10.12159/j.issn.2095-6630.2019.13.0346
    [86] 卢一铭, 曹东兴, 申永军等. 局域共振型声子晶体板缺陷态带隙及其俘能特性研究. 力学学报, 2021, 53(4): 1114-1123 (Lu Yiming, Cao Dongxing, Shen Yongjun, et al. Study on the bandgaps of defect states and application of energy harvesting of local resonant phononic crystal plate. Chinese Journal of Theoretical and Applied Mechanics, 2021, 53(4): 1114-1123 (in Chinese) doi: 10.6052/0459-1879-20-436STUDY
    [87] 温华兵, 李军, 李兵. 质量块-支架梁局域共振板结构的低频振动带隙特性研究. 江苏科技大学学报(自然科学版), 2019, 33(3): 43-48 (Wen Huabing, Li Jun, Li Bing. Low-Frequency vibration characteristics of periodic mass-beam resonantors in phononic crystal plate. Journal of Jiangsu University of Science and Technology (Natural Science Edition), 2019, 33(3): 43-48 (in Chinese)
    [88] Rao SS. Mechanical Vibrations. New York: Pearson Prentice Hall, 2010
    [89] 李昊, 赵发刚, 周徐斌. 基于混杂双稳定层合板的准零刚度隔振装置. 力学学报, 2019, 51(2): 354-363 (Li Hao, Zhao Fagang, Zhou Xubin. A quasi-zero stiffness vibration isolator based on hybrid bistable composite laminate. Chinese Journal of Theoretical and Applied Mechanics, 2019, 51(2): 354-363 (in Chinese) doi: 10.2514/6.2019-1860
    [90] Wang K, Zhou J, Xu D. Sensitivity analysis of parametric errors on the performance of a torsion quasi-zero-stiffness vibration isolator. International Journal of Mechanical Sciences, 2017, 134: 336-346 doi: 10.1016/j.ijmecsci.2017.10.026
    [91] Wang K, Zhou J, Ouyang H, et al. A dual quasi-zero-stiffness sliding-mode triboelectric nanogenerator for harvesting ultralow-low frequency vibration energy. Mechanical Systems and Signal Processing, 2021, 151: 107368 doi: 10.1016/j.ymssp.2020.107368
    [92] Cai C, Zhou J, Wu L, et al. Design and numerical validation of quasi-zero-stiffness metamaterials for very low-frequency band gaps. Composite Structures, 2020, 236: 111862 doi: 10.1016/j.compstruct.2020.111862
    [93] Zhou J, Wang K, Xu D, et al. Multi-low-frequency flexural wave attenuation in Euler–Bernoulli beams using local resonators containing negative-stiffness mechanisms. Physics Letters, Section A: General, Atomic and Solid State Physics, 2017, 381(37): 3141-3148 doi: 10.1016/j.physleta.2017.08.020
    [94] Xie B, Sheng M. Ultralow-frequency band gap in a quasi-zero-stiffness multi-resonator periodic hybrid structure. Wave Motion, 2021, 107: 102825 doi: 10.1016/j.wavemoti.2021.102825
    [95] Zhou J, Lingling D, Wang K, et al. A nonlinear resonator with inertial amplification for very low-frequency flexural wave attenuations in beams. Nonlinear Dynamics, 2019, 96(1): 647-665 doi: 10.1007/s11071-019-04812-1
    [96] Wang K, Zhou J, Cai C, et al. Mathematical modeling and analysis of a meta-plate for very low-frequency band gap. Applied Mathematical Modelling, 2019, 73: 581-597 doi: 10.1016/j.apm.2019.04.033
    [97] He F, Shi Z, Qian D, et al. Flexural wave bandgap properties in metamaterial dual-beam structure. Physics Letters, Section A: General, Atomic and Solid State Physics, 2022, 429: 127950 doi: 10.1016/j.physleta.2022.127950
    [98] Wu Z, Liu W, Li F, et al. Band-gap property of a novel elastic metamaterial beam with X-shaped local resonators. Mechanical Systems and Signal Processing, 2019, 134: 106357 doi: 10.1016/j.ymssp.2019.106357
    [99] Wang K, Zhou J, Cai C, et al. Bidirectional deep-subwavelength band gap induced by negative stiffness. Journal of Sound and Vibration, 2021, 515: 116474 doi: 10.1016/j.jsv.2021.116474
