格栅型周期声学黑洞及其加强结构减振性能

文湘隆; 邓思贤; 宋春生; 江友亮

doi:10.3969/j.issn.0258-2724.20250577

格栅型周期声学黑洞及其加强结构减振性能

doi: 10.3969/j.issn.0258-2724.20250577

文湘隆^{1, 2,},
邓思贤¹,
宋春生^{1, 2, ,},
江友亮^{1, 2}

1.
武汉理工大学机电工程学院，湖北武汉 430070
2.
武汉理工大学湖北省磁悬浮工程技术研究中心，湖北武汉 430070

基金项目: 国家自然科学基金项目（52501397）

详细信息

作者简介:
文湘隆（1969—），男，副教授，研究方向为高性能复合材料结构设计与应用，E-mail：wenxl@whut.edu.cn

通讯作者:
宋春生（1981—），男，教授，研究方向为机械振动主动控制与磁悬浮主动隔振技术，E-mail： song_chsh@163.com

中图分类号: TB535
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出版历程
- 收稿日期: 2025-11-14
- 修回日期: 2026-03-02
- 网络出版日期: 2026-10-16

Vibration Damping Performance of Grid-Type Periodic Acoustic Black Holes and Reinforcement Structures

WEN Xianglong^{1, 2
,},
DENG Sixian¹,
SONG Chunsheng^{1, 2
, ,},
JIANG Youliang^{1, 2}

1.
School of Mechanical and Electrical Engineering, Wuhan University of Technology, Wuhan 430070, China
2.
Hubei Provincial Engineering Technology Research Center for Magnetic Suspension, Wuhan University of Technology, Wuhan 430070, China

摘要

摘要:
周期声学黑洞是一种兼具带隙特性和宽带减振性能的新型减振结构，目前对其的研究存在难以在二维层面形成全向低频带隙和结构强度低等问题. 基于此，本文围绕低频宽带减振目标，采用实能带和复能带相结合的分析方法，提出了一种格栅型周期声学黑洞结构，证明其能够在二维层面形成全方向带隙，具有较好的低频带隙特性与宽频减振性能；同时，又提出了2种加强的格栅型周期声学黑洞结构，并运用振动传输实验对理论分析进行了验证. 结果表明：带有加强筋的加强结构第一带隙起始频率上升了170.1%，带隙范围缩小为原来的42.1%；带有加强格栅的加强结构第一带隙起始频率上升了69.3%，带隙范围缩小为原来的42.3%；加强结构虽在低频带隙特性上不及原结构，但在中高频段表现出更优的减振性能，具有良好的宽频减振性能；2种加强结构相比，带有加强格栅的加强结构保持了较好的低频带隙特性与宽带减振性能.
- 声学黑洞 /
- 复能带 /
- 带隙 /
- 减振
Abstract:
A periodic acoustic black hole is a new type of vibration-damping structure that exhibits both bandgap characteristics and broadband vibration-damping performance. The current research on periodic acoustic black holes has difficulty in forming an omnidirectional low-frequency bandgap at the two-dimensional level and low structural strength. Based on this, the analysis method of combining real and complex energy bands was adopted to achieve low-frequency broadband vibration damping, and a grid-type periodic acoustic black hole structure was proposed, verifying its favorable omnidirectional bandgap characteristics at the two-dimensional level with low-frequency bandgap characteristics and broadband vibration-damping performance. Then, two reinforcement structures of grid-type acoustic periodic black holes were proposed, and the theoretical analysis was validated by employing the vibration transmission experiment. The results show that the first bandgap onset frequency of the reinforcement structure with stiffeners increases by 170.1%, while its bandgap range is reduced to 42.1% of the original value. For the reinforcement structure with stiffening grids, the first bandgap onset frequency increases by 69.3%, with its bandgap range reducing to 42.3% of the original one. The low-frequency bandgap characteristics of the reinforcement structures are not as good as those of the original structure, but the vibration-damping performance is better than that of the original structure in the medium and high frequency bands, and the reinforcement structures have excellent broadband vibration-damping performance. Through comparison of two reinforcement structures, the one with stiffening grids has better low-frequency bandgap characteristics and broadband vibration-damping performance.
- acoustic black hole /
- complex energy band /
- bandgap /
- vibration damping

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图 1 格栅型周期声学黑洞结构与最小布里渊区

Figure 1. Grid-type periodic acoustic black hole structure and minimum Brillouin zone

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图 2 格栅型无声学黑洞结构

Figure 2. Grid-type structure without acoustic black hole

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图 3 格栅型周期声学黑洞结构加强方案Ⅰ

Figure 3. Grid-type periodic acoustic black hole structure with reinforcement scheme Ⅰ

