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

弯曲波宽频分波超栅拓扑优化设计和表征

李林 张雪彬 刘涛 章俊

李林, 张雪彬, 刘涛, 章俊. 弯曲波宽频分波超栅拓扑优化设计和表征. 力学学报, 2023, 55(1): 1-11 doi: 10.6052/0459-1879-22-373
引用本文: 李林, 张雪彬, 刘涛, 章俊. 弯曲波宽频分波超栅拓扑优化设计和表征. 力学学报, 2023, 55(1): 1-11 doi: 10.6052/0459-1879-22-373
Li Lin, Zhang Xuebin, Liu Tao, Zhang Jun. Topology design and characterization of broadband wave-splitting metagratings for flexural waves. Chinese Journal of Theoretical and Applied Mechanics, 2023, 55(1): 1-11 doi: 10.6052/0459-1879-22-373
Citation: Li Lin, Zhang Xuebin, Liu Tao, Zhang Jun. Topology design and characterization of broadband wave-splitting metagratings for flexural waves. Chinese Journal of Theoretical and Applied Mechanics, 2023, 55(1): 1-11 doi: 10.6052/0459-1879-22-373

弯曲波宽频分波超栅拓扑优化设计和表征

doi: 10.6052/0459-1879-22-373
基金项目: 国家自然科学基金(12072051)和中央高校基本科研业务费(300102251513)资助项目
详细信息
    作者简介:

    章俊, 副教授, 主要研究方向: 弹性波调控(超材料和超表面)、计算固体力学. E-mail: mejzhang@cqu.edu.cn

  • 中图分类号: O326

TOPOLOGY DESIGN AND CHARACTERIZATION OF BROADBAND WAVE-SPLITTING METAGRATINGS FOR FLEXURAL WAVES

  • 摘要: 超表面/超栅的出现, 使得波前调控变得越来越方便和灵活. 然而大多数现有超表面/超栅均基于经验设计, 其波前调控性能往往没有到达最佳, 并且工作频率带宽窄, 严重制约着它们在实际工程中的应用. 同时, 研究人员发现当入射角大于某一临界角时, 用来设计各种超表面的广义斯涅耳定理将失效. 为了解决上述问题, 本文基于高阶衍射定理, 提出了一种利用遗传算法的宽频分波超栅拓扑优化设计方法. 基于上述优化设计方法, 针对薄板中弯曲波, 具体设计了的三种宽频分波超栅, 其胞元由两个相位差为${\text{π} }$的子功能单元组成. 首先, 利用有限元方法对这三种超栅性能进行了数值表征; 然后, 利用3D打印技术加工试件开展了实验验证; 最后, 与其他两种方法设计的同类超栅进行了比较. 结果表明本文所设计的弯曲波宽频分波超栅在设定的宽频范围内功能稳定, 达到宽频分波效果. 虽然本文仅考虑了弯曲波, 但设计思路同样适用于其他形式的弹性波. 研究结果将为其他宽频超栅设计提供一种可能有效途径.

     

  • 图  1  不同衍射阶次的衍射角与入射角的关系: (a) η = 0.8 和(b) η = 1.5

    Figure  1.  Relationship between diffraction angles of different diffraction orders and incident angles at (a) η = 0.8 and (b) η = 1.5

    图  2  超栅子功能单元二维拓扑优化模型示意图

    Figure  2.  Schematic of topology optimization 2D models for the subunits in a supercell

    图  3  薄板弯曲波超栅整体结构俯视图, 本文中子功能单元数为2

    Figure  3.  Top view of metagratings for flexural waves in thin plates. In this paper, the number of subunits is 2

    图  4  优化区域高度H = 3h, 在2.4 kHz中心频率激励下的胞元拓扑结构的进化历程

    Figure  4.  Evolutionary history of topological structure of a unit cell as the optimization region height H = 3h and under excitation of a 2.4 kHz loading

    图  5  三种不同优化区域高度下所得到的胞元最终拓扑优化结构

    Figure  5.  The optimized topological structures of unit cells under three different optimization region heights

