Study on the complex band gap characteristic of controllable metastructure
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摘要: 可控超结构可根据目标需求调节结构的带隙特性，实现对不同工况下结构减振的可控调节，在航空航天、轨道交通等工程领域具有广泛的应用前景。本文提出一种新型可控超结构构型，可同时产生局域共振和布拉格散射两种带隙，通过施加位移可实现对带隙的有效调控。应用COMSOL软件建立了该结构的有限元模型，研究了4种可控超结构构型的能带分布及其在外加位移激励作用下的带隙特性调控规律，开展了该结构的振动传输特性实验，并与数值结果进行对比验证。研究结果表明，四振子复合带隙可控超结构在0~800 Hz范围内共有3条完全带隙，第一阶带隙范围低至134.48~287.53 Hz，第二阶带隙范围为307.26~447.81 Hz，第三阶带隙范围为662.44~679.43 Hz。对比分析4种元胞构型带隙特性，在一定频率范围内，随着振子数量增加，带隙数量减少，带宽增加，带隙位置逐渐上移；施加结构位移可有效调控结构带隙，随着位移值增加，结构中低频局域共振带隙变化较小，布拉格带隙中心频率逐渐上移，并出现新带隙。本研究表明该结构在带隙范围内具有良好的减振特性。结果表明所设计的复合带隙可控超结构可实现对复合带隙的调控，为超结构减振设计研究提供有益的参考。Abstract: The controllable metastructure can adjust the band gap characteristic of the structure according to the target requirements, and realize the controllable adjustment of structural vibration reduction under different working conditions. It has a wide application prospect in aerospace, rail transit and other engineering fields. A new controllable metastructure configuration was proposed, which can simultaneously generate two kinds of band gaps, local resonance and Bragg scattering. The band gap can be effectively controlled by applying displacement. The finite element model of the structure was established by COMSOL software. The energy band distribution of four controllable metastructure configurations and the regulation of band gap characteristics under external displacement excitation were studied. The vibration transmission characteristics of the structure were tested and compared with the numerical results. The results show that the four-oscillator composite band gap controllable metastructure has three complete band gaps in the range of 0-800 Hz. The first-order band gap range is as low as 134.48-287.53 Hz, the second-order band gap range is 307.26-447.81 Hz, and the third-order band gap range is 662.44-679.43 Hz. The band gap characteristics of four cell configurations were compared and analyzed. In a certain frequency range, as the number of oscillators increases, the number of band gaps decreases, the bandwidth increases, and the band gap position gradually moves up. The application of structural displacement can effectively control the structural band gap. As the displacement value increases, the low-frequency local resonance band gap in the structure changes little, and the center frequency of the Bragg band gap gradually moves up, and a new band gap appears. This study shows that the structure has good vibration reduction characteristics in the band gap range. The results show that the designed composite band gap controllable metastructure can realize the regulation of the composite band gap, which provides a useful reference for the research of metastructure vibration reduction design.
