含螺旋孔的超材料夹层板的带隙特性研究

摘要/Abstract

摘要： 本文提出一种新型低频宽带的穿孔超材料夹层板,旨在有效抑制板间横向振动。该结构的单胞由上下层面板、螺旋板、圆柱振子和支撑部件等构成。其中,螺旋板上设计4个螺纹孔,圆柱振子通过螺栓固定于板中心,螺旋板通过两侧横板与支撑部分连接。采用COMSOL仿真软件对胞元进行有限元分析,获得了无限周期结构的能带和共振模态,并计算了有限周期结构的传输透射率。结果表明,该结构能够产生两个宽幅的低频振动带隙,带隙范围内的振动衰减明显。本文进一步揭示了带隙机理,优化了结构参数,实现了两带隙的低频耦合,给出了符合工程实际需求的带隙。

关键词: 超材料夹层板, 螺旋结构, 能带结构, 局域共振, 低频宽带, 振动控制

Abstract: In this paper, a new type of low frequency broadband perforated metamaterial sandwich plate is designed to suppress the transverse vibration between the plates. The unit cell of the structure is composed of the upper and the lower layer plates, spiral plates, cylindrical oscillators and support components. Among them, the spiral plate with four threaded holes is connected with the upper and lower plates through the support parts on both sides, and the oscillator is fixed at the center of the plate by bolts. The finite element analysis of the cell is carried out by COMSOL Multiphysics, and the energy band structure and resonance mode of the infinite periodic structure are obtained. In addition, the transmission transmittance of the finite-period structure is calculated. The results show that the structure generate two wide band gaps of low frequency vibration, and the vibration attenuation is obvious in the band gap range. Furthermore, this paper unveils the mechanism of the band gap, optimizes structural parameters, achieves low-frequency coupling of the two band gaps, and provides band gap configurations that meet the practical engineering requirements.

Key words: metamaterial sandwich plate, spiral structure, band structure, local resonant, low frequency broadband, vibration control

中图分类号:

TB535

张玖林, 田霞. 含螺旋孔的超材料夹层板的带隙特性研究[J]. 人工晶体学报, 2024, 53(3): 511-518.

ZHANG Jiulin, TIAN Xia. Bandgap Characteristics of Metamaterial Sandwich Plates with Spiral Holes[J]. JOURNAL OF SYNTHETIC CRYSTALS, 2024, 53(3): 511-518.