    图  6  以图 5中三种拓扑结构为胞元分别形成的三种一维声子晶体梁的能带图

    Figure  6.  Band structures of the three 1D phononic crystals constituted by the three units presented in Fig. 5

    6  以图 5中三种拓扑结构为胞元分别形成的三种一维声子晶体梁的能带图(续)

    6.  Band structures of the three 1D phononic crystals constituted by the three units presented in Fig. 5 (continued)

    图  7  三种拓扑优化结构分别组成的子功能单元在中心频率激励下透射波行为数值模拟表征结果

    Figure  7.  Numerical characterization of wave transmission behavior through three subunits composed by each of the three optimized structures under the central frequency excitation

    图  8  分别由三种拓扑优化结构构成的三种子功能单元在三个采样点频率下的(a)相移和(b)透射率

    Figure  8.  (a) Phase shifts and (b) transmittances of subunits composed by the three optimized structures at three different frequencies

    图  9  由图 5中三种胞元分别形成的三种超栅整体结构

    Figure  9.  Three metagratings constituted by each of the three unit cells presented in Fig. 5

    图  10  超栅结构有限元数值模拟模型

    Figure  10.  Numerical simulation models of metagratings with the Finite Element Method

    图  11  三种超栅在三个采样点频率激励下响应的数值模拟结果

    Figure  11.  Numerical simulation results for the three metagratings under excitation of three different frequencies

    图  12  实验试件

    Figure  12.  Experiment specimens

    12  实验试件(续)

    12.  Experiment specimens (continued)

    图  13  本研究实验测试平台

    Figure  13.  Experimental setup in this study

    图  14  激励频率为2160 Hz时, 测得的三个时刻的超栅离面速度场

    Figure  14.  Snapshots of measured out-of-plane velocity fields under the excitation of 2160 Hz at three instants

    图  15  激励频率为2400 Hz时, 测得的三个时刻的超栅离面速度场

    Figure  15.  Snapshots of measured out-of-plane velocity fields under the excitation of 2400 Hz at three instants

    图  16  激励频率为2640 Hz时, 测得的三个时刻的超栅离面速度场

    Figure  16.  Snapshots of measured out-of-plane velocity fields under the excitation of 2640 Hz at three instants

    图  17  三个采样点频率激励下, 拓扑优化梁与直梁实测相位比较

    Figure  17.  Comparison of phases of transmitted waves between optimized beams and straight beams at three different frequencies

    图  18  直梁型分波超栅数值模拟结果

    Figure  18.  Numerical simulation results of straight-beam-type wave-splitting metagratings

    图  19  锯齿型分波超栅数值模拟结果

    Figure  19.  Numerical simulation results of zigzag-type wave-splitting metagratings