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图 1 不同构型复合带隙可控超结构元胞
Figure 1. Composite band gap controllable metastructure cells with different configurations
图 2 不同轴向压缩下二振子构型超结构元胞及试件示意图
Figure 2. Schematic diagram of the metastructure cells and specimens of two-oscillator configurations under different axial compressions
$ {Y_{P} } $ is the axial compression of the structure
图 3 $ {Y_{{\mathrm{P}}} } = 0\;{{\mathrm{mm}}} $时二振子构型超结构元胞及其第一不可约布里渊区(蓝色区域)
Figure 3. Two-oscillator configuration metastructure cell and its first irreducible Brillouin zone (blue region) in $ {Y_{{\mathrm{P}}} } = 0\;{{\mathrm{mm}}} $
图 4 不同元胞构型$ {Y_{{\mathrm{P}}} } = 0\;{{\mathrm{mm}}} $时能带结构对比图
Figure 4. Energy band structure comparison diagram of different cell configurations $ {Y_{{\mathrm{P}}} } = 0\;{{\mathrm{mm}}} $
图 5 四振子复合带隙可控超结构$ {Y_{{\mathrm{P}}} } = 0\;{{\mathrm{mm}}} $时能带结构及振动模态
Figure 5. Band structure and vibration mode of the four-oscillator composite band gap controllable metastructure $ {Y_{{\mathrm{P}}} } = 0\;{{\mathrm{mm}}} $
图 6 单振子元胞在不同轴向压缩值下的能带结构对比图
Figure 6. Energy band structure comparison diagram of single-oscillator cell under different axial compression values
图 7 二振子元胞在不同轴向压缩值下的能带结构对比图
Figure 7. Energy band structure comparison diagram of two-oscillator cell under different axial compression values
图 8 三振子元胞在不同轴向压缩值下的能带结构对比图
Figure 8. Energy band structure comparison diagram of three-oscillator cell under different axial compression values
图 9 四振子元胞在不同轴向压缩值下的能带结构对比图
Figure 9. Energy band structure comparison diagram of four-oscillator cell under different axial compression values
图 10 有限周期二振子超结构振动传输特性分析示意图
Figure 10. Analysis diagram of vibration transmission characteristics of finite period two-oscillator metastructure
图 11 不同轴向压缩值下两种尺寸有限周期二振子超结构振动传输特性曲线对比图
Figure 11. Comparison of vibration transmission characteristics curves of finite-period two-oscillator metastructures with two different sizes under different axial compression values
图 12 不同轴向压缩值二振子构型超结构的能带结构及振动传输特性曲线
Figure 12. Energy band structure and vibration transmission characteristic curves of two-oscillator configuration metastructures with different axial compression values
图 16 不同轴向压缩值下二振子构型超结构的实验、数值振动传输特性曲线对比图
Figure 16. Comparison of experimental and numerical vibration transmission characteristic curves of two-oscillator configuration metastructure under different axial compression values
表 1 几何参数和材料参数
Table 1. Geometric parameters and material parameters
Geometric parameters Value Material Material parameters Value R/mm 17.5 Silicon rubber E/MPa 0.870 ρ/(kg·m−3) 1230 D/mm 7.426 ν 0.499 Lead E/MPa 40.8 θ/(°) 45 ρ/(kg·m−3) 11340 ν 0.37 Notes：E is elastic modulus；ρ is density；ν is Poisson’s ratio. 
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[1] 肖勇, 王洋, 赵宏刚, 等. 面向减振降噪应用的声学超构材料研究进展[J]. 机械工程学报, 2023, 59(19): 277-298. doi: 10.3901/JME.2023.19.277Xiao Yong, Wang Yang, Zhao Honggang, et al. Research progress of acoustic metamaterials for vibration and noise reduction applications[J]. Journal of Mechanical Engineering, 2023, 59(19): 277-298(in Chinese). doi: 10.3901/JME.2023.19.277 [2] 代洪庆. 基于声学超材料的声场调控及微粒操控研究[D]. 