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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): 148-158 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): 148-158 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): 148-158 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): 148-158 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
    通讯作者:

    章俊, 副教授, 主要研究方向为弹性波调控(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达到最佳, 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

    Figure  1.  Relationship between diffraction angles of different diffraction orders and incident angles

    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  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  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  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

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  • 收稿日期:  2022-08-15
  • 录用日期:  2022-11-15
  • 网络出版日期:  2022-11-16
  • 刊出日期:  2023-01-04

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