基于磁流变弹性体多包覆层声学超材料带隙及传输谱特性

刘少刚; 赵跃超; 赵丹

doi:10.7498/aps.68.20191334

摘要

在不改变结构的情况下实现声学超材料对外部响应的可调性, 一直是声学超材料所面临的挑战之一. 因此, 本文提出了以磁流变弹性体(MRE)作为单、双包覆层的声学超材料元胞结构, 研究其在磁场作用下的可调带隙以及传输谱特性. 通过改变作用于包覆层MRE的磁场强度, 控制MRE的剪切模量, 使声学超材料的带隙和传输谱在磁场作用下具有可调性. 应用有限元法对两种声学超材料的带隙及传输谱特性进行了仿真分析. 仿真结果表明, 在磁场作用下, 两种声学超材料的带隙频率和宽度随着磁场强度的增强而增加; 传输谱随着磁场强度的增强其最大衰减频率向高频移动, 最大衰减量也随之增加. 同时, 采用质量-弹簧模型对声学超材料的带隙频率进行了估算, 仿真结果与估算结果具有很好的一致性. 此外, 讨论了芯体、壳体的材料参数以及填充率对带隙和传输谱特性的影响. 这些研究可为声学超材料对弹性波的主动控制, 以及为新型隔振、抑振结构的开发和应用提供理论基础.

关键词:

Abstract

One of the challenges relating to acoustic metamaterials is to achieve a tunable performance without modifying the structure. In this paper, we propose two types of acoustic metamaterials with a magnetorheological elastomer (MRE), and their tunable band gap structures and the transmission spectra are investigated by the finite element method (FEM). The MRE acts as a cladding layer, and its shear modulus can be changed by an externally applied magnetic field. The cell resonance frequency of acoustic metamaterial is changed. The band gap structures and the transmission spectra of the two kinds of acoustic metamaterials are calculated under various magnetic fields, and it is found that the frequency and width of band gap, the maximum attenuation frequency and transmission loss of transmission spectrum increase with externally applied magnetic field intensity increasing. Meanwhile, two types of the mass-spring models are used to estimate the band gap frequencies of the two kinds of acoustic metamaterials. The FEM results are in good agreement with the estimation results. In addition, the effects of material parameters of core and shell and filling rate on the band gap and transmission spectrum are also studied. The effects of core material parameters on the band gap and transmission spectrum of single-layer acoustic metamaterial are analyzed. It is found that the core mass has an effect on the band gap frequency and width, and the elastic parameter of the core affects the transmission loss of the transmission spectrum. The influences of core and shell material parameter on the band gap and transmission spectrum of double-layer acoustic metamaterial is analyzed by the control variable method. The results show that the core and shell mass affect the band gap frequency, width and pass-band width, and the elastic parameter of the core and the shell affect the transmission loss of the transmission spectrum. As the filling rate increases, the band gap frequency and width of the single- and double-layer MRE acoustic metamaterial increase, the maximum attenuation frequency of the transmission spectrum does not change, and the transmission loss increases. These results will greatly contribute to the application of acoustic metamaterials to controlling the active noise and vibration.

Keywords:

acoustic metamaterials /
magnetorheological elastomer cladding layers /
bandgap and transmission spectra /
magnetic field intensity

作者及机构信息

哈尔滨工程大学机电工程学院, 哈尔滨　150001

通信作者: 赵丹, heuzhaodan@outlook.com

基金项目: 国家自然科学基金(批准号: 51675111, 51775123)资助的课题

Authors and contacts

College of Mechanical and Electrical Engineering, Harbin Engineering University, Harbin 150001, China

Corresponding author: Zhao Dan, heuzhaodan@outlook.com

Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 51675111, 51775123)

文章全文 : translate this paragraph

参考文献

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施引文献

图 1 MRE包覆层声学超材料元胞结构和不可约布里渊区　(a) 单包覆层MRE声学超材料; (b) 双包覆层MRE声学超材料; (c) 正方晶格第一不可约布里渊区

Fig. 1. Schematic of the MRE acoustic metamaterial cells and the irreducible first Brillouin zone: (a) Single-layer MRE acoustic metamaterial; (b) double-layer MRE acoustic metamaterial; (c) the irreducible first Brillouin zone of square lattices.

下载: 全尺寸图片幻灯片

图 2 单包覆层MRE声学超材料带隙结构　(a) 磁场强度H = 0; (b) 磁场强度H = 6 kOe

Fig. 2. The band gap structures of single-layer MRE acoustic metamaterial: (a) Magnetic field intensity of H = 0; (b) magnetic field intensity of H = 6 kOe.

下载: 全尺寸图片幻灯片

图 3 单包覆层MRE声学超材料带隙边界位移场　(a) 带隙下边界; (b) 带隙上边界

Fig. 3. Displacement field of the band gap boundaries of the single-layer MRE acoustic metamaterial: (a) The lower boundary of the band gap; (b) the upper boundary of the band gap.