湖南大学, 2022.Dai Hongqing. Research on sound field control and particle manipulation based on acoustic metamaterials [D]. Hunan University, 2022(in Chinese). [3] LIU Z Y, ZHANG X X, MAO Y W, et al. Locally resonant sonic materials[J]. Science, 2000, 289(5485): 1734-1736. doi: 10.1126/science.289.5485.1734 [4] Amer Y A, El-Sayed A T, Ahmed E E. Vibration reduction of a non-linear ship model using positive position feedback controllers[J]. International Journal of Dynamics and Control, 2022, 10(2): 409-426. doi: 10.1007/s40435-021-00801-8 [5] Jinfeng R, Lin W, Pei L. Summary of research on supporting facilities and structure vibration and noise reduction of high-rise buildings[C]//IOP conference series: earth and environmental science. IOP Publishing, 2021, 791(1): 012023. [6] Desai R, Guha A, Seshu P. Modelling and simulation of active and passive seat suspensions for vibration attenuation of vehicle occupants[J]. International Journal of Dynamics and Control, 2021: 1-21. [7] 郁殿龙. 基于声子晶体理论的梁板类周期结构振动带隙特性研究[D]. 国防科学技术大学, 2007.Yu Dianlong. Research on the vibration band gap characteristics of beam-plate periodic structures based on phononic crystal theory [D]. National University of Defense Science and Technology, 2007(in Chinese). [8] 王刚. 声子晶体局域共振带隙机理及减振特性研究[D]. 国防科学技术大学, 2007.Wang Gang. Study on the local resonance band gap mechanism and vibration reduction characteristics of phononic crystals [D]. University of Defense Science and Technology, 2007(in Chinese). [9] Lee T, Iizuka H. Bragg scattering based acoustic topological transition controlled by local resonance[J]. Physical Review B, 2019, 99(6): 064305. doi: 10.1103/PhysRevB.99.064305 [10] Zhou X, Wang L. Opening complete band gaps in two dimensional locally resonant phononic crystals[J]. Journal of Physics and Chemistry of Solids, 2018, 116: 174-179. doi: 10.1016/j.jpcs.2018.01.025 [11] 肖鹏, 缪林昌, 郑海忠, 等. 一种新型二维三组元水泥基拟声子晶体复合材料的低频带隙特性与应用[J/OL]. 复合材料学报: 1-162024-03-13]. Xiao Peng, Miao Linchang, Zheng Haizhong, et al. Low-frequency band gap properties and applications of a new two-dimensional three-component cement-based phononic crystal composite [J/OL]. Composite Journal: 1-16 [2024-03-13] (in Chinese). [12] Gao N, Hou H, Wu J H, et al. Low frequency band gaps below 10 Hz in radial flexible elastic metamaterial plate[J]. Journal of Physics D: Applied Physics, 2016, 49(43): 435501. doi: 10.1088/0022-3727/49/43/435501 [13] Zhou X, Xu Y, Liu Y, et al. Extending and lowering band gaps by multilayered locally resonant phononic crystals[J]. Applied Acoustics, 2018, 133: 97-106. doi: 10.1016/j.apacoust.2017.12.012 [14] 张思文, 吴九汇. 局域共振复合单元声子晶体结构的低频带隙特性研究[J]. 物理学报, 2013, 62(13): 134302. doi: 10.7498/aps.62.134302Zhang Siwen, Wu Jiuhui. Low-frequency band gap characteristics of phononic crystal structure of locally resonant composite unit[J]. Physical Journal, 2013, 62(13): 134302(in Chinese). doi: 10.7498/aps.62.134302 [15] Li X F, Cheng S L, Yang H Y, et al. Optimization of vibration characteristics and directional propagation of plane waves in branching ligament structures of wind models[J]. Results in Physics, 2023, 47: 106345. doi: 10.1016/j.rinp.2023.106345 [16] Coffy E, Lavergne T, Addouche M, et al. Ultra-wide acoustic band gaps in pillar-based phononic crystal strips[J]. Journal of Applied Physics, 2015, 118(21): 214902. doi: 10.1063/1.4936836 [17] 李孟昶, 郭少杰, 张红艳. 管道超结构轴向带隙特性分析及实验研究[J]. 人工晶体学报, 2023, 52(1): 65-72. doi: 10.3969/j.issn.1000-985X.2023.01.009Li Mengchang, Guo Shaojie, Zhang Hongyan. Analysis and experimental study on axial band gap characteristics of pipe metastructure[J]. Journal of Artificial Crystallography, 2023, 52(1): 65-72(in Chinese). doi: 10.3969/j.issn.1000-985X.2023.01.009 [18] 李潘玉, 游世辉, 李维, 等. 磁流变弹性体基拓扑声子晶体弹性波传输可调性研究[J]. 功能材料, 2021, 52(5): 5151-5158. doi: 10.3969/j.issn.1001-9731.2021.05.023Li Panyu, You Shihui, Li Wei, et al. Study on the tunability of elastic wave transmission in magnetorheological elastomer-based topological phononic crystals[J]. Functional materials, 2021, 52(5): 5151-5158(in Chinese). doi: 10.3969/j.issn.1001-9731.2021.05.023 [19] 王婷英, 柴怡君, 耿谦, 等. 