  • [1] Khorasaninejad M, Capasso F. Metalenses: versatile multifunctional photonic components. Science, 2017, 358(6367): 1146
    [2] Loyez M, Derosa MC, Caucheteur C, et al. Overview and emerging trends in optical fiber aptasensing. Biosensors & Bioelectronics, 2022, 196: 113694
    [3] Shen L, Zhu YF, Mao FL, et al. Broadband low-frequency acoustic metamuffler. Physical Review Applied, 2021, 16(6): 064057 doi: 10.1103/PhysRevApplied.16.064057
    [4] Chen AL, Wang Y, Wang YF, et al. Design of acoustic/elastic phase gradient metasurfaces: principles, functional elements, tunability, and coding. Applied Mechanics Reviews, 2022, 74(2): 020801-020836 doi: 10.1115/1.4054629
    [5] Yu NF, Genevet P, Kats MA, et al. Light propagation with phase discontinuities: generalized laws of reflection and refraction. Science, 2011, 334(6054): 333-337 doi: 10.1126/science.1210713
    [6] 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
    [7] Assouar B, Liang B, Wu Y, et al. Acoustic metasurfaces. Nature Reviews Materials, 2018, 3(12): 460-472 doi: 10.1038/s41578-018-0061-4
    [8] Hu YB, Zhang YH, Su GY, et al. Realization of ultrathin waveguides by elastic metagratings. Communications Physics, 2022, 5(1): 1-10 doi: 10.1038/s42005-021-00784-0
    [9] 任鑫, 张相玉, 谢亿民. 负泊松比材料和结构的研究进展. 力学学报, 2019, 51(3): 656-687 (Ren Xin, Zhang Xiangyu, Xie Yimin. Research progress in auxetic materials and structures. Chinese Journal of Theoretical and Applied Mechanics, 2019, 51(3): 656-687 (in Chinese)
    [10] Liu F, Shi PT, Xu YL, et al. Total reflection of flexural waves by circular meta-slab and its application in vibration isolation. International Journal of Mechanical Sciences, 2021, 212: 106806 doi: 10.1016/j.ijmecsci.2021.106806
    [11] Zhang J, Zhang XB, Zhang H, et al. Rainbow zigzag metamaterial beams as broadband vibration isolators for beam-like structures. Journal of Sound and Vibration, 2022, 530: 116945 doi: 10.1016/j.jsv.2022.116945
    [12] Ma TX, Fan QS, Zhang CZ, et al. Flexural wave energy harvesting by the topological interface state of a phononic crystal beam. Extreme Mechanics Letters, 2022, 50: 101578 doi: 10.1016/j.eml.2021.101578
    [13] Alshaqaq M, Erturk A. Graded multifunctional piezoelectric metastructures for wideband vibration attenuation and energy harvesting. Smart Materials and Structures, 2021, 30(1): 015029 doi: 10.1088/1361-665X/abc7fa
    [14] De Ponti JM, Colombi A, Ardito R, et al. Graded elastic metasurface for enhanced energy harvesting. New Journal of Physics, 2020, 22(1): 013013 doi: 10.1088/1367-2630/ab6062
    [15] 王芳隆, 沈一舟, 徐艳龙等. 弯曲波彩虹捕获效应及其在能量俘获中的应用. 力学学报, 2022, 54(10): 1-13 (Wang Fanglong, Shen Yizhou, Xu Yanlong, et al. Rainbow trapping of flexural waves and its application in energy havesting. Chinese Journal of Theoretical and Applied Mechanics, 2022, 54(10): 1-13 (in Chinese)
    [16] Zareei A, Darabi A, Leamy MJ, et al. Continuous profile flexural GRIN lens: Focusing and harvesting flexural waves. Applied Physics Letters, 2018, 112(2): 023901 doi: 10.1063/1.5008576
    [17] Yan X, Zhu R, Huang G, et al. Focusing guided waves using surface bonded elastic metamaterials. Applied Physics Letters, 2013, 103(12): 121901 doi: 10.1063/1.4821258
    [18] Yi K, Collet M, Ichchou M, et al. Flexural waves focusing through shunted piezoelectric patches. Smart Materials and Structures, 2016, 25(7): 075007 doi: 10.1088/0964-1726/25/7/075007
    [19] Tol S, Degertekin FL, Erturk A. Phononic crystal Luneburg lens for omnidirectional elastic wave focusing and energy harvesting. Applied Physics Letters, 2017, 111(1): 013503 doi: 10.1063/1.4991684
    [20] Shen YZ, Xu YL, Liu F, et al. 3 D-printed meta-slab for focusing flexural waves in broadband. Extreme Mechanics Letters, 2021, 48: 101410 doi: 10.1016/j.eml.2021.101410
