Low frequency bandgap characteristics and application of a novel two-dimensional three-component cement-based phononic-like crystal composite material
-
摘要: 为了拓宽混凝土超材料的弹性波带隙宽度和数量，本文基于局域共振理论设计了一种新型二维三组元水泥基拟声子晶体。首先，采用有限元方法计算和研究了该新型二维三组元水泥基拟声子晶体的能带结构、振动模态、位移场和衰减特性。其次，分析了带隙形成机制和影响因素，并根据质量-弹簧系统模型推导了带隙范围的理论估计式。最后，将该水泥基拟声子晶体应用到地铁道床上，分析了水泥基拟声子晶体地铁道床的减振性能。结果表明：该新型二维三组元水泥基拟声子晶体在200 Hz频段内打开了5条低频带隙，在带隙频率范围内，衰减值大多都在10 dB以上，衰减效果较好；带隙的打开与各原胞的振动特征呈现出对应关系，因特定原胞的平移振动触发，由特定原胞与基体的耦合作用的强度所控制；散射体材料的密度、包裹层材料的弹性模量及厚度是影响其带隙的主要因素；由新型二维三组元水泥基拟声子晶体组成的水泥基拟声子晶体地铁道床在1~200 Hz频段内的振动加速度均小于普通混凝土地铁道床，最大插入损失为10.22 dB，插入损失平均值为8.76 dB，具有显著的减振性能。Abstract: In order to widen the width and number of elastic bandgap of concrete metamaterials, a novel two-dimensional three-component cement-based phononic-like crystal was designed based on local resonance theory. Firstly, the finite element method was used to calculate and study the energy band structure, vibration mode, displacement field and attenuation characteristics of the novel two-dimensional three-component cement-based phononic-like crystal. Secondly, the formation mechanism and influencing factors of the bandgap were analyzed, and the theoretical estimation of the bandgap range was derived according to the mass-spring system model. Finally, the cement-based phononic-like crystal was applied to the subway track bed, and the vibration reduction performance of the cement-based phononic-like crystal subway track bed was analyzed. The results show that the novel two-dimensional three-component cement-based phononic-like crystal opens 5 low-frequency bandgaps in the 200 Hz frequency range, and the attenuation values are mostly above 10 dB within the bandgap frequency range, and the attenuation effect is good. The opening of the bandgap corresponds to the vibration characteristics of each primitive cell, which is triggered by the translational vibration of a specific primitive cell and controlled by the strength of the coupling between the specific primitive cell and the matrix. The density of scatterer material, elastic modulus and thickness of cladding material are the main factors affecting the bandgap. In the 1-200 Hz frequency band, the vibration acceleration of the cement-based phononic-like crystal subway track bed composed of the novel two-dimensional three-component cement-based phononic-like crystal is lower than that of the ordinary concrete subway track bed, and the maximum insertion loss is 10.22 dB and the average insertion loss is 8.76 dB, which has remarkable vibration reduction performance.