    [100] Wang K, Zhou J, Daolin X, et al. Tunable low-frequency torsional-wave band gaps in a meta-shaft. Journal of Physics D: Applied Physics, 2019, 52: 055104 doi: 10.1088/1361-6463/aaf039
    [101] Wang K, Zhou J, Wang Q, et al. Low-frequency band gaps in a metamaterial rod by negative-stiffness mechanisms: Design and experimental validation. Applied Physics Letters, 2019, 114(25): 251902 doi: 10.1063/1.5099425
    [102] Wang K, Zhou J, Xu D, et al. Lower band gaps of longitudinal wave in a one-dimensional periodic rod by exploiting geometrical nonlinearity. Mechanical Systems and Signal Processing, 2019, 124: 664-678 doi: 10.1016/j.ymssp.2019.02.008
    [103] Lin Q, Zhou J, Pan H, et al. Numerical and experimental investigations on tunable low-frequency locally resonant metamaterials. Acta Mechanica Solida Sinica, 2021, 34(5): 612-623 doi: 10.1007/s10338-021-00220-4
    [104] Cai C, Zhou J, Wang K, et al. Flexural wave attenuation by metamaterial beam with compliant quasi-zero-stiffness resonators. Mechanical Systems and Signal Processing, 2022, 174: 109119 doi: 10.1016/j.ymssp.2022.109119
    [105] Lin Q, Zhou J, Wang K, et al. Low-frequency locally resonant band gap of the two-dimensional quasi-zero-stiffness metamaterials. International Journal of Mechanical Sciences, 2022, 222: 107230 doi: 10.1016/j.ijmecsci.2022.107230
    [106] Liu J, Guo H, Wang T. A review of acoustic metamaterials and phononic crystals. Crystals, 2020, 10(4): 305 doi: 10.3390/cryst10040305
    [107] Chen S, Fan Y, Fu Q, et al. A review of tunable acoustic metamaterials. Applied Sciences, 2018, 8(9): 1480 doi: 10.3390/app8091480
    [108] Wu L, Wang Y, Chuang K, et al. A brief review of dynamic mechanical metamaterials for mechanical energy manipulation. Materials Today, 2021, 44: 168-193 doi: 10.1016/j.mattod.2020.10.006
    [109] Bao H, Wu C, Wang K, et al. An enhanced dual-resonator metamaterial beam for low-frequency vibration suppression. Journal of Applied Physics, 2021, 129: 095106 doi: 10.1063/5.0040414
    [110] Li Y, Li H. Bandgap merging and widening of elastic metamaterial with heterogeneous resonator. Journal of Physics D: Applied Physics, 2020, 53: 475302 doi: 10.1088/1361-6463/abab2b
    [111] Wen S, Xiong Y, Hao S, et al. Enhanced band-gap properties of an acoustic metamaterial beam with periodically variable cross-sections. International Journal of Mechanical Sciences, 2020, 166: 105229 doi: 10.1016/j.ijmecsci.2019.105229
    [112] Lu K, Wu JH, Jing L, et al. The two-degree-of-freedom local resonance elastic metamaterial plate with broadband low-frequency bandgaps. Journal of Physics D: Applied Physics, 2017, 50: 095104 doi: 10.1088/1361-6463/50/9/095104
    [113] Wang F, Sun X, Meng H, et al. Tunable broadband low-frequency band gap of multiple-layer metastructure induced by time-delayed vibration absorbers. Nonlinear Dynamics, 2022, 107: 1903-1918 doi: 10.1007/s11071-021-07065-z
    [114] Fang X, Chuang KC, Jin X, et al. Band-gap properties of elastic metamaterials with inerter-based dynamic vibration absorbers. Journal of Applied Mechanics, 2018, 85(7): 071010 doi: 10.1115/1.4039898
    [115] Kulkarni PP, Manimala JM. Longitudinal elastic wave propagation characteristics of inertant acoustic metamaterials. Journal of Applied Physics, 2016, 119: 245101 doi: 10.1063/1.4954074