    [21] Zhang J, Zhang XB, Xu FL, et al. Vibration control of flexural waves in thin plates by 3 D-printed metasurfaces. Journal of Sound and Vibration, 2020, 481: 115440 doi: 10.1016/j.jsv.2020.115440
    [22] Liu F, Yang ZC, Shi PT, et al. Refraction of flexural waves by ultra-broadband achromatic meta-slab with wavelength-dependent phase shifts. Journal of Applied Mechanics-Transactions of the Asme, 2022, 89(4): 041003 doi: 10.1115/1.4053201
    [23] Zhang J, Su X, Liu Y, et al. Metasurface constituted by thin composite beams to steer flexural waves in thin plates. International Journal of Solids and Structures, 2019, 162: 14-20 doi: 10.1016/j.ijsolstr.2018.11.025
    [24] Cao LY, Yang ZC, Xu YL, et al. Deflecting flexural wave with high transmission by using pillared elastic metasurface. Smart Materials and Structures, 2018, 27(7): 075051 doi: 10.1088/1361-665X/aaca51
    [25] Xu Y, Cao LY, Yang Z. Deflecting incident flexural waves by nonresonant single-phase meta-slab with subunits of graded thicknesses. Journal of Sound and Vibration, 2019, 454: 51-62 doi: 10.1016/j.jsv.2019.04.028
    [26] Cho S, Yang W, Lee S, et al. Flexural wave cloaking via embedded cylinders with systematically varying thicknesses. Journal of the Acoustical Society of America, 2016, 139(6): 3320-3324 doi: 10.1121/1.4950738
    [27] Brun M, Colquitt DJ, Jones IS, et al. Transformation cloaking and radial approximations for flexural waves in elastic plates. New Journal of Physics, 2014, 16(9): 093020 doi: 10.1088/1367-2630/16/9/093020
    [28] Colquitt DJ, Brun M, Gei M, et al. Transformation elastodynamics and cloaking for flexural waves. Journal of the Mechanics and Physics of Solids, 2014, 72: 131-143 doi: 10.1016/j.jmps.2014.07.014
    [29] Zareei A, Alam MR. Broadband cloaking of flexural waves. Physical Review E, 2017, 95(6): 063002 doi: 10.1103/PhysRevE.95.063002
    [30] Liu Y, Ma Z, Su X. Linear transformation method to control flexural waves in thin plates. Journal of the Acoustical Society of America, 2016, 140(2): 1154-1161 doi: 10.1121/1.4961005
    [31] Farhat M, Guenneau S, Enoch S. Ultrabroadband elastic cloaking in thin plates. Physical Review Letters, 2009, 103(2): 025301 doi: 10.1103/PhysRevLett.103.025301
    [32] Stenger N, Wilhelm M, Wegener M. Experiments on elastic cloaking in thin plates. Physical Review Letters, 2012, 108(1): 014301 doi: 10.1103/PhysRevLett.108.014301
    [33] Farhat M, Guenneau S, Enoch S, et al. Cloaking bending waves propagating in thin elastic plates. Physical Review B, 2009, 79(3): 033102 doi: 10.1103/PhysRevB.79.033102
    [34] Futhazar G, Parnell WJ, Norris AN. Active cloaking of flexural waves in thin plates. Journal of Sound and Vibration, 2015, 356: 1-19 doi: 10.1016/j.jsv.2015.06.023
    [35] Colombi A, Roux P, Guenneau S, et al. Directional cloaking of flexural waves in a plate with a locally resonant metamaterial. Journal of the Acoustical Society of America, 2015, 137(4): 1783-1789 doi: 10.1121/1.4915004
    [36] Cao LY, Yang ZC, Xu YL, et al. Flexural wave absorption by lossy gradient elastic metasurface. Journal of the Mechanics and Physics of Solids, 2020, 143: 104052 doi: 10.1016/j.jmps.2020.104052
    [37] Xu YL, Cao LY, Peng P, et al. Beam splitting of flexural waves with a coding meta-slab. Applied Physics Express, 2019, 12(9): 097002 doi: 10.7567/1882-0786/ab36bd
    [38] Li XS, Wang YF, Wang YS. Sparse binary metasurfaces for steering the flexural waves. Extreme Mechanics Letters, 2022, 52: 101675 doi: 10.1016/j.eml.2022.101675
    [39] Cao LY, Xu YL, Assouar B, et al. Asymmetric flexural wave transmission based on dual-layer elastic gradient metasurfaces. Applied Physics Letters, 2018, 113(18): 183506 doi: 10.1063/1.5050671