-
图 1 水泥基拟声子晶体原胞结构及第一布里渊区
Figure 1. Cement-based phononic-like crystal primitive cell and first Brillouin region
Rs—Scatterer inner diameter; Rc—Wrapping layerouter diameter; a—Lattice constant; M—Matrix; Γ, M—High symmetry point; kx, ky—Wave vector in the x and y directions
图 3 传统水泥基声子晶体能带结构
Figure 3. Band structure of traditional cement-based phononic crystal
图 4 新型二维三组元水泥基拟声子晶体能带结构
Figure 4. Band structure of novel two-dimensional three-component cement-based phononic-like crystal
图 15 新型二维三组元水泥基拟声子晶体的频率响应函数计算模型
Figure 15. Frequency response function calculation model of novel two-dimensional three-component cement-based phononic-like crystal
图 16 新型二维三组元水泥基拟声子晶体的频率响应函数
Figure 16. Frequency response function of novel two-dimensional three-component cement-based phononic-like crystal
图 17 新型二维三组元水泥基拟声子晶体的散射体材料参数对带隙的影响
Figure 17. Effect of scatterer material parameters on bandgap of novel two-dimensional three-component cement-based phononic-like crystal
图 18 新型二维三组元水泥基拟声子晶体的散射体结构参数对带隙的影响
Figure 18. Effect of scatterer structure parameters on bandgap of novel two-dimensional three-component cement-based phononic-like crystal
图 19 新型二维三组元水泥基拟声子晶体的包裹层材料参数对带隙的影响
Figure 19. Effect of material parameters of wrapping layer on bandgap of novel two-dimensional three-component cement-based phononic-like crystal
图 20 新型二维三组元水泥基拟声子晶体的包裹层结构参数对带隙的影响
Figure 20. Effect of structure parameters of wrapping layer on bandgap of novel two-dimensional three-component cement-based phononic-like crystal
图 21 新型二维三组元水泥基拟声子晶体的水泥砂浆基体材料参数对带隙的影响
Figure 21. Effect of material parameters of cement mortar matrix on bandgap of novel two-dimensional three-component cement-based phononic-like crystal
图 22 新型二维三组元水泥基拟声子晶体的水泥砂浆基体结构参数对带隙的影响
Figure 22. Effect of structure parameters of cement mortar matrix on bandgap of novel two-dimensional three-component cement-based phononic-like crystal
图 23 不同散射体形状的新型二维三组元水泥基拟声子晶体的计算模型
Figure 23. Calculation models of novel two-dimensional three-component cement-based phononic-like crystal with different scatterer shapes
图 24 不同形状散射体的新型二维三组元水泥基拟声子晶体的能带结构
Figure 24. Band structure of novel two-dimensional three-component cement-based phononic-like crystal with different scatterer shapes
图 25 新型二维三组元水泥基拟声子晶体内部散射体的多形状耦合的计算模型
Figure 25. Calculation models of multi-shape coupling of internal scatterers in novel two-dimensional three-component cement-based phononic-like crystal
图 26 新型二维三组元水泥基拟声子晶体原胞内部散射体多形状耦合的能带结构
Figure 26. Band structure of multi-shape coupling of internal scatterers in novel two-dimensional three-component cement-based phononic-like crystal
图 27 单振子和多振子局域共振声子晶体原胞的弹簧-质量系统等效模型
Figure 27. Spring-mass system equivalent models of single-oscillator and multi-oscillator local resonance phononic crystal primitive cell
k0-k5—Equivalent stiffness of oscillators; m0-m5—Equivalent mass of oscillators
图 28 多振子局域共振声子晶体的无限质量-质量晶格结构
Figure 28. Infinite mass-in-mass lattice structure of local resonance phononic crystal with multiple oscillators
L—Lattice constant
图 29 等效模型分析法计算结果
Figure 29. Calculation result of equivalent model analysis method
q—Wave vector; a—Lattice constant
图 30 水泥基拟声子晶体地铁道床和普通混凝土地铁道床计算模型