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图 4 单包覆层MRE声学超材料的质量-弹簧模型　(a) 带隙下边界; (b) 带隙上边界

Fig. 4. The mass-spring model of single-layer MRE acoustic metamaterial: (a) Lower boundary of band gap; (b) upper boundary of band gap.

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图 5 单包覆层MRE声学超材料带隙随磁场强度变化及有限元法与质量-弹簧模型对比　(a) 磁场强度H = 0—10 kOe; (b) 有限元法与质量弹簧-模型对比

Fig. 5. Dependence of the band gap boundaries on the applied magnetic field of single-layer MRE acoustic metamaterial and a comparison of the FEM and the mass-spring model for (a) magnetic field intensity of H = 0–10 kOe, (b) comparison of the FEM and mass-spring model.

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图 6 单包覆层MRE声学超材料带隙随材料和结构参数变化　(a) 随芯体质量增加变化; (b) 随填充率增加变化

Fig. 6. The band gap of single-layer MRE acoustic metamaterial changes with (a) the core mass and (b) the filling rate.

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图 7 双包覆层MRE声学超材料带隙结构　(a) H = 0; (b) H = 6 kOe

Fig. 7. The band gap structures of the double-layer MRE acoustic metamaterial: (a) H = 0; (b) H = 6 kOe.

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图 8 双包覆层MRE声学超材料带隙边界处位移向量场　(a) 第一阶带隙下边界; (b) 第一阶带隙上边界; (c) 第二阶带隙下边界; (d) 第二阶带隙上边界; (e) 图7(a)中E点

Fig. 8. Displacement field of the band gap boundaries of the double-layer MRE acoustic metamaterial: (a) The lower boundary and (b) the upper boundary of the first band gaps; (c) the lower boundary and (d) the upper boundary of the second band gap; (e) point E in Fig.7 (a).

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图 9 双包覆层MRE声学超材料质量-弹簧模型　(a) 第一阶与第二阶带隙下边界; (b) 第一阶与第二阶带隙上边界

Fig. 9. The mass-spring model of the double-layer MRE acoustic metamaterial: (a) Lower boundary of the first and second band gap; (b) upper boundary of the first and second band gap.

下载: 全尺寸图片幻灯片

图 10 双包覆层MRE声学超材料带隙随磁场强度变化及有限元法与质量-弹簧模型对比　(a) 磁场强度H = 0—10 kOe; (b) 有限元法与质量-弹簧模型对比

Fig. 10. Dependence of the band gap boundaries on the applied magnetic field of double-layer MRE acoustic metamaterial and a comparison of the FEM and mass-spring model for (a) magnetic field intensity of H = 0–10 kOe, (b) comparison of the FEM and mass-spring model.

下载: 全尺寸图片幻灯片

图 11 双包覆层MRE声学超材料带隙随材料和结构参数变化　(a) 芯体质量增加; (b) 壳体质量增加; (c) 填充率增加

Fig. 11. The band gap of double-layer MRE acoustic metamaterial changes with (a) the core mass, (b) the shell mass, (c) the filling rate.

下载: 全尺寸图片幻灯片

图 12 单包覆层MRE声学超材料传输谱变化　(a) 磁场强度为0, 4, 6, 8 kOe; (b) 芯体材料分别为铝、钛、铜、铅和钨; (c) 填充率增加

Fig. 12. Transmission spectra of single-layer MRE acoustic metamaterial change with (a) At magnetic field intensity of 0, 4, 6, and 8 kOe, (b) core materials for aluminum, titanium, copper, lead, and tungsten, (c) the filling rate.

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图 13 双包覆层MRE声学超材料传输谱变化　(a) 磁场强度为0, 4, 6, 8 kOe; (b) 芯体材料分别为铝、钛、铜、铅和钨; (c) 壳体材料分别为铝、钛、铜、铅和钨; (d) 随填充率变化

Fig. 13. Transmission spectra change of double-layer MRE acoustic metamaterial: (a) At the magnetic field intensity of 0, 4, 6, and 8 kOe; (b) with the core materials for aluminum, titanium, copper, lead, and tungsten, (c) with the shell materials of aluminum, titanium, copper, lead, and tungsten, (d) with filling rate.

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表 1 构成MRE声学超材料的材料参数

Table 1. Material properties of the MRE acoustic metamaterials.

材料密度$\rho /{\rm{kg}} \cdot {{\rm{m}}^{ - 3}}$ 拉梅常数
λ/GPa μ/GPa

纯铁 7900 115.38 76.92
环氧树脂 1180 4.52 1.59
MRE 3009 6.26×10^-3 0.4×10^-3

下载: 导出CSV

表 2 材料参数

Table 2. The material parameters.