    [40] Fu YY, Tao JQ, Song AL, et al. Controllably asymmetric beam splitting via gap-induced diffraction channel transition in dual-layer binary metagratings. Frontiers of Physics, 2020, 15(5): 131-136
    [41] 郑周甫, 尹剑飞, 温激鸿等. 基于声子晶体板的弹性波拓扑保护边界态. 物理学报, 2020, 69(15): 279-288 (Zheng Zhoufu, Yin Jianfei, Wen Jihong, et al. Topologically protected edge states of elastic waves in phononic crystal plates. Acta Physica Sinica, 2020, 69(15): 279-288 (in Chinese) doi: 10.7498/aps.69.20200542
    [42] Chaunsali R, Chen CW, Yang JY. Experimental demonstration of topological waveguiding in elastic plates with local resonators. New Journal of Physics, 2018: 20
    [43] Cao L, Yang Z, Xu Y, et al. Pillared elastic metasurface with constructive interference for flexural wave manipulation. Mechanical Systems and Signal Processing, 2021, 146: 107035 doi: 10.1016/j.ymssp.2020.107035
    [44] Liu Y, Liang Z, Liu F, et al. Source illusion devices for flexural lamb waves using elastic metasurfaces. Physical Review Letters, 2017, 119(3): 1
    [45] Xie YB, Wang WQ, Chen HY, et al. Wavefront modulation and subwavelength diffractive acoustics with an acoustic metasurface. Nature Communications, 2014, 5(11): 5553
    [46] Li Y, Shen C, Xie YB, et al. Tunable asymmetric transmission via lossy acoustic metasurfaces. Physical Review Letters, 2017, 119(3): 1
    [47] Wang WQ, Xie YB, Popa BI, et al. Subwavelength diffractive acoustics and wavefront manipulation with a reflective acoustic metasurface. Journal of Applied Physics, 2016, 120(19): 1-7
    [48] Li B, Hu Y, Chen J, et al. Efficient asymmetric transmission of elastic waves in thin plates with lossless metasurfaces. Physical Review Applied, 2020, 14(5): 054029 doi: 10.1103/PhysRevApplied.14.054029
    [49] Kim SY, Lee W, Lee JS, et al. Longitudinal wave steering using beam-type elastic metagratings. Mechanical Systems and Signal Processing, 2021, 156: 107688 doi: 10.1016/j.ymssp.2021.107688
    [50] Wang YF, Wang YZ, Wu B, et al. Tunable and active phononic crystals and metamaterials. Applied Mechanics Reviews, 2020, 72(4): 040801-040835 doi: 10.1115/1.4046222
    [51] Wang C, Zhao Z, Zhou M, et al. A comprehensive review of educational articles on structural and multidisciplinary optimization. Structural and Multidisciplinary Optimization, 2021, 64(5): 2827-2880 doi: 10.1007/s00158-021-03050-7
    [52] Rong JJ, Ye WJ, Zhang SY, et al. Frequency-coded passive multifunctional elastic metasurfaces. Advanced Functional Materials, 2020, 30(50): 2005285 doi: 10.1002/adfm.202005285
    [53] Rong JJ, Ye WJ. Multifunctional elastic metasurface design with topology optimization. Acta Materialia, 2020, 185: 382-399 doi: 10.1016/j.actamat.2019.12.017
    [54] Wang SY, Tai K, Wang MY. An enhanced genetic algorithm for structural topology optimization. International Journal for Numerical Methods in Engineering, 2006, 65(1): 18-44 doi: 10.1002/nme.1435
    [55] Wang SY, Tai K. Structural topology design optimization using genetic algorithms with a bit-array representation. Computer Methods in Applied Mechanics and Engineering, 2005, 194(36-38): 3749-3770 doi: 10.1016/j.cma.2004.09.003
    [56] Dong HW, Su XX, Wang YS, et al. Topological optimization of two-dimensional phononic crystals based on the finite element method and genetic algorithm. Structural and Multidisciplinary Optimization, 2014, 50(4): 593-604 doi: 10.1007/s00158-014-1070-6
    [57] Deb K, Pratap A, Agarwal S, et al. A fast and elitist multiobjective genetic algorithm: NSGA-II. Ieee Transactions on Evolutionary Computation, 2002, 6(2): 182-197 doi: 10.1109/4235.996017
  • 加载中
图(21)
计量
  • 文章访问数:  55
  • HTML全文浏览量:  21
  • PDF下载量:  15
  • 被引次数: 0
出版历程
  • 收稿日期:  2022-08-15
  • 录用日期:  2022-11-15
  • 网络出版日期:  2022-11-16

目录

    /

    返回文章
    返回