多振子声子晶体的低频特性研究

摘要/Abstract

摘要： 本文设计了一种由硅橡胶包覆层包裹4个钨振子的新型声子晶体结构,通过有限元法计算该结构的色散曲线、振动模态和传输损失谱。结果表明,该结构的带隙范围为18.85~225.28 Hz,与传输损失谱频率衰减范围相吻合,能够有效抑制20~200 Hz的弹性波在声子晶体中传播。通过分析色散曲线上点的振动模态,说明带隙产生的原因。本文讨论了声子晶体板的缺口角度和振子之间的纵向和横向间距对带隙的影响,结果表明:当缺口角度减小时,带隙下边界几乎保持不变,带隙上边界升高从而增加了带隙的宽度;振子之间横向或纵向间距增大时,带隙下边界和上边界均上升,带隙变宽,进而优化了声子晶体模型的带隙。同时声子晶体板的缺口设计能够节省材料,从而减轻结构的质量。

关键词: 声子晶体, 局域共振, 多振子结构, 低频带隙, 缺口角度, 硅橡胶

Abstract: In this paper, a new phononic crystal structure with periodic units consisting of four tungsten vibrators wrapped by silicone rubber coating is designed. The dispersion curve, vibration mode and transmission loss spectrum of the structure were calculated by finite-element method(FEM). The results show that the bandgap range of this structure is 18.85~225.28 Hz, which is consistent with the frequency attenuation range of transmission loss spectrum, and can effectively suppress the propagation of elastic waves of 20~200 Hz in phononic crystals. By analyzing the vibration mode corresponding to the point on the dispersion curve, the formation mechanism of the bandgap is explained. The influence of the notch angle of the phononic crystal plate and the longitudinal and transverse spacing between the phonons on the bandgap was discussed in this paper. The results show that as the notch angle decreases, the lower boundary of the bandgap remains almost unchanged, and the upper boundary of the bandgap rises, thus increasing the width of the bandgap.As the transverse or longitudinal spacing between the vibrators increases, the lower and upper boundaries of the bandgap rise, and the width of the bandgap increases, thus the bandgap of the phononic crystal model is optimized. At the same time, the notch design of the phononic crystal plate save the material and reduce the weight of the structure.

Key words: phononic crystal, local resonance, multivibrator structure, low frequency bandgap, notch angle, silicone rubber

中图分类号:

李天杰, 伍根生, 袁志山, 尹富强, 顾云风. 多振子声子晶体的低频特性研究[J]. 人工晶体学报, 2022, 51(12): 2022-2030.

LI Tianjie, WU Gensheng, YUAN Zhishan, YIN Fuqiang, GU Yunfeng. Low Frequency Characteristics of a Multivibrator Phononic Crystal[J]. JOURNAL OF SYNTHETIC CRYSTALS, 2022, 51(12): 2022-2030.