    [116] Russillo AF, Failla G, Alotta G. Ultra-wide low-frequency band gap in locally-resonant plates with tunable inerter-based resonators. Applied Mathematical Modelling, 2022, 106: 682-695 doi: 10.1016/j.apm.2022.02.015
    [117] Liu Y, Yang J, Yi X, et al. Enhanced suppression of low-frequency vibration transmission in metamaterials with linear and nonlinear inerters. Journal of Applied Physics, 2022, 131: 105103 doi: 10.1063/5.0084399
    [118] Zhou L, Han W, Wan S. Low frequency band gap for box girder attached IDVAs. Thin-Walled Structures, 2022, 174: 109088 doi: 10.1016/j.tws.2022.109088
    [119] Lin S, Zhang Y, Liang Y, et al. Bandgap characteristics and wave attenuation of metamaterials based on negative-stiffness dynamic vibration absorbers. Journal of Sound and Vibration, 2021, 502: 116088 doi: 10.1016/j.jsv.2021.116088
    [120] Hu G, Tang L, Xu J, et al. Metamaterial with local resonators coupled by negative stiffness springs for enhanced vibration suppression. Journal of Applied Mechanics, Transactions ASME, 2019, 86(8): 081009 doi: 10.1115/1.4043827
    [121] Hu G, Tang L, Das R, et al. Acoustic metamaterials with coupled local resonators for broadband vibration suppression. AIP Advances, 2017, 7: 025211 doi: 10.1063/1.4977559
    [122] Bao H, Wu C, Zheng W, et al. Vibration bandgap of a locally resonant beam considering horizontal springs. Journal of Vibration and Control, 2022, 28(3-4): 452-464 doi: 10.1177/1077546320980190
    [123] Zhao P, Zhang K, Zhao C, et al. Multi-resonator coupled metamaterials for broadband vibration suppression. Applied Mathematics and Mechanics (English Edition) , 2021, 42(1): 53-64 doi: 10.1007/s10483-021-2684-8
    [124] Hu GCM, Austin A, Sorokin V, et al. Metamaterial beam with graded local resonators for broadband vibration suppression. Mechanical Systems and Signal Processing, 2021, 146: 106982 doi: 10.1016/j.ymssp.2020.106982
    [125] Banerjee A, Das R, Calius EP. Frequency graded 1D metamaterials: A study on the attenuation bands. Journal of Applied Physics, 2017, 122: 075101 doi: 10.1063/1.4998446
    [126] Li Y, Dong X, Li H, et al. Hybrid multi-resonators elastic metamaterials for broad low-frequency bandgaps. International Journal of Mechanical Sciences, 2021, 202-203: 106501
    [127] Wu Q, Huang G, Liu C, et al. Low-frequency multi-mode vibration suppression of a metastructure beam with two-stage high-static-low-dynamic stiffness oscillators. Acta Mechanica, 2019, 230(12): 4341-4356 doi: 10.1007/s00707-019-02515-7
    [128] Al Ba'ba'a H, Nouh M, Singh T. Formation of local resonance band gaps in finite acoustic metamaterials: A closed-form transfer function model. Journal of Sound and Vibration, 2017, 410: 429-446 doi: 10.1016/j.jsv.2017.08.009
    [129] 杜春阳, 郁殿龙, 刘江伟等. X形超阻尼局域共振声子晶体梁弯曲振动带隙. 物理学报, 2017, 66(14): 140701 (Du Chunyang, Yu Dianlong, Liu Jiangwei, et al. Flexural vibration band gaps for a phononic crystal beam with X-shaped local resonance metadamping structure. Acta Physica Sinica, 2017, 66(14): 140701 (in Chinese) doi: 10.7498/aps.66.140701
    [130] Wang K, Zhou J, Ouyang H, et al. A semi-active metamaterial beam with electromagnetic quasi-zero-stiffness resonators for ultralow-frequency band gap tuning. International Journal of Mechanical Sciences, 2020, 176: 105548 doi: 10.1016/j.ijmecsci.2020.105548
    [131] Fang X, Wen J, Yu D, et al. Bridging-coupling band gaps in nonlinear acoustic metamaterials. Physical Review Applied, 2018, 10: 054049 doi: 10.1103/PhysRevApplied.10.054049