Figure 30. Calculation models of cement-based phononic-like crystal subway track bed and ordinary concrete subway track bed
图 31 水泥基拟声子晶体地铁道床和普通混凝土地铁道床时域和频域曲线
Figure 31. Time domain and frequency domain curves of cement-based phononic-like crystal subway track bed and ordinary concrete subway track bed
图 32 水泥基拟声子晶体地铁道床和普通混凝土地铁道床1/3倍频程及插入损失
Figure 32. One-third octave and insertion loss of cement-based phononic-like crystal subway track bed and ordinary concrete subway track bed
表 1 结构参数
Table 1. Structure parameters
Scatterer i Rs/m Rc/m a/m 1 0.0275 0.033 0.1 2 0.018 0.0216 3 0.013 0.0156 4 0.01 0.012 5 0.007 0.0084 
下载: 导出CSV
表 2 材料参数
Table 2. Material parameters
Component Density
ρ/(kg·m−3)Elastic modulus
E/PaShear modulus
G/PaScatterer 3300 1.2×1011 4.8×1010 Wrapping layer 12 1.34×105 5.93×104 Matrix 2000 3.45×1010 1.44×1010
下载: 导出CSV
表 3 新型二维三组元水泥基拟声子晶体的带隙影响因素及其水平
Table 3. Bandgap influencing factors and their levels of novel two-dimensional three-component cement-based phononic-like crystal
Influence factor Level 1 Level 2 Level 3 Level 4 Level 5 Material parameters Scatterer E/Pa 1.2×109 1.2×1010 1.2×1011 1.2×1012 1.2×1013 ρ/(kg·m−3) 2300 2800 3300 3800 4300 v 0.15 0.20 0.25 0.30 0.35 Wrapping layer E/Pa 1.34×103 1.34×104 1.34×105 1.34×106 1.34×107 ρ/(kg·m−3) 6 9 12 15 18 v 0.09 0.11 0.13 0.15 0.17 Matrix E/Pa 3.45×108 3.45×109 3.45×1010 3.45×1011 3.45×1012 ρ/(kg·m−3) 1000 1500 2000 2500 3000 v 0.10 0.15 0.20 0.25 0.30 Structure parameters Scatterer Rs/m 0.8R1 0.9R1 R1 – – Wrapping layer Rc/m 0.8R2 0.9R2 R2 – – Matrix a/m – – 0.1 0.12 0.14 Notes: R1—Inner diameter of scatterer; R2—Outer diameter of wrapping layer; v—Poisson's ratio.
下载: 导出CSV
-
[1] 陈俊豪, 曾晓辉, 谢友均, 等. 具有减振功能的混凝土超材料的带隙特性[J]. 硅酸盐学报, 2023, 51(5): 1272-1282.CHEN Junhao, ZENG Xiaohui, XIE Youjun, et al. Band gap properties of metaconcrete with vibration reduction function[J]. Journal of the Chinese Ceramic Society, 2023, 51(5): 1272-1282(in Chinese). [2] JIN H X, HAO H, CHEN W S, et al. Effect of enhanced coating layer on the bandgap characteristics and response of metaconcrete[J]. Mechanics of Advanced Materials and Structures, 2021, 30(1): 175-188. [3] 韩洁, 路国运, 赵一涛. 超材料混凝土单胞骨料的有阻尼自由振动特性研究[J]. 振动与冲击, 2022, 41(4): 239-245, 269.HAN Jie, LU Guoyun, ZHAO Yitao. A study of damped free vibration characteristics on a metaconcrete unit cell[J]. Journal of Vibration and Shock, 2022, 41(4): 239-245, 269(in Chinese). [4] XU C, CHEN W S, HAO H, et al. Damping properties and dynamic responses of metaconcrete beam structures subjected to transverse loading[J]. Construction and Building Materials, 2021, 311: 125273. doi: 10.1016/j.conbuildmat.2021.125273 [5] 靳贺欣, 陈文苏, 郝洪, 等. 超材料混凝土抗冲击效应数值研究[J]. 中国科学: 物理学 力学 天文学, 2020, 50(2): 78-89.JIN Hexin, CHEN Wensu, HAO Hong, et al. Numerical study on impact resistance of metaconcrete[J]. SCIENTIA SINICA Physica, Mechanica & Astronomica, 2020, 50(2): 78-89(in Chinese). [6] BRICCOLA D, PANDOLFI A. Analysis on the dynamic wave attenuation properties of metaconcrete considering a quasi-random arrangement of inclusions[J]. Frontiers in Materials, 2021, 7: 615189. doi: 10.3389/fmats.2020.615189 [7] 熊剑荣, 任凤鸣, 田时雨, 等. 超材料混凝土减振性能研究现状与展望[J]. 