An acoustic metasurface composed by unidirectional fiber composite materials
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摘要: 声学超表面是一种能够调节声波反射、透射和吸收特性的超薄人工结构，对于空间受限的应用领域具有重要价值，目前声学超表面主要借助超构材料来实现。提出一种非超构材料的新型声学超表面，采用单向纤维周期复合材料对声波进行调制，实现了声波的定向反射调控。借助复合材料细观力学方法，采用均匀化理论和优化方法设计周期复合材料单胞的组分，使单胞具有特定的等效力学性能与声学性能，并满足特性阻抗匹配，从而形成超表面所需的声速梯度分布。通过能带分析获得了单胞纵波波速与频率的关系，显示出复合材料超表面的宽频特性。定向反射仿真展示了复合材料超表面操控声波的有效性，并验证了对于垂直入射声波纵波是影响波控性能的主要因素。研究工作为声学超表面及其他声学波控装置的设计提供了一种新途径。Abstract: Acoustic metasurfaces are artificial materials of subwavelength thickness capable of manipulating reflection, transmission and absorption of acoustic waves. Acoustic metasurfaces have important values for space limi-ted application fields. At present, the strategy for the design of acoustic metasurfaces depends on the metamaterials. Therefore, we proposed a scheme by designing a kind of non-metamaterials acoustic metasurface to manipulate the wavefont in fluids. Based on this idea, a new type of reflection acoustic metasurface composed by the unidirectional fiber composites with periodicity was studied. Through homogenization theory and optimization method of micromechanics the fractions of composites unit cells were designed in order to obtain the effective mechani-cal and acoustics prosperities of unit cells to satisfy the densities and longitudinal velocities of discrete metasurfaces needed, as well as the impedance matching condition. Finally, the gradient longitudinal velocity of the acoustic metasurfaces needed was achieved. Using Bloch-Floquet analysis, the relationship between longitudinal velocity and frequency was studied. The band diagrams exhibit the broadband characteristics of the designed metasurfaces. Simulations of reflection control were studied for the designed metasurfaces with normally incident plan wave. Excellent wavefont manipulation effects were observed in broadband frequencies. Accordingly, it is verified that longitudinal modes are the most important factors for wave manipulation under normally incident waves. The research work provides a novel idea and potential method for the design and physical implementation of the acoustic metasurfaces as well as the other acoustic wave manipulation devices.
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图 1 单向纤维复合材料超表面离散示意图
Figure 1. Schematic diagram of discrete metasurfaces composed by unidirectional fiber composite materials
图 2 单向纤维复合材料与单胞示意图
Figure 2. Schematic diagram of the unidirectional fiber composites and unit cell
图 3 单向钢纤维聚乙烯(PE)基复合材料超表面仿真模型
Figure 3. Simulation model diagram of metasurface composed by unidirectional steel fibers and polyethylene (PE) matrix composites
图 4 单向纤维复合材料超表面的正方晶格周期性边界条件和第一布里渊区
Figure 4. Periodic boundary conditions and the first brillouin zone of square unit cell composed by unidirectional fiber composite materials
图 5 单向纤维复合材料超表面的1号与20号单胞ΓX和ΓJ方向能带图
Figure 5. Band diagrams of ΓX and ΓJ directions in the first and the twentieth unit cells of metasurfaces composed by unidirectional fiber composite materials
图 6 单向纤维复合材料超表面的单胞沿ΓX方向的六阶振动模态
Figure 6. Six vibration modes of unit cell from the ΓX direction composed by unidirectional fiber composite materials
图 7 单向纤维复合材料超表面对水下1 kHz至8 kHz频率垂直入射平面波的10°定向反射声压场
Figure 7. Simulation acoustic field maps of metasurfaces composed by unidirectional fiber composite materials of 10° reflection for a plane wave normally incident from the top side with frequencies 1 kHz to 8 kHz under water
图 8 单向纤维复合材料超表面的仿真定向反射角与理论反射角度对比
Figure 8. Comparison of simulated directional reflection angles with theoretical reflection angles of metasurfaces composed by unidirectional fiber composite materials
表 1 PE基体和钢纤维力学性能
Table 1. Mechanical properties of steel fiber and PE matrix
Mechanical property PE matrix Steel fiber Young’s modulus/GPa 0.15-1.00 210.00 Poisson’s ratio 0.46 0.30 Density/(kg·m−3) 940 7850 
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表 2 单向纤维复合材料超表面的单胞基体杨氏模量和体积分数优化结果
Table 2. Optimization results of the Young’s modulus of matrix and fiber volume fraction of unit cells of metasurfaces composed by unidirectional fiber composite materials
Unit cell Young’s modulus
of matrix/MPaFiber volume
fraction/vol%1 371.7 4.4 2 342.2 5.7 3 316.4 6.9 4 293.5 8.1 5 273.1 9.4 6 254.8 10.7 7 238.3 11.9 8 223.3 13.2 9 209.7 14.4 10 197.2 15.7 11 185.8 17.0 12 175.3 18.2 13 165.5 19.5 14 156.5 20.7 15 148.1 22.0 16 140.3 23.2 17 133.0 24.5 18 126.2 25.8 19 119.8 27.0 20 113.7 28.3
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表 3 单向纤维复合材料超表面的单胞等效声速
${\bar c^i}$ 与等效密度${\bar \rho ^i}$ Table 3. Effective velocity
${\bar c^i}$ and effective density${\bar \rho ^i}$ of metasurface unit cells composed by unidirectional fiber composite materialsUnit cell Theory velocity
/(m·s−1)Effective velocity
/(m·s−1)Theory density
/(kg·m−3)Effective density
/(kg·m−3)1 1206 1204 1243 1243 2 1128 1127 1330 1330 3 1059 1057 1417 1417 4 997 992 1504 1503 5 943 939 1591 1590 6 894 894 1678 1677 7 850 852 1764 1764 8 810 815 1 851 1 851 9 774 774 1 938 1 937 10 741 741 2 025 2 024 11 710 710 2112 2111 12 682 681 2198 2198 13 656 657 2285 2284 14 632 632 2372 2371 15 610 612 2459 2458 16 589 587 2546 2545 17 570 568 2633 2631 18 552 551 2719 2718 19 535 535 2806 2805 20 518 519 2893 2892
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表 4 单向纤维复合材料超表面的单胞沿ΓX方向等效纵波波速
${\bar c^i}$ 误差分析Table 4. Errors of longitudinal velocities
${\bar c^i}$ in unit cells from ΓX direction of metasurfaces composed by unidirectional fiber composite materialsUnit cell No. A point B point C point ${\bar c^i}$/(m·s−1) Error
/%f
/kHz${\bar c^i}$/(m·s−1) Error
/%f
/kHz${\bar c^i}$/(m·s−1) Error
/%f
/kHz1 1202 0.3 2.11 1188 1.5 5.97 1087 9.9 11.42 5 938 0.5 2.11 919 2.6 4.60 897 4.9 6.06 10 734 0.9 2.02 704 5.0 4.58 665 10.3 6.15 15 602 1.3 2.11 573 6.1 4.30 522 14.4 6.01 20 516 0.4 1.16 489 5.6 3.79 424 18.1 5.94
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