    [132] Fang X, Wen J, Yin J, et al. Broadband and tunable one-dimensional strongly nonlinear acoustic metamaterials: Theoretical study. Physical Review E, 2016, 94(5): 052206 doi: 10.1103/PhysRevE.94.052206
    [133] Mi Y, Yu X. Sound transmission of acoustic metamaterial beams with periodic inertial amplification mechanisms. Journal of Sound and Vibration, 2021, 499: 116009 doi: 10.1016/j.jsv.2021.116009
    [134] Sheng P, Fang X, Wen J, et al. Vibration properties and optimized design of a nonlinear acoustic metamaterial beam. Journal of Sound and Vibration, 2021, 492: 115739 doi: 10.1016/j.jsv.2020.115739
    [135] Fang X, Wen J, Yu D, et al. Wave propagation in a nonlinear acoustic metamaterial beam considering third harmonic generation. New Journal of Physics, 2018, 20: 123028 doi: 10.1088/1367-2630/aaf65e
    [136] Beli D, Ruzzene M, De Marqui C. Bridging-coupling phenomenon in linear elastic metamaterials by exploiting locally resonant metachain isomers. Physical Review Applied, 2020, 14(3): 034032 doi: 10.1103/PhysRevApplied.14.034032
    [137] 张印, 尹剑飞, 温激鸿等. 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, 2016, 35(17): 26-32 (Zhang Yin, Yin Jianfei, Wen Jihong, et al. Low frequency vibration reduction design for inertial local resonance phononic crystals based on inertial amplification. Journal of Vibration and Shock, 2016, 35(17): 26-32 (in Chinese)
    [138] Yilmaz C, Hulbert GM, Kikuchi N. Phononic band gaps induced by inertial amplification in periodic media. Physical Review B - Condensed Matter and Materials Physics, 2007, 76: 054309 doi: 10.1103/PhysRevB.76.054309
    [139] Wang S, Wang M, Guo Z. Adjustable low-frequency bandgap of flexural wave in an Euler-Bernoulli meta-beam with inertial amplified resonators. Physics Letters, Section A: General, Atomic and Solid State Physics, 2021, 417: 127671 doi: 10.1016/j.physleta.2021.127671
    [140] Taniker S, Yilmaz C. Generating ultra wide vibration stop bands by a novel inertial amplification mechanism topology with flexure hinges. International Journal of Solids and Structures, 2017, 106-107: 129-138
    [141] Frandsen NMM, Bilal OR, Jensen JS, et al. Inertial amplification of continuous structures: Large band gaps from small masses. Journal of Applied Physics, 2016, 119: 124902 doi: 10.1063/1.4944429
    [142] Yilmaz C, Kikuchi N. Analysis and design of passive low-pass filter-type vibration isolators considering stiffness and mass limitations. Journal of Sound and Vibration, 2006, 293(1-2): 171-195 doi: 10.1016/j.jsv.2005.09.016
    [143] Wang Z, Zhang Q, Zhang K, et al. Tunable digital metamaterial for broadband vibration isolation at low frequency. Advanced Materials, 2016, 28: 9857-9861 doi: 10.1002/adma.201604009
    [144] Wu L, Wang Y, Zhai Z, et al. Mechanical metamaterials for full-band mechanical wave shielding. Applied Materials Today, 2020, 20: 100671 doi: 10.1016/j.apmt.2020.100671
    [145] Yoo J, Park NC. Bandgap analysis of a tunable elastic-metamaterial-based vibration absorber with electromagnetic stiffness. Microsystem Technologies, 2020, 26(11): 3339-3348 doi: 10.1007/s00542-020-04807-8
    [146] Yi K, Matten G, Ouisse M, et al. Programmable metamaterials with digital synthetic impedance circuits for vibration control. Smart Materials and Structures, 2020, 29: 035005 doi: 10.1088/1361-665X/ab6693