力-压电混合弹性超材料梁的带隙调节特性[J]. 固体力学学报, 2022, 43(4): 406-418.Wang Tingying, Chai Yijun, Geng Qian, et al. Band gap tuning properties of force-piezoelectric hybrid elastic metamaterial beams[J]. Journal of Solid Mechanics, 2022, 43(4): 406-418(in Chinese). [20] Wu Y, Yu K P, Yang L Y, et al. Effect of thermal stresses on frequency band structures of elastic metamaterial plates[J]. Journal of Sound and Vibration, 2018, 413: 101-119. doi: 10.1016/j.jsv.2017.10.014 [21] Yao Y W, Wu F G, Zhang X, et al. Thermal tuning of Lamb wave band structure in a two-dimensional phononic crystal plate[J]. Journal of Applied Physics, 2011, 110(12): 123503. doi: 10.1063/1.3669391 [22] Geng Q, Cai T, Li Y. Flexural wave manipulation and energy harvesting characteristics of a defect phononic crystal beam with thermal effects[J]. Journal of Applied Physics, 2019, 125(3): 035103. doi: 10.1063/1.5063949 [23] Dai H, Xia B, Yu D. Temperature-controlled tunable underwater acoustic topological insulators[J]. Journal of Applied Physics, 2019, 125(23): 235105. doi: 10.1063/1.5090789 [24] Li X F, Cheng S L, Yang H Y, et al. Integrated analysis of bandgap optimization regulation and wave propagation mechanism of hexagonal multi-ligament derived structures[J]. European Journal of Mechanics-A/Solids, 2023, 99: 104952. doi: 10.1016/j.euromechsol.2023.104952 [25] Li X F, Cheng S L, Yang H Y, et al. Bandgap tuning and in-plane wave propagation of chiral and anti-chiral hybrid metamaterials with assembled six oscillators[J]. Physica A: Statistical Mechanics and its Applications, 2023, 615: 128600. doi: 10.1016/j.physa.2023.128600 [26] Bertoldi K, Boyce M C. Wave propagation and instabilities in monolithic and periodically structured elastomeric materials undergoing large deformations[J]. Physical Review B, 2008, 78(18): 184107. doi: 10.1103/PhysRevB.78.184107 [27] Shan S, Kang S H, Wang P, et al. Harnessing multiple folding mechanisms in soft periodic structures for tunable control of elastic waves[J]. Advanced Functional Materials, 2014, 24(31): 4935-4942. doi: 10.1002/adfm.201400665 [28] Li J, Wang Y S, Chen W Q, et al. Harnessing inclusions to tune post-buckling deformation and bandgaps of soft porous periodic structures[J]. Journal of Sound and Vibration, 2019, 459: 114848. doi: 10.1016/j.jsv.2019.114848 [29] Gei M. Wave propagation in quasiperiodic structures: stop/pass band distribution and prestress effects[J]. International Journal of Solids and Structures, 2010, 47(22): 3067-3075. [30] 黄屹澜. 软材料周期结构中波传播行为主动调控[D]. 浙江大学, 2020.Huang Yilan . Active control of wave propagation behavior in periodic structures of soft materials [D]. Zhejiang University, 2020(in Chinese). [31] Huang Y, Li J, Chen W Q, et al. Tunable bandgaps in soft phononic plates with spring-mass-like resonators[J]. International Journal of Mechanical Sciences, 2019, 151: 300-313. doi: 10.1016/j.ijmecsci.2018.11.029 [32] Huang Y, Gao N, Chen W Q, et al. Extension/compression-controlled complete band gaps in 2D chiral square-lattice-like structures[J]. Acta Mechanica Solida Sinica, 2018, 31(1): 51-65. 、 [33] 付强, 姚飞, 张红艳. 局域共振夹芯超结构梁带隙特性及实验研究[J]. 人工晶体学报, 2024, 53(1): 65-72. doi: 10.3969/j.issn.1000-985X.2024.01.007Fu Qiang, Yao Fei, Zhang Hongyan. Band gap characteristics and experimental study of locally resonant sandwich metastructure beams[J]. Journal of Artificial Crystallography, 2024, 53(1): 65-72(in Chinese). doi: 10.3969/j.issn.1000-985X.2024.01.007 -
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