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图 4 格栅型周期声学黑洞结构加强方案Ⅱ

Figure 4. Grid-type periodic acoustic black hole structure with reinforcement scheme Ⅱ

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图 5 格栅型无声学黑洞结构加强方案Ⅱ

Figure 5. Grid-type structure without acoustic black hole with reinforcement scheme Ⅱ

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图 6 实能带对比

Figure 6. Comparison of real energy bands

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图 7 能带曲线中标注点振型

Figure 7. Vibration mode at marked points of energy band curves

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图 8 域的分割

Figure 8. Domain partitioning

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图 9 格栅型周期声学黑洞复能带

Figure 9. Complex energy band of grid-type periodic acoustic black holes

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图 10 衰减因子对比

Figure 10. Comparison of attenuation factors

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图 11 结构加强后的能带变化

Figure 11. Energy band changes after structural reinforcement

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图 12 能带曲线中标注点振型

Figure 12. Vibration mode at marked points of energy band curves

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图 13 加强方案复能带

Figure 13. Complex energy bands of reinforcement schemes

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图 14 衰减因子对比

Figure 14. Comparison of attenuation factors

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图 15 试验件与试验设备

Figure 15. Specimen and test equipment

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图 16 试验系统示意

Figure 16. Schematic diagram of experiment system

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图 17 振动传递曲线对比

Figure 17. Comparison of vibration transmission curves

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表 1 结构参数

Table 1. Structural parameters

名称	参数	名称	参数
晶格常数a/mm	100	弹性模量E/GPa	2.85
声学黑洞长度L/mm	70	泊松比ν	0.40
最大厚度h/mm	8	密度ρ/（kg•m⁻³）	1165
残余厚度h₀/mm	0.8	阻尼损耗因子η	0.05
声学黑洞指数m	2.5	声学黑洞宽度b/mm	20
加强格栅宽度b₁/mm	2

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参考文献(25)