    [147] Ren T, Liu C, Li F, et al. Active tunability of band gaps for a novel elastic metamaterial plate. Acta Mechanica, 2020, 231(10): 4035-4053 doi: 10.1007/s00707-020-02728-1
    [148] Zhou W, Muhammad, Chen W, et al. Actively controllable flexural wave band gaps in beam-type acoustic metamaterials with shunted piezoelectric patches. European Journal of Mechanics, A/Solids, 2019, 77: 103807 doi: 10.1016/j.euromechsol.2019.103807
    [149] Sugino C, Ruzzene M, Erturk A. Design and analysis of piezoelectric metamaterial beams with synthetic impedance shunt circuits. IEEE/ASME Transactions on Mechatronics, 2018, 23(5): 2144-2155 doi: 10.1109/TMECH.2018.2863257
    [150] Hu G, Xu J, Tang L, et al. Tunable metamaterial beam using negative capacitor for local resonators coupling. Journal of Intelligent Material Systems and Structures, 2020, 31(3): 389-407 doi: 10.1177/1045389X19891575
    [151] Tan X, Chen S, Wang B, et al. Real-time tunable negative stiffness mechanical metamaterial. Extreme Mechanics Letters, 2020, 41: 100990 doi: 10.1016/j.eml.2020.100990
    [152] Ning S, Yan Z, Chu D, et al. Ultralow-frequency tunable acoustic metamaterials through tuning gauge pressure and gas temperature. Extreme Mechanics Letters, 2021, 44: 101218 doi: 10.1016/j.eml.2021.101218
    [153] De Sousa VC, Tan D, De Marqui C, et al. Tunable metamaterial beam with shape memory alloy resonators: Theory and experiment. Applied Physics Letters, 2018, 113: 143502 doi: 10.1063/1.5050213
    [154] Chuang KC, Lü XF, Wang YH. A bandgap switchable elastic metamaterial using shape memory alloys. Journal of Applied Physics, 2019, 125: 055101 doi: 10.1063/1.5065557
    [155] Lv XF, Xu SF, Huang ZL, et al. A shape memory alloy-based tunable phononic crystal beam attached with concentrated masses. Physics Letters, Section A:General, Atomic and Solid State Physics, 2020, 384(2): 126056 doi: 10.1016/j.physleta.2019.126056
    [156] Yuan Y, Li J, Bao R, et al. A double-layer metastructured beam with contact-separation switchability. Mechanics of Advanced Materials and Structures, 2022, 29(7): 1011-1019 doi: 10.1080/15376494.2020.1804017
    [157] Wang Y, Yang J, Chen Z, et al. Investigation of a novel MRE metamaterial sandwich beam with real-time tunable band gap characteristics. Journal of Sound and Vibration, 2022, 527: 116870 doi: 10.1016/j.jsv.2022.116870
    [158] Xu J, Lu H, Qin W, et al. Mechanical shunt resonators-based piezoelectric metamaterial for elastic wave attenuation. Materials, 2022, 15: 891 doi: 10.3390/ma15030891
    [159] 吴九汇, 马富银, 张思文等. 声学超材料在低频减振降噪中的应用评述. 机械工程学报, 2016, 52(13): 68-78 (Wu Jiuhui, Ma Fuyin, Zhang Siwen, et al. Application of acoustic metamaterials in low-frequency vibration and noise reduction. Journal of Vibration Engineering, 2016, 52(13): 68-78 (in Chinese) doi: 10.3901/JME.2016.13.068
    [160] Yu D, Wen J, Zhao H, et al. Vibration reduction by using the idea of phononic crystals in a pipe-conveying fluid. Journal of Sound and Vibration, 2008, 318: 193-205 doi: 10.1016/j.jsv.2008.04.009
    [161] 刘江伟, 郁殿龙, 温激鸿等. 周期附加质量充液管路减振特性研究. 振动与冲击, 2016, 35(6): 141-145 (Liu Jiangwei, Yu Dianlong, Wen Jihong, et al. Vibration reduction of pipes conveying fluid with periodically added mass. Journal of Vibration and Shock, 2016, 35(6): 141-145 (in Chinese)