复合材料学报, 2024, 41(2): 656-671.XIONG Jianrong, REN Fengming, TIAN Shiyu, et al. Status and prospects of research on vibration reduction performance of metaconcrete[J]. Acta Materiae Compositae Sinica, 2024, 41(2): 656-671(in Chinese). [8] MITCHELL S J, PANDOLFI A, ORTIZ M. Metaconcrete: Designed aggregates to enhance dynamic performance[J]. Journal of the Mechanics and Physics of Solids, 2014, 65: 69-81. [9] XU C, CHEN W S, HAO H. The influence of design parameters of engineered aggregate in metaconcrete on bandgap region[J]. Journal of the Mechanics and Physics of Solids, 2020, 139: 103929. doi: 10.1016/j.jmps.2020.103929 [10] 张恩, 路国运, 杨会伟, 等. 超材料混凝土的带隙特征及对冲击波的衰减效应[J]. 爆炸与冲击, 2020, 40(6): 69-77. doi: 10.11883/bzycj-2019-0252ZHANG En, LU Guoyun, YANG Huiwei, et al. Band gap features of metaconcrete and shock wave attenuation in it[J]. Explosion and Shock Waves, 2020, 40(6): 69-77(in Chinese). doi: 10.11883/bzycj-2019-0252 [11] MIRANDA E J P, ANGELIN A F, SILVA F M, et al. Passive vibration control using a metaconcrete thin plate[J]. Cerâmica, 2019, 65(1): 27-33. [12] 陈俊豪, 曾晓辉, 谢友均, 等. 多重谐振水泥基声子晶体带隙特性研究[J]. 材料导报, 2024, 38(12): 94-102.CHEN Junhao, ZENG Xiaohui, XIE Youjun, et al. Research on band gaps characteristics of multiple resonant cement-based phononic crystals[J]. Materials Reports, 2024, 38(12): 94-102(in Chinese). [13] LIU Y, AN X Y, CHEN H L, et al. Vibration attenuation of finite-size metaconcrete: Mechanism, prediction and verification[J]. Composites Part A: Applied Science and Manufacturing, 2021, 143: 106294. doi: 10.1016/j.compositesa.2021.106294 [14] LEI L J, MIAO L C, 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. doi: 10.1142/S0217984921503346 [15] GOFFAUX C, SÁNCHEZ-DEHESA J, LAMBIN P. Comparison of the sound attenuation efficiency of locally resonant materials and elastic band-gap structures[J]. Physical Review B, 2004, 70(18): 3352-3359. [16] GOFFAUX C, SÁNCHEZ-DEHESA J, YEYATI A L, et al. Evidence of Fano-like interference phenomena in locally resonant materials[J]. Physical Review Letters, 2002, 88(22): 225502. doi: 10.1103/PhysRevLett.88.225502 [17] WANG G, SHAO L H, LIU Y Z, et al. Accurate evaluation of lowest band gaps in ternary locally resonant phononic crystals[J]. Chinese Physics, 2006, 15(8): 1843-1848. doi: 10.1088/1009-1963/15/8/036 [18] HUANG G L, SUN C T. Band gaps in a multiresonator acoustic metamaterial[J]. Journal of Vibration and Acoustics, 2010, 132(3): 031003. doi: 10.1115/1.4000784 [19] ZHOU X Q, WANG J, WANG R Q, et al. Effects of relevant parameters on the bandgaps of acoustic metamaterials with multi-resonators[J]. Applied Physics A, 2016, 122(4): 427. [20] HUANG H H, SUN C T, HUANG G L. On the negative effective mass density in acoustic metamaterials[J]. International Journal of Engineering Science, 2009, 47(4): 610-617. doi: 10.1016/j.ijengsci.2008.12.007 [21] MIAO L C, LEI L J, LI C, et al. Vibration reduction of phononic-like crystal metaconcrete track bed for underground railway[J]. Journal of Materials in Civil Engineering, 2023, 35(8): 04023254. doi: 10.1061/JMCEE7.MTENG-15400 -
下载:
点击查看大图
计量
- 文章访问数: 192
- HTML全文浏览量: 147
- PDF下载量: 18
- 被引次数: 0
