| Citation: |
YANG Ziyue, LIU Huan, ZHANG Hongyan. Study on the complex band gap characteristic of controllable metastructure[J]. Acta Materiae Compositae Sinica, 2025, 42(2): 782-790. DOI: 10.13801/j.cnki.fhclxb.20240514.002
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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.
The traditional metastructure design method cannot achieve continuous parameter control. In practical engineering, the structure changes with the dynamic characteristic of different working conditions. 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. By introducing external excitation ( such as mechanical load, electric field, magnetic field and temperature field ) into the metastructure, the band structure of the structure can be changed to achieve the purpose of real-time control of the band gap. In this paper, a new controllable metastructure configuration is proposed. The structure is composed of porous soft materials and local resonant oscillators, 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 structure can realize the band gap regulation of the structure under different working conditions, and has broad application prospects in aerospace, rail transit and other fields.
The finite element models of four controllable metastructures are established by COMSOL software, and periodic boundary conditions are applied. Let the wave vector scan the boundary of the first irreducible Brillouin zone ,,and calculate the first 50 order characteristic frequency of the structure, and then the dispersion curve of the wave vector and frequency can be obtained. The energy band distribution of four kinds of controllable metastructure configurations and the regulation of band gap characteristics under the action of external displacement excitation are studied. A two-oscillator cell structure specimen was fabricated, and an experimental platform for vibration transmission characteristics of finite-period structures was built. The force hammer was used to generate excitation along the horizontal direction, and the acceleration responses of the input and output ends were collected. The vibration transmission characteristic curve of the structure was obtained and compared with the numerical results.
The four configurations of the composite band gap controllable metastructure can produce two kinds of band gaps : local resonance type and Bragg scattering type. The four-oscillator configuration has three complete band gaps in the range of 0~800Hz. The first-order band gap range is as low as 134.48~287.53Hz, the second-order band gap range is 307.26~447.81Hz, and the third-order band gap range is 662.44~679.43Hz. The band gap characteristic of the four configurations are compared and analyzed. As the number of local resonant oscillators in the cell increases, the low-order band gap width within 300Hz increases, and the number of band gaps in the structure gradually decreases. The increase in the number of oscillators gradually increases the structural stiffness, which leads to an increase in the center frequency of the band gap and a gradual upward shift in the band gap position. The axial compression has a certain regulating effect on the band gap distribution of the structure. With the increase of the vertical displacement, the local resonance band gap changes little, the center frequency of the Bragg scattering band gap gradually moves upward, and new complete band gaps and directional band gaps appear in a higher frequency range, and the axial compression has the same band gap regulation law for the four composite band gap controllable metastructures. The transmission characteristic of the two-oscillator composite band gap controllable metastructure are calculated. The numerical results show that it has a good vibration reduction effect in the band gap range. The maximum attenuation of the uncompressed structure and the axial compression structure can reach 150dB, and the experimental results of the vibration transmission characteristic curve are basically consistent with the attenuation part of the numerical results. Therefore, the elastic wave will have a significant attenuation in the band gap frequency range.Conclusions: The composite band gap controllable metastructure proposed in this paper is composed of porous soft materials and locally resonant vibrators embedded inside. According to the different distribution positions of vibrators, there are four configurations of single vibrator, two vibrator, three vibrator and four vibrator. The structure can simultaneously generate a low-frequency local resonance band gap and a high-frequency Bragg scattering band gap. By adjusting the position of the vibrator, the low-frequency local resonance band gap can be controlled, and the higher-frequency Bragg scattering band gap can be adjusted by applying a controllable displacement. The structure has good vibration reduction characteristics in the band gap range. The composite band gap controllable metastructure can realize the regulation of the composite band gap, which provides a useful reference for the research of vibration reduction design of metastructure, and has broad application prospects in aerospace, rail transit and other fields.
| [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.2023.19.277
XIAO 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]. 长沙: 湖南大学, 2022.
DAI Hongqing. Research on sound field control and particle manipulation based on acoustic metamaterials [D]. Changsha: 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] |
RUI J F, WANG L, LU P. Summary of research on supporting facilities and structure vibration and noise reduction of high-rise buildings[C]//IOP Conference Series: Earth and Environmental Science. Bristol: 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, 9(4): 1423-1443.
|
| [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]. 长沙: 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]. Changsha: 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]. 长沙: 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]. Changsha: 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]. 复合材料学报, 2024, 41(10): 5607-5621.
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]. Acta Materiae Compositae Sinica, 2024, 41(10): 5607-5621(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.62.134302
ZHANG 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.2023.01.009
LI 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.1001-9731.2021.05.023
LI 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]. 杭州: 浙江大学, 2020.
HUANG Yilan . Active control of wave propagation behavior in periodic structures of soft materials [D]. Hangzhou: 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.2024.01.007
FU 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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