[1]	Mironov M. Propagation of a flexural wave in a plate whose thickness decreases smoothly to zero in a finite interval[J]. Sov Phys Acoust, 1988, 34: 318-9.
[2]	Zhu H F, Semperlotti F. Two-dimensional structure-embedded acoustic lenses based on periodic acoustic black holes[J]. Journal of Applied Physics, 2017, 122(6): 065104. doi: 10.1063/1.4998524
[3]	Tang L L, Cheng L. Broadband locally resonant band gaps in periodic beam structures with embedded acoustic black holes[J]. Journal of Applied Physics, 2017, 121(19): 194901. doi: 10.1063/1.4983459
[4]	Gao N S, Guo X Y, Deng J, et al. Elastic wave modulation of double-leaf ABH beam embedded mass oscillator[J]. Applied Acoustics, 2021, 173: 107694. doi: 10.1016/j.apacoust.2020.107694
[5]	Gao N S, Wei Z Y, Zhang R H, et al. Low-frequency elastic wave attenuation in a composite acoustic black hole beam[J]. Applied Acoustics, 2019, 154: 68-76. doi: 10.1016/j.apacoust.2019.04.029
[6]	Gao N, Wei Z, Hou H, et al. Design and experimental investigation of V-folded beams with acoustic black hole indentations[J]. The Journal of the Acoustical Society of America, 2019, 145(1): EL79-83. doi: 10.1121/1.5088027
[7]	Gao N S, Wang B Z, Lu K, et al. Complex band structure and evanescent Bloch wave propagation of periodic nested acoustic black hole phononic structure[J]. Applied Acoustics, 2021, 177: 107906. doi: 10.1016/j.apacoust.2020.107906
[8]	Deng J, Xu Y X, Guasch O, et al. A two-dimensional wave and Rayleigh–Ritz method for complex dispersion in periodic arrays of circular damped acoustic black holes[J]. Mechanical Systems and Signal Processing, 2023, 200: 110507. doi: 10.1016/j.ymssp.2023.110507
[9]	Tang L L, Cheng L, Chen K A. Complete sub-wavelength flexural wave band gaps in plates with periodic acoustic black holes[J]. Journal of Sound and Vibration, 2021, 502: 116102. doi: 10.1016/j.jsv.2021.116102
[10]	Hao S T, Sheng H, Liu X S, et al. Low-frequency and broadband vibration absorption of a metamaterial plate with acoustic black hole resonators[J]. Thin-Walled Structures, 2024, 202: 112073. doi: 10.1016/j.tws.2024.112073
[11]	Hao S T, Sheng H, Li H Q, et al. Broadband vibration isolation of floating raft system via sandwich metamaterial with acoustic black hole absorbers[J]. Ocean Engineering, 2025, 341: 122600. doi: 10.1016/j.oceaneng.2025.122600
[12]	王小东, 季宏丽, 裘进浩. 声学黑洞原理的双层加筋板⁃腔系统降噪研究[J]. 振动工程学报, 2022, 35(2): 503-513. doi: 10.16385/j.cnki.issn.1004-4523.2022.02.026 Wang Xiaodong, Ji Hongli, Qiu Jinhao. Noise reduction of a double-layer stiffened plate-cavity system based on acoustic black hole principle[J]. Journal of Vibration Engineering, 2022, 35(2): 503-513. doi: 10.16385/j.cnki.issn.1004-4523.2022.02.026
[13]	Han S H, Ma N F, Han Q, et al. Machine learning-based optimal design of an acoustic black hole metaplate for enhanced bandgap and load-bearing capacity[J]. Mechanical Systems and Signal Processing, 2024, 215: 111436. doi: 10.1016/j.ymssp.2024.111436
[14]	李军军. 碳纤维复合材料声学黑洞梁减振特性研究[D]. 重庆: 重庆大学, 2024.
[15]	Deng J, Gao N S, Chen X, et al. Evanescent waves in a metabeam attached with lossy acoustic black hole pillars[J]. Mechanical Systems and Signal Processing, 2023, 191: 110182. doi: 10.1016/j.ymssp.2023.110182
[16]	Deng J, Gao N S, Chen X. Ultrawide attenuation bands in gradient metabeams with acoustic black hole pillars[J]. Thin-Walled Structures, 2023, 184: 110459. doi: 10.1016/j.tws.2022.110459
[17]	邹宇琪, 朱沈延, 王超炎, 等. 附加式声学黑洞对悬臂板振动寿命影响研究[J]. 振动工程学报, 2024, 37(10): 1669-1678. doi: 10.16385/j.cnki.issn.1004-4523.2024.10.004 Zou Yuqi, Zhu Shenyan, Wang Chaoyan, et al. Study on the effect of additional acoustic black hole on vibration life of cantilever plate[J]. Journal of Vibration Engineering, 2024, 37(10): 1669-1678. doi: 10.16385/j.cnki.issn.1004-4523.2024.10.004
[18]	郭新, 李伟, 温华兵, 等. 附加式声学黑洞梁对平板的振动影响分析[J]. 噪声与振动控制, 2025, 45(5): 98-103. Guo Xin, Li Wei, Wen Huabing, et al. Analysis of the influence of additional acoustic black hole beam on the vibration of plate structures[J]. Noise and Vibration Control, 2025, 45(5): 98-103.
[19]	赵艳菊, 陈大伟, 朱雷威, 等. 弧形声学黑洞超结构带隙机理及减振应用探索[J]. 铁道科学与工程学报, 2025, 22(9): 4120-4132. doi: 10.19713/j.cnki.43-1423/u.T20241944 Zhao Yanju, Chen Dawei, Zhu Leiwei, et al. Bandgap mechanism and vibration attenuation exploration of circular acoustic black holes metastructure[J]. Journal of Railway Science and Engineering, 2025, 22(9): 4120-4132. doi: 10.19713/j.cnki.43-1423/u.T20241944
[20]	Deng J, Guasch O. Sound waves in continuum models of periodic sonic black holes[J]. Mechanical Systems and Signal Processing, 2023, 205: 110853. doi: 10.1016/j.ymssp.2023.110853
[21]	Deng J, Xu Y X, Guasch O, et al. A wave and Rayleigh–Ritz method to compute complex dispersion curves in periodic lossy acoustic black holes[J]. Journal of Sound and Vibration, 2023, 546: 117449. doi: 10.1016/j.jsv.2022.117449
[22]	李军军, 李剑辉, 郑玲, 等. 声学黑洞约束阻尼板半解析耦合建模与振动特性研究[J]. 振动工程学报, 2024, 37(5): 847-855. Li Junjun, Li Jianhui, Zheng Ling, et al. Semi analytical coupling modeling and vibration characteristics of ABH plate with constrained damping layer[J]. Journal of Vibration Engineering, 2024, 37(5): 847-855.
[23]	Bowyer E P, Krylov V V. Experimental investigation of damping flexural vibrations in glass fibre composite plates containing one- and two-dimensional acoustic black holes[J]. Composite Structures, 2014, 107: 406-415.
[24]	Wang Y F, Wang Y S, Laude V. Wave propagation in two-dimensional viscoelastic metamaterials[J]. Physical Review B, 2015, 92(10): 104110.
[25]	García V R, Garcia Raffi L M, Sánchez Pérez J V. Evanescent waves and deaf bands in sonic crystals[J]. AIP Advances, 1(4): 41601.