压电周期板中耦合禁带影响规律分析

doi:10.13700/j.bh.1001-5965.2020.0230

北京航空航天大学学报 ›› 2021, Vol. 47 ›› Issue (7): 1422-1437.doi: 10.13700/j.bh.1001-5965.2020.0230

压电周期板中耦合禁带影响规律分析

姜周¹, 李琳^1,2, 范雨^1,2, 王文君¹

1. 北京航空航天大学能源与动力工程学院, 北京 100083;
2. 北京航空航天大学先进航空发动机协同创新中心, 北京 100083

收稿日期:2020-06-01 发布日期:2021-08-06
通讯作者: 范雨 E-mail:fanyu04@buaa.edu.cn
基金资助:
国家自然科学基金（51675022，11702011）；航空科学基金（2019ZB051002）

Influence analysis of coupled band gap in piezoelectric periodic plate

JIANG Zhou¹, LI Lin^1,2, FAN Yu^1,2, WANG Wenjun¹

1. School of Energy and Power Engineering, Beihang University, Beijing 100083, China;
2. Collaborative Innovation Center for Advanced Aero-Engine, Beihang University, Beijing 100083, China

Received:2020-06-01 Published:2021-08-06
Supported by:
National Natural Science Foundation of China (51675022,11702011); Aeronautical Science Foundation of China (2019ZB051002)

摘要/Abstract

摘要： 近年来，利用周期结构中弹性波禁带特性减振的研究思路受到了广泛关注。针对以往周期结构难以实现宽频且可调禁带的问题，设计了一种含电路网络的压电周期结构。该结构中的弯曲波和电路网络中的电波通过压电效应可以产生一个较宽的耦合禁带，且通过调整电路参数就可以达到调节禁带位置的目的。首先，为了高效计算该结构的波动特性，开发了适用于压电周期结构的减缩波有限元算法，该算法可以在保证结果准确性的基础上节约90%以上的计算时间。利用该算法研究了压电材料尺寸和形状对耦合禁带性能的影响。结果表明：相同电学参数下，随着压电片尺寸的增大，耦合禁带向低频移动，且禁带带宽增加；相同面积下含圆形和方形压电片的机电系统内耦合禁带差异较小，即形状对耦合禁带的分布影响不大。其次，针对不同尺寸和形状的机电系统，设计了电学参数使得在同一频率附近产生耦合禁带，并分析了其性能差异。最后，为了证明耦合禁带的减振效果，设计了一种有限压电周期板模型，其强迫响应的结果证明了耦合禁带对结构内弹性波可以进行有效调控。

关键词: 压电材料, 周期结构, 耦合禁带, 波有限元算法, 减缩算法, 参数分析

Abstract: In recent years, researches on the elastic band gaps in periodic structures to reduce vibration have attracted widespread attention. However, it is difficult to design a band gap with wide bandwidth and good tunability. Aiming at this problem, we designed a periodic structure with piezoelectric network. By bonding piezoelectric patches periodically into structure, a coupled band gap can be created between the elastic waves and electric waves thanks to the piezoelectric effect. This band gap can be tailored with the help of external circuits. In order to calculate the propagation characteristics of the structure efficiently, a reduced wave finite element method suitable for piezoelectric periodic structures was developed to improve the calculation efficiency. It was found that more than 90% of the calculation time can be saved with great accuracy. Using this method, the influence of the size and shape of the piezoelectric material on the performance of the coupled band gap was studied. The results show that when fixing the electrical parameters, as the size of the piezoelectric patches increases, the coupled band gap moves to lower frequency range and its bandwidth increases. Moreover, the bandwidth in the system with square patches is slightly wider than that with circular patches. However, these two shapes have little impact on the directional distribution of coupled band gap. Then, the guideline is proposed for designing electrical parameters to make sure that coupled band gaps are generated around the desired frequency for electromechanical systems with different sizes and shapes. Finally, in order to prove the vibration reduction effect of the coupled band gap, a finite periodic piezoelectric plate was employed. The results show that the coupled band gap can effectively control the elastic wave in structure.