    [162] 郭旭, 崔洪宇, 洪明. 局域共振声子晶体板的减振降噪研究. 船舶力学, 2021, 25(4): 509-516 (Guo Xu, Cui Hongyu, Hong Ming. Research on vibration and noise reduction of local resonant phononic crystal plate. Journal of Ship Mechanics, 2021, 25(4): 509-516 (in Chinese) doi: 10.3969/j.issn.1007-7294.2021.04.014
    [163] Nanda A, Karami MA. Tunable bandgaps in a deployable metamaterial. Journal of Sound and Vibration, 2018, 424: 120-136 doi: 10.1016/j.jsv.2018.03.015
    [164] 麻乘榕, 邵晨, 万庆冕等. 用于汽车低频振动控制的局域共振声子晶体. 应用声学, 2018, 37(1): 152-158 (Ma Chengrong, Shao Chen, Wan Qingmian, et al. A locally-resonant phononic crystal for low-frequency vibration control of vehicle. Journal of Applied Acoustics, 2018, 37(1): 152-158 (in Chinese) doi: 10.11684/j.issn.1000-310X.2018.01.022
    [165] 左曙光, 谭钦文, 孙庆等. 声子晶体梁在燃料电池车副车架减振中的应用研究. 振动与冲击, 2013, 32(18): 26-30 (Zuo Shuguang, Tan Qinwen, Sun Qing, et al. Vibration reduction with phononic crystals beams for subframe of a fuel-cell car. Journal of Vibration and Shock, 2013, 32(18): 26-30 (in Chinese) doi: 10.3969/j.issn.1000-3835.2013.18.005
    [166] Zhu R, Liu XN, Hu GK, et al. A chiral elastic metamaterial beam for broadband vibration suppression. Journal of Sound and Vibration, 2014, 333(10): 2759-2773 doi: 10.1016/j.jsv.2014.01.009
    [167] Hu G, Tang L, Liang J, et al. Acoustic-elastic metamaterials and phononic crystals for energy harvesting: A review. Smart Materials and Structures, 2021, 30: 085025 doi: 10.1088/1361-665X/ac0cbc
    [168] Xu X, Wu Q, Pang Y, et al. Multifunctional metamaterials for energy harvesting and vibration control. Advanced Functional Materials, 2022, 32: 2107896 doi: 10.1002/adfm.202107896
    [169] 赵龙, 陆泽琦, 丁虎等. 低频振动隔离和能量采集双功能超材料. 力学学报, 2021, 53(11): 2973-2983 (Zhao Long, Lu Zeqi, Ding Hu, et al. Low-frequency vibration isolation and energy harvesting simultaneously implemented by a metamaterial with lcoal resonance. Chinese Journal of Theoretical and Applied Mechanics, 2021, 53(11): 2973-2983 (in Chinese) doi: 10.6052/0459-1879-21-471
    [170] Mei T, Meng Z, Zhao K, et al. A mechanical metamaterial with reprogrammable logical functions. Nature Communications, 2021, 12: 7234 doi: 10.1038/s41467-021-27608-7
    [171] Raney JR, Nadkarni N, Daraio C, et al. Stable propagation of mechanical signals in soft media using stored elastic energy. Proceedings of the National Academy of Sciences, 2016, 113(35): 9722-9727 doi: 10.1073/pnas.1604838113
    [172] El Helou C, Buskohl PR, Tabor CE, et al. Digital logic gates in soft, conductive mechanical metamaterials. Nature Communications, 2021, 12: 1633 doi: 10.1038/s41467-021-21920-y
    [173] Fan H, Xia B, Tong L, et al. Elastic higher-order topological insulator with topologically protected corner states. Physical Review Letters, 2019, 122(20): 204301 doi: 10.1103/PhysRevLett.122.204301
    [174] Lyu X, Ding Q, Yang T. Merging phononic crystals and acoustic black holes. Applied Mathematics and Mechanics (English Edition) , 2020, 41(2): 279-288 doi: 10.1007/s10483-020-2568-7
    [175] 刘东彦, 李发, 张建兴等. 流体特性对周期管路弯曲振动带隙的影响. 机床与液压, 2016, 44(2): 74-77 (Liu Dongyan, Li Fa, Zhang Jianxing, et al. Effects of fluid property on flexural vibration band gap of periodic pipe. Machine Tool &Hydraulics, 2016, 44(2): 74-77 (in Chinese)
  • 加载中
图(9)
计量
  • 文章访问数:  2145
  • HTML全文浏览量:  657
  • PDF下载量:  509
  • 被引次数: 0
出版历程
  • 收稿日期:  2022-03-16
  • 录用日期:  2022-05-07
  • 网络出版日期:  2022-05-08
  • 刊出日期:  2022-10-18

目录

    /

    返回文章
    返回