TOPOLOGY DESIGN AND CHARACTERIZATION OF BROADBAND WAVE-SPLITTING METAGRATINGS FOR FLEXURAL WAVES
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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.Abstract: Appearance of metasurfaces/metagratings makes anomalous control of wavefronts more and more convenient and flexible. However, most of the existing metasurfaces/metagratings are designed based on experience. As a result, their wavefront manipulation performance is often not optimal, and their working frequency bandwidth is narrow, which seriously limits their applications. Meanwhile, researchers found that as the incident angle is greater than a critical value, the generalized Snell’s law fails to estimate behavior of metasurfaces. In order to solve the above problems, based on the high-order diffraction theory, we propose a genetic optimization algorithm based method to design broadband wave-splitting metagratings. Based on the above technique, we specifically design three wave-splitting metagratings for flexural waves in thin plates, in which the supercells are composed of two subunits with a phase shift of$ {\text{π} } $ . First, extensive numerical simulations are carried out to characterize the performance of our proposed metagratings and the optimized subunits. Then, a 3D printing technology is employed to fabricate metagratings and subunits to conduct experimental verification. Finally, our designed metagratings are compared with similar metagratings designed by two other methods. The results show that our metagratings work well as the designed functionality in the prescribed broad frequency range. However, the metagratings designed by two other methods only work well within a narrow frequency range. Although only flexural waves are considered in this work, our proposed technique is also applicable to other elastic waves. The results in this work provide a possible and effective way to design broadband metagratings for other waves.-
Key words:
- genetic algorithm /
- topology optimization /
- metagratings /
- high-order diffraction /
- wave splitting
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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 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 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 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
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