Key words: piezoelectric material, periodic structure, coupled band gap, wave finite element method, reduction algorithm, parametric analysis

中图分类号:

V241.8

姜周, 李琳, 范雨, 王文君. 压电周期板中耦合禁带影响规律分析[J]. 北京航空航天大学学报, 2021, 47(7): 1422-1437.

JIANG Zhou, LI Lin, FAN Yu, WANG Wenjun. Influence analysis of coupled band gap in piezoelectric periodic plate[J]. Journal of Beijing University of Aeronautics and Astronautics, 2021, 47(7): 1422-1437.

参考文献

[1] HUSSEIN M I,LEAMY M J,RUZZENE M.Dynamics of phononic materials and structures:Historical origins,recent progress,and future outlook[J].Applied Mechanics Reviews,2014,66(4):1-38.
[2] 张荣英, 姜根山,王璋奇,等.声子晶体的研究进展及应用前景[J].声学技术,2006,25(1):35-42.ZHANG R Y,JIANG G S,WANGE Z Q,et al.Progress in researches of phononic crystal and the application perspectives[J].Technical Acoustics,2006,25(1):35-42(in Chinese).
[3] ROCA D,YAGO D,CANTE J,et al.Computational design of locally resonant acoustic metamaterials[J].Computer Methods in Applied Mechanics and Engineering,2019,345(1):161-182.
[4] NING L,WANG Y Z,WANG Y S,et al.Active control of elastic metamaterials consisting of symmetric double Helmholtz resonator cavities[J].International Journal of Mechanical Sciences,2019,153-154:287-298.
[5] PELAT A,GALLOT T,GAUTIER F.On the control of the first Bragg band gap in periodic continuously corrugated beam for flexural vibration[J].Journal of Sound and Vibration,2019,446:249-262.
[6] FAN Y,COLLET M,ICHCHOU M,et al.Energy flow prediction in built-up structures through a hybrid finite element/wave and finite element approach[J].Mechanical Systems and Signal Processing, 2016,66-67(1):137-158.
[7] QI S,OUDICH M,LI Y,et al.Acoustic energy harvesting based on a planar acoustic metamaterial[J].Applied Physics Letters,2016,108(26):1-4.
[8] WU Y G,LI L,FAN Y,et al.Design of dry friction and piezoelectric hybrid ring dampers for integrally bladed disks based on complex nonlinear modes[J].Computers and Structures,2020,233:1-19.
[9] WEN S R,XIONG Y H,HAO S M,et al.Enhanced band-gap properties of an acoustic metamaterial beam with periodically variable cross-sections[J].International Journal of Mechanical Sciences,2020,166:1-10.
[10] MOSCATELLI M,ARDITO R,DRIEMEIER L,et al.Band-gap structure in two- and three-dimensional cellular locally resonant materials[J].Journal of Sound and Vibration,Academic Press,2019,454(18):73-84.
[11] LI L,JIANG Z,FAN Y,et al.Creating the coupled band gaps in piezoelectric composite plates by interconnected electric impedance[J].Materials,2018,11(9):1656.
[12] 舒海生, 张法,刘少刚,等.一种特殊的布拉格型声子晶体杆振动带隙研究[J].振动与冲击,2014,33(19):147-151.SHU H S,ZHANG F,LIU S G,et al.Vibration band gap of a special rod of phononic crystals[J].Journal of Vibration and Shock,2014,33(19):147-151(in Chinese).
[13] 舒海生, 董立强,李世丹,等.布拉格型声子晶体弦的横向振动带隙研究[J].人工晶体学报,2013,42(9):1918-1923.SHU H S,DONG L Q,LI S D,et al.Study on the lateral band gap of string of phononic crystals[J].Journal of Synthetic Crystals,2013,42(9):1918-1923(in Chinese).
[14] 张若军, 肖勇,温激鸿,等.四边固支局域共振型板的低频隔声特性研究[J].振动工程学报,2016,29(5):905-912.ZHANG R J,XIAO Y,WEN J H,et al.Analysis of sound transmission through clamped locally resonant plate in low frequency[J].Journal of Vibration Engineering,2016,29(5):905-912(in Chinese).
[15] LIU L,HUSSEIN M I.Wave motion in periodic flexural beams and characterization of the transition between bragg scattering and local resonance[J].Journal of Applied Mechanics,2012,79(1):1-17.
[16] XIAO Y,WEN J,WANG G,et al.Theoretical and experimental study of locally resonant and bragg band gaps in flexural beams carrying periodic arrays of beam-like resonators[J].Journal of Vibration and Acoustics,2013,135(4):1-17.
[17] DONG Y,YAO H,DU J,et al.Research on local resonance and Bragg scattering coexistence in phononic crystal[J].Modern Physics Letters B,2017,31(11):1-10.
[18] CAI C,WANG Z,CHU Y,et al.The phononic band gaps of Bragg scattering and locally resonant pentamode metamaterials[J].Journal of Physics D:Applied Physics,2017,50(41):1-7.