材料密度ρ/kg·m^–3 弹性参数
弹性模量E/GPa 泊松比$\upsilon $

钨 19100 344 0.28
铅 11600 16 0.42
铜 8950 115 0.32
钛 4540 102 0.3
铝 2730 68 0.33

下载: 导出CSV

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[8]	Xiao W, Zeng G W, Cheng Y S 2008 Appl. Acoust. 69 255 Google Scholar
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[11]	Zhou X L, Xu Y L, Liu Y, Lü L L, Peng F J, Wang L Q 2018 Appl. Acoust. 133 97 Google Scholar
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[14]	Zhu R R, Ma C, Zheng B, Musa M Y, Jing L Q, Yang Y H, Wang H P, Dehdashti S, Fang N X, Chen H S 2017 Appl. Phys. Lett. 110 113503 Google Scholar
[15]	Bi Y F, Jia H, Lu W J, Ji P F, Yang J 2017 Sci. Rep. 7 705 Google Scholar
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[19]	Zhu X F, Ramezani H, Shi C Z, Zhu J, Zhang X 2014 Phys. Rev. X 4 031042
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[27]	Liu Z Y, Zhang X X, Mao Y W, Zhu Y Y, Yang Z Y, Chan C T, Sheng P 2000 Science 289 1734 Google Scholar
[28]	Li J, Chan C T 2004 Phys. Rev. E 70 055602 Google Scholar
[29]	Goffaux C, Vigneron J P 2001 Phys. Rev. B 64 075118 Google Scholar
[30]	Bertoldi K, Boyce M C 2008 Phys. Rev. B 77 052105
[31]	Larabi H, Pennec Y, Djafari-Rouhani B, Vasseur J O 2007 Phys. Rev. E 75 066601 Google Scholar
[32]	Lewińska M A, Kouznetsova V G, van Dommelen J A W, Krushynska A O, Geers M G D 2017 Int. J. Solids Struct. 126–127 163
[33]	Gao W T, Xia J P, Sun H X, Yuan S Q, Ge Y, Liu X J 2019 Appl. Phys. Express 12 044002 Google Scholar
[34]	Cheng Y, Zhou C, Yuan B G, Wu D J, Wei Q, Liu X J 2015 Nat. Mater. 14 1013 Google Scholar
[35]	Zhu X F, Liang B, Kan W W, Peng Y G, Cheng J C 2016 Phys. Rev. Appl. 5 054015 Google Scholar
[36]	Chen S B, Wang G, Wen J H, Wen X S 2013 J. Sound Vibr. 332 1520 Google Scholar
[37]	Chen S B, Wen J H, Wang G, Wen X S 2013 Chin. Phys. B 22 074301 Google Scholar
[38]	Xiao S W, Ma G C, Li Y, Yang Z Y, Sheng P 2015 Appl. Phys. Lett. 106 091904 Google Scholar
[39]	贺子厚, 赵静波, 姚宏, 蒋娟娜, 陈鑫 2019 物理学报 68 134302 Google Scholar He Z H, Zhao J B, Yao H, Jiang J N, Chen X 2019 Acta Phys. Sin. 68 134302 Google Scholar
[40]	Shen Y X, Zhu X F, Cai F Y, Ma T, Li F, Xia X X, Li Y C, Wang C Z, Zheng H R 2019 Phys. Rev. Appl. 11 034009 Google Scholar
[41]	Zhou X L, Chen C Q 2013 Physica B 431 23 Google Scholar
[42]	Carlson J D, Jolly M R 2000 Mechatronics 10 555 Google Scholar
[43]	Ginder J M, Clark S M, Schlotter W F, Nichols M E 2002 Int. J. Mod. Phys. B 16 472
[44]	Chen L, Gong X L, Jiang W Q, Yao J J, Xia D H, Li W H 2007 J. Mater. Sci. 42 5483 Google Scholar
[45]	Chen X, Xu X C, Ai S G, Chen H S, Pei Y M 2014 Appl. Phys. Lett. 105 071913 Google Scholar
[46]	Xu Z L, Tong J, Wu F G 2018 Solid State Commun. 271 51 Google Scholar
[47]	Wu B, He C F, Wei R J, Zhao H Y 2009 IEEE International Ultrasonics Symposium Beijing, China, November 2−5, 2008 p1484
[48]	Davis L C 1999 J. Appl. Phys. 85 3348 Google Scholar
[49]	Wang G, Shao L H, Liu Y Z, Wen J H 2006 Chin. Phys. B 15 1843 Google Scholar
[50]	张帅, 郭书祥, 姚宏, 赵静波, 蒋娟娜, 张吉宁, 贺子厚 2018 人工晶体学报 47 1 Google Scholar Zhang S, Guo S X, Yao H, Zhao J B, Jiang J N, Zhang J N, He Z H 2018 J. Synth. Cryst. 47 1 Google Scholar

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基于磁流变弹性体多包覆层声学超材料带隙及传输谱特性