参考文献

[1] 何晓栋. 基于声学超材料的飞机壁板隔声特性研究[D]. 长沙: 国防科技大学, 2018.
HE X D. Sound insulation properties of metamaterial-based aircraft panels[D]. Changsha: National University of Defense Technology, 2018 (in Chinese).
[2] YU D L, LIU Y Z, WANG G, et al. Low frequency torsional vibration gaps in the shaft with locally resonant structures[J]. Physics Letters A, 2006, 348(3/4/5/6): 410-415.
[3] LIU Z, ZHANG X, MAO Y, et al. Locally resonant sonic materials[J]. Science, 2000, 289(5485): 1734-1736.
[4] 郁殿龙, 刘耀宗, 王刚, 等. 二维声子晶体薄板的振动特性[J]. 机械工程学报, 2006, 42(2): 150-154.
YU D L, LIU Y Z, WANG G, et al. Vibration property of two dimension phononic crystals thin plate[J]. Chinese Journal of Mechanical Engineering, 2006, 42(2): 150-154 (in Chinese).
[5] 温激鸿, 蔡力, 郁殿龙, 等. 声学超材料基础理论与应用[M]. 北京: 科学出版社, 2018.
WEN J H, CAI L, YU D L, et al. Basic theory and application of acoustic metamaterials[M]. Beijing: Science Press, 2018 (in Chinese).
[6] 靳奉华, 郭辉, 孙裴, 等. 方形晶格夹层板减振性能仿真与优化[J]. 人工晶体学报, 2022, 51(2): 248-255.
JIN F H, GUO H, SUN P, et al. Simulation and optimization of vibration reduction performance of square lattice sandwich plate[J]. Journal of Synthetic Crystals, 2022, 51(2): 248-255 (in Chinese).
[7] 陈鼎康, 李欣欣, 李应刚, 等. 局域共振船体板架超结构低频隔振特性研究[J]. 噪声与振动控制, 2023, 43(5): 221-226.
CHEN D K, LI X X, LI Y G, et al. Low frequency vibration isolation characteristics of hull grillage metastructures with local resonators[J]. Noise and Vibration Control, 2023, 43(5): 221-226 (in Chinese).
[8] 李寅, 肖勇. 声学超材料板的弯曲波带隙与减振降噪特性[J]. 噪声与振动控制, 2018, 38(增刊1): 35-40.
LI Y, XIAO Y. Flexural wave band gaps and vibration attenuation characteristics of acoustic metamaterial plates[J]. Noise and Vibration Control, 2018, 38(supplement 1): 35-40 (in Chinese).
[9] PENNEC Y, DJAFARI-ROUHANI B, LARABI H, et al. Low-frequency gaps in a phononic crystal constituted of cylindrical dots deposited on a thin homogeneous plate[J]. Physical Review B, 2008, 78(10): 104105.
[10] LAI Y, WU Y, SHENG P, et al. Hybrid elastic solids[J]. Nature Materials, 2011, 10(8): 620-624.
[11] 吴九汇, 张思文, 沈礼. 螺旋局域共振单元声子晶体板结构的低频振动带隙特性研究[J]. 机械工程学报, 2013, 49(10): 62-69.
WU J H, ZHANG S W, SHEN L. Low-frequency vibration characteristics of periodic spiral resonators in phononic crystal plates[J]. Journal of Mechanical Engineering, 2013, 49(10): 62-69 (in Chinese).
[12] 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.
ZHANG S W, WU J H. Low-frequency band gaps in phononic crystals with composite locally resonant structures[J]. Acta Physica Sinica, 2013, 62(13): 134302 (in Chinese).
[13] 刘金辉, 李金强, 张垚, 等. 双层薄膜型超材料夹层板的多带隙设计[J]. 动力学与控制学报, 2023, 21(7): 20-27.
LIU J H, LI J Q, ZHANG Y, et al. Multi-bandgap design of double membrane-type acoustic metamaterials[J]. Journal of Dynamics and Control, 2023, 21(7): 20-27 (in Chinese).
[14] 肖伟民, 李禹昕, 户文成, 等. 双层超材料板的弯曲波超低频带隙特性研究[J]. 功能材料, 2023, 54(2): 2146-2152.
XIAO W M, LI Y X, HU W C, et al. Ultralow frequency band gaps of flexural wave in metamaterial bipanel[J]. Journal of Functional Materials, 2023, 54(2): 2146-2152 (in Chinese).
[15] 李东庭, 黄思博, 莫方朔, 等. 基于微穿孔板和卷曲背腔复合结构的低频宽带吸声体[J]. 科学通报, 2020, 65(15): 1420-1427.
LI D T, HUANG S B, MO F S, et al. Low-frequency broadband absorbers based on coupling micro-perforated panel and space-curling chamber[J]. Chinese Science Bulletin, 2020, 65(15): 1420-1427 (in Chinese).
[16] FOEHR A, BILAL O R, HUBER S D, et al. Spiral-based phononic plates: from wave beaming to topological insulators[J]. Physical Review Letters, 2018, 120(20): 205501.
[17] TIAN X Y, CHEN W J, GAO R J, et al. Merging Bragg and local resonance bandgaps in perforated elastic metamaterials with embedded spiral holes[J]. Journal of Sound and Vibration, 2021, 500: 116036.
[18] TIAN X Y, CHEN W J, GAO R J, et al. Design of pore layout for perforated auxetic metamaterials with low-frequency band gaps[J]. Applied Physics Express, 2020, 13(4): 045503.
[19] 麻乘榕, 邵晨, 万庆冕, 等. 用于汽车低频振动控制的局域共振声子晶体[J]. 应用声学, 2018, 37(1): 152-158.
MA C R, SHAO C, WAN Q M, et al. A locally-resonant phononic crystal for low-frequency vibration control of vehicles[J]. Journal of Applied Acoustics, 2018, 37(1): 152-158 (in Chinese).
[20] WU F, XIAO Y, YU D L, et al. Low-frequency sound absorption of hybrid absorber based on micro-perforated panel and coiled-up channels[J]. Applied Physics Letters, 2019, 114(15): 151901.