[19] LIU Z,ZHANG X,MAO Y,et al.Locally resonant sonic materials[J].Science,2000,289(5485):1734-1736.
[20] 朱兴一, 钟盛,叶安珂,等.声子晶体禁带特性及局域共振现象的试验研究[J].人工晶体学报,2014(11):2852-2859.ZHU X Y,ZHONG S,YE A K,et al.Experimental study on band gap properties and local resonance phenomenon of phononic crystals[J].Journal of Synthetic Crystals,2014(11):2852-2859(in Chinese).
[21] LEE T,IIZUKA H.Bragg scattering based acoustic topological transition controlled by local resonance[J].Physical Review B,2019,99(6):1-11.
[22] MANCONI E,MACE B.Veering and strong coupling effects in structural dynamics[J].Journal of Vibration and Acoustics,2017,139(2):1-10.
[23] MACE B R,MANCONI E.Wave motion and dispersion phenomena:Veering,locking and strong coupling effects[J].The Journal of the Acoustical Society of America,2012,131(2):1015-1028.
[24] THOMPSON D J,FERGUSON N S,YOO J W,et al.Structural waveguide behaviour of a beam-plate system[J].Journal of Sound and Vibration,2008,318(1):206-226.
[25] YU D,WEN J,ZHAO H,et al.Vibration reduction by using the idea of phononic crystals in a pipe-conveying fluid[J].Journal of Sound and Vibration,2008,318(1):193-205.
[26] LIU J,LI L,FAN Y.A comparison between the friction and piezoelectric synchronized switch dampers for blisks[J].Journal of Intelligent Material Systems and Structures,2018,29(12):2693-2705.
[27] LIU J,LI L,HUANG X,et al.Dynamic characteristics of the blisk with synchronized switch damping based on negative capacitor[J].Mechanical Systems and Signal Processing,2017,95:425-445.
[28] YE G,YAN J,WONG Z J,et al.Optimisation of a piezoelectric system for energy harvesting from traffic vibrations[C]//Proceedings of the IEEE Ultrasonics Symposium.Piscataway:IEEE Press,2009:759-762.
[29] WANG W,LI L,FAN Y,et al.Piezoelectric transducers for structural health monitoring of joint structures in cylinders:A wave-based design approach[J].Sensors,2020,20(3):1-25.
[30] LI L,JIANG Z,FAN Y,et al.Coupled band gaps in the piezoelectric composite plate with interconnected electric impedance[C]//ASME 2018 Conference on Smart Materials,Adaptive Structures and Intelligent Systems,2018:1-27.
[31] MEITZLER A H,BERLINCOURT D,WELSH F S,et al.IEEE standard on piezoelectricity:ANSI/IEEE Std 176-1987[S].Piscataway:IEEE Press,1988.
[32] CHEN S,WANG G,SONG Y.Low-frequency vibration isolation in sandwich plates by piezoelectric shunting arrays[J].Smart Materials and Structures,2016,25(12):1-8.
[33] WANG G,CHEN S.Large low-frequency vibration attenuation induced by arrays of piezoelectric patches shunted with amplifier-resonator feedback circuits[J].Smart Materials and Structures,2015,25(1):1-15.
[34] DUHAMEL D,MACE B R,BRENNAN M J.Finite element analysis of the vibrations of waveguides and periodic structures[J].Journal of Sound and Vibration,2006,294(1):205-220.
[35] FAN Y,COLLET M,ICHCHOU M,et al.A wave-based design of semi-active piezoelectric composites for broadband vibration control[J].Smart Materials and Structures,2016,25(5):1-15.
[36] ZHOU C W,LAINÉ J P,ICHCHOU M N,et al.Numerical and experimental investigation on broadband wave propagation features in perforated plates[J].Mechanical Systems and Signal Processing,2016,75:556-575.
[37] ZHOU C W,LAINÉ J P,ICHCHOU M N,et al.Multi-scale modelling for two-dimensional periodic structures using a combined mode/wave based approach[J].Computers and Structures,2015,154:145-162.
[38] BAMPTON M C C,CRAIG J R R.Coupling of substructures for dynamic analyses[J].AIAA Journal,1968,6(7):1313-1319.
[39] WILCOX C H.Theory of Bloch waves[J].Journal d'Analyse Mathématique,1978,33(1):146-167.
[40] MING-HUI L U,ZHANG C,FENG L,et al.Negative birefraction of acoustic waves in a sonic crystal[J].Nature Materials,2007,6(10):744-748.
[41] YANG W P,WU L Y,CHEN L W.Refractive and focusing behaviours of tunable sonic crystals with dielectric elastomer cylindrical actuators[J].Journal of Physics D Applied Physics,2008,41(13):135408.