参考文献

[1] 温熙森,温激泓,郁殿龙.声子晶体[M].北京:国防工业出版社,2009.
WEN X S, WEN J H, YU D L. Phononic crystals[M]. Beijing: National Defense Industry Press, 2009(in Chinese).
[2] 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,2006.
YU D L. Research on the vibration band gaps of periodic beams and plates based on the theory of phononic crystals[D]. Changsha: National University of Defense Technology, 2006(in Chinese).
[3] 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,2005.
WANG G. Research on the mechanism and the vibration attenuation characteristic of locally resonant band gap in phononic crystals[D]. Changsha: National University of Defense Technology, 2005(in Chinese).
[4] 祁鹏山,杜军,姜久龙,等.新型局域共振声子晶体结构的低频带隙特性研究[J].人工晶体学报,2016,45(4):1094-1099.
QI P S, DU J, JIANG J L, et al. Low-frequency band gaps in phononic crystals with novel locally resonant structure[J]. Journal of Synthetic Crystals, 2016, 45(4): 1094-1099(in Chinese).
[5] 许林云,周宏平,马梦楠.Helmholtz型脉冲发动机噪声构成分析[J].中国农机化学报,2014,35(3):183-186+196.
XU L Y, ZHOU H P, MA M N. Noise analysis of Helmholtz type of pulse jet engine[J]. Journal of Chinese Agricultural Mechanization, 2014, 35(3): 183-186+196(in Chinese).
[6] 陈鑫,姚宏,赵静波,等.双局域共振Helmholtz声子晶体带隙研究[J].人工晶体学报,2019,48(1):13-17.
CHEN X, YAO H, ZHAO J B, et al. Study on the bandgap of double local resonance Helmholtz phononic crystals[J]. Journal of Synthetic Crystals, 2019, 48(1): 13-17(in Chinese).
[7] WANG X P, JIANG P, SONG A L. Low-frequency and tuning characteristic of band gap in a symmetrical double-sided locally resonant phononic crystal plate with slit structure[J]. International Journal of Modern Physics B, 2016, 30: 1650203.
[8] SUN X W, ZHU H F, GAO X L, et al. Tunable low-frequency bandgaps of a new two-dimensional multi-component phononic crystal under different pressures, geometric parameters and pre-compression strains[J]. Mechanics of Advanced Materials and Structures, 2021: 1-16.
[9] DONG Y K, YAO H, DU J, et al. Research on low-frequency band gap property of a hybrid phononic crystal[J]. Modern Physics Letters B, 2018, 32(15): 1850165.
[10] GAO N S, WU J H, YU L. Research on bandgaps in two-dimensional phononic crystal with two resonators[J]. Ultrasonics, 2015, 56: 287-293.
[11] GUO J C, LI J R, ZHANG Z. Interface design of low-frequency band gap characteristics in stepped hybrid phononic crystals[J]. Applied Acoustics, 2021, 182: 108209.
[12] 刘威,何泽银,范爱军,等.双侧空心不对称散射体声子晶体带隙机理[J].硅酸盐学报,2022,50(3):775-781.
LIU W, HE Z Y, FAN A J, et al. Band gap characteristics of phononic crystals with bilateral asymmetric two-dimensional hollow scatterers[J]. Journal of the Chinese Ceramic Society, 2022, 50(3): 775-781(in Chinese).
[13] MA X F, XIANG H, YANG X E, et al. Optimal geometric parameters for a double panel structure with low frequency forbidden characteristics[J]. Applied Acoustics, 2021, 177: 107944.
[14] BADREDDINE ASSOUAR M, SUN J H, LIN F S, et al. Hybrid phononic crystal plates for lowering and widening acoustic band gaps[J]. Ultrasonics, 2014, 54(8): 2159-2164.
[15] ZHOU P, WAN S, WANG X, et al. A novel hybrid composite phononic crystal plate with multiple vibration band gaps at low frequencies[J]. Physica B: Condensed Matter, 2021, 623: 413366.
[16] LEI L, MIAO L, LI C, et al. The effects of composite primitive cells on band gap property of locally resonant phononic crystal[J]. Modern Physics Letters B, 2021, 35(20): 2150334.
[17] ZHU H F, SUN X W, SONG T, et al. Tunable characteristics of low-frequency bandgaps in two-dimensional multivibrator phononic crystal plates under prestrain[J]. Scientific Reports, 2021, 11: 8389.
[18] 唐荣江,潘朝远,郑伟光,等.开口圆环类声子晶体传播禁带特性研究[J].人工晶体学报,2021,50(3):428-434.
TANG R J, PAN C Y, ZHENG W G, et al. Propagation band gap characteristics of open ring-like phononic crystal[J]. Journal of Synthetic Crystals, 2021, 50(3): 428-434(in Chinese).
[19] 颜克龙.螺旋结构声子晶体板带隙特性研究[D].成都:电子科技大学,2019.
YAN K L. Study on the band gap characteristics of spiral structure phononic crystal plates[D]. Chengdu: University of Electronic Science and Technology of China, 2019(in Chinese).
[20] 张凯威.桶型局域共振单元声子晶体板的低频带隙特性研究[D].成都:电子科技大学,2019.
ZHANG K W. Study on the low-frequency band gap characteristics of periodic barrel-type resonators in phononic crystal plates[D]. Chengdu: University of Electronic Science and Technology of China, 2019(in Chinese).