Research progress on metamaterials for wave function regulation
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摘要: 超构材料是人工构造的复合结构材料，通过设计基元的结构参数，可以实现丰富的波动调控功能，并可突破传统材料的波动响应极限，在航空航天、轨道交通等民用和国防各领域都具有极大的应用潜力。首先简要介绍了超构材料的基本概念、性质和发展历史，然后从超构材料的禁带减振及其智能设计、低频宽带降噪和能量采集三个方面详细介绍超构材料的基本功能，再从实际应用的多需求出发介绍了轻质-承载-减振降噪和能量采集-减振降噪等类型的多功能一体化超构材料设计原理和性能。最后，总结上述研究进展，并展望超构材料与复合材料、人工智能和非厄米时变系统等的交叉研究，进一步提升超构材料性能和应用能力。Abstract: Metamaterials are artificially constructed composite structural materials. By designing the structural parameters of units, we can realize a great wealth of wave functions and even break the wave response limit of traditional materials. Metamaterials have great potential application in civil and defense industries such as aerospace engineering, transportation, among others. First, we briefly introduce the basic concept, properties and development history of metamaterials. Then, we introduce the basic functions of metamaterials in detail from three aspects: Band gap induced vibration reduction and its intelligent design, low-frequency broadband noise reduction and energy harvesting. Furthermore, based on the multi requirements of practical applications, we introduce the design principles and properties of different types of multi-functions integrated metamaterials such as lightweight-load bearing-vibration/noise reduction integration and energy harvesting-vibration/noise reduction integration. Finally, we summarize the above research progress and give a perspective on the cross research of metamaterials with composite materials, artificial intelligence and non-Hermitian time-varying systems, which can further improve the performance and application ability of metamaterials in future.
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图 2 ((a)、(c)) 超构材料梁的单胞示意图及纵波能带结构[32]；((b)、(d)) 超构材料板的单胞示意图及弯曲波能带结构[33]
Figure 2. ((a),(c)) Schematic diagrams for unit cell of metamaterial beam and the corresponding band structure of longitudinal wave[32]; ((b),(d)) Schematic diagrams for unit cell of metamaterial plate and the corresponding band structure of flexural wave[33]
k—Wave number; a—Lattice constant; R—Arrangement radius of resonators; M, Γ and K—High symmetry points of the first irreducible Brillouin zone
图 3 (a) 设计超构材料梁的强化学习框架；(b) 重复测试下最后一个训练片段的参数演化路径；(c) 不同初始状态下最后一个训练片段的参数演化路径[32]
Figure 3. (a) Reinforcement learning framework for designing metamaterial beam; (b) Parameter-evolution path of the last episode in the four tests; (c) Parameter-evolution path of the last episode at different initial states[32]
图 4 (a) 设计超构材料板的神经网络中数据流循环示意图；(b) 正向神经网络预测带隙与真实带隙对比；(c) 应用逆向神经网络设计的超构材料板对应的能带结构[33]
Figure 4. (a) Schematic diagram of data flow cycle in neural network for designing metamaterial plate; (b) Comparison between predicted and real bandgap width of forward neural network; (c) Band structure corresponding to the metamaterial plate designed by inverse neural network[33]
图 5 (a) 不同纤维增强的声学测试样件；(b) 天然纤维和合成纤维的吸声系数对比；(c) 不同放大倍率下剑麻纤维的多尺度空腔结构[38]
Figure 5. (a) Acoustic test samples reinforced with different fibers; (b) Comparison of acoustic absorption coefficients of natural and synthetic fibers; (c) Multi-scale cavity structure of sisal fibers at different magnification rates[38]
图 6 (a) 由16个Fabry-Perot共振通道组成的超构材料单元示意图；(b) 该超构材料吸声谱和有反射硬壁的1 cm海棉的吸声谱；(c) 超构材料覆盖1 cm吸声海棉后的吸声谱[51]；(d) 包含36个级联内插管亥姆霍兹共振体的非局域超构材料示意图；(e) 对应的3 D打印样品图；(f) 该非局域超材料的理论和实验吸声谱[54]
Figure 6. (a) Schematics of the metamaterial unit consisting of 16 Fabry-Perot resonant channels; (b) Absorption spectrum of the acoustic metamaterial sample and that for a 1 cm sponge backed by a reflecting hard wall; (c) Acoustic metamaterial measurement of absorption coefficient of sample covered with 1 cm sound absorbing sponge[51]; (d) Schematic of the non-local metamaterial of 36 cascade neck-embedded Helmholtz resonators; (e) 3D-printed sample; (f) Theoretical and measured absorption spectra of the non-local metamaterial absorber[54]
Pi and Pr—Incident acoustic pressure and reflected acoustic pressure, respectively
图 7 周期性超构材料中缺陷诱导产生的单点局域态[61](a) 和双点局域态[62](b)；(c) 梯度超构材料中缺陷诱导的局域态[63]；麦克斯韦-鱼眼透镜型[68](d) 和龙勃透镜型[69](e) 梯度折射率超构材料点聚焦效应；超构表面聚焦效应 (f) 及其焦斑处压电能量采集输出功率与焦斑半峰全宽关系 (g)[60, 70-71]
Figure 7. Defect induced single point localized states[61](a) and two-point localized states[62](b) in periodic metamaterials; (c) Defect induced localized states in graded metamaterials[63]; Point focusing effect of Maxwell fisheye lens[68](d) and Luneburg lens[69](e) graded index metamaterials; Focusing effect of metasurface (f) and relationship between piezoelectric energy harvesting output power at focal spot and full width at half peak[60, 70-71]
λ—Working wavelength
图 8 (a) 拓扑彩虹能量捕获器[75]；(b) Kekulé相位调制能量采集器[76-77]；(c) 手性系统与C6v系统能量采集功率与频率扰动关系图[78]；(d) 手性系统结构示意图及位移场图[78]
Figure 8. (a) Topological rainbow energy harvester[75]; (b) Kekulé phase modulation energy harvester[76-77]; (c) Relationship between output power and frequency disturbance in chiral and C6v systems[78]; (d) Displacement field of chirality protected edge states[78]
CW—Clockwise; CCW—Counter clockwise
图 10 (a) 多功能超结构示意图及基元的空间布置[80]；(b) 优化后的超结构与优化基元的吸声曲线[80]；(c) 面心立方芯复合材料夹层板实验样品[84-85]；(d) 通过数值模拟和实验测量得到的传声损失曲线[85]
Figure 10. (a) Schematic diagram of the proposed multifunctional metastructure and the spatial arrangement of units[80]; (b) Sound absorption curves of the optimized metastructure and the optimized units[80]; (c) Specimen of composite sandwich panel with face-centered cubic core[84-85]; (d) Sound transmission loss obtained by numerical model and experimental measurement[85]
CRIET—Cavity resonators with internally extended tubes
图 11 (a) 振动控制-能量采集多功能超构材料[86]；(b) 吸声-能量采集多功能超构材料[87]
Figure 11. (a) Multi-functional metamaterials for energy harvesting and vibration control[86]; (b) Energy harvesting and sound absorption[87]
PTFE—Abbreviation of polytetrafluoroethylene; t0—Thickness of unit cell; d—Gap between the central mass and the rigid dam-board in the bottom; E(z)—Lectric field
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