压电周期板中耦合禁带影响规律分析

Influence analysis of coupled band gap in piezoelectric periodic plate

RichHTML

PDF (PC)

可视化

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 10

编辑推荐

Metrics

本文评价

[1]	熊瑛, 李小健, 王天楠, 赵晓凡. 基于INBC的周期结构FDTD方法[J]. 北京航空航天大学学报, 2021, 47(1): 31-37.
[2]	徐斌, 田富刚. 基于双模式驱动的飞行汽车起飞阶段动力匹配分析[J]. 北京航空航天大学学报, 2018, 44(4): 662-669.
[3]	冯进军, 蔡军, 胡银富, 邬显平. 周期结构电磁特性在高频真空器件中的应用[J]. 北京航空航天大学学报, 2015, 41(10): 1785-1791.
[4]	刘遂, 关志东, 郭霞, 席国芬. 平面编织混杂铺层层板穿透挖补修理参数分析[J]. 北京航空航天大学学报, 2013, 39(2): 248-253,263.
[5]	杨海峰, 王晓军, 邱志平. 压电柔性结构振动的鲁棒控制[J]. 北京航空航天大学学报, 2009, 35(8): 957-961.
[6]	苑凯华, 邱志平. 压电复合材料壁板颤振的控制[J]. 北京航空航天大学学报, 2009, 35(12): 1429-1433.
[7]	代海涛,程伟,李明志. 哈密顿体系下功能梯度压电板/管静动力三维解[J]. 北京航空航天大学学报, 2008, 34(01): 104-107.
[8]	赵国伟, 黄海, 夏人伟. 柔性自适应桁架及其振动最优控制实验[J]. 北京航空航天大学学报, 2005, 31(04): 434-438.
[9]	任秀华, 丁桦, 麦汉超, 陆萌. 压电类智能梁元的优化布局[J]. 北京航空航天大学学报, 2000, 26(5): 584-587.
[10]	唐纪晔, 黄海, 夏人伟, 黄海博. 压电层合板自适应结构的静力变形控制[J]. 北京航空航天大学学报, 2000, 26(2): 239-243.