基于分形曲线近零密度声学超材料的声波调控研究

PDF(2514 KB)

振动与冲击 ›› 2024, Vol. 43 ›› Issue (22) : 174-180.

论文

基于分形曲线近零密度声学超材料的声波调控研究

肖蓉蓉，何川，张崇卓，陶猛*

作者信息 +

Acoustic wave modulation and control in fractal curve-based near-zero density acoustic metamaterials

XIAO Rongrong,HE Chuan,ZHANG Chongzhuo,TAO Meng*

Author information +

文章历史 +

摘要

本文将空间卷曲理念和分形自相似原理结合，提出了一种具有“之”字型特征的空间卷曲型声学超材料，利用等效参数法提取了该分形声学超材料结构单元的等效质量密度，结果表明：在特定的频率范围内该分形结构单元具有近零密度特性。有限元法分析结果表明，利用该近零密度分形结构单元进行特定的周期性排列后组成的声学超材料，可以在特定频率范围内实现高效调控声波的目的，例如实现声隐身、声隧穿、弯曲狭缝传输和波前整形，同时分析了这些声特殊现象的出现与近零密度声学超材料透射系数峰值频率的对应关系。最后进行了实验验证，利用3D打印技术加工制得1阶、2阶近零密度声学超材料单元样品，并测试其透射系数，通过对比可以发现：实测结果和有限元分析结果符合良好，证明了结果的准确性和所设计结构的有效性。

Abstract

This paper introduces a novel spatially curved acoustic metamaterial incorporating the principles of spatial curvature and fractal self-similarity. Utilizing the equivalent parameter method, the effective mass density of the fractal acoustic metamaterial unit cell is extracted, revealing near-zero density characteristics within a specific frequency range. Finite element analysis demonstrates that arranging these near-zero density fractal unit cells in a specific periodic arrangement forms an acoustic metamaterial capable of efficiently controlling acoustic waves in a targeted frequency range. This includes achieving objectives such as sound invisibility, acoustic tunneling, bending of narrow slit transmission, and wavefront shaping. The study further analyzes the correlation between the occurrence of these acoustic phenomena and the peak frequency of the transmission coefficient in the near-zero density acoustic metamaterial. Experimental validation is conducted through the fabrication of 1st and 2nd order near-zero density acoustic metamaterial unit cell samples using 3D printing technology. Transmission coefficient tests are performed, and a comparison with finite element analysis results demonstrates a good agreement, affirming the accuracy of the results and the effectiveness of the designed structure.

导出引用

肖蓉蓉, 何川, 张崇卓, 陶猛 . 基于分形曲线近零密度声学超材料的声波调控研究[J]. 振动与冲击, 2024, 43(22): 174-180

XIAO Rongrong, HE Chuan, ZHANG Chongzhuo, TAO Meng . Acoustic wave modulation and control in fractal curve-based near-zero density acoustic metamaterials[J]. Journal of Vibration and Shock, 2024, 43(22): 174-180

参考文献

[1] Yang X, Yin J, Yu G, et al. Acoustic superlens using Helmholtz-resonator-based metamaterials[J]. Applied Physics Letters, 2015, 107(19).
[2] Gu Y, Cheng Y, Liu X. Acoustic planar hyperlens based on anisotropic density-near-zero metamaterials[J]. Applied Physics Letters, 2015, 107(13).
[3] Ma F, Huang Z, Liu C, et al. Acoustic focusing and imaging via phononic crystal and acoustic metamaterials[J]. Journal of Applied Physics, 2022, 131(1).
[4] 孙宏祥，方欣，葛勇，等. 基于蜷曲空间结构的近零折射率声聚焦透镜[J]. 物理学报. 2017, 66(24): 145-153.
SUN Hong-xiang，FANG Xin，GE Yong, et al. Near-zero refractive index acoustic focusing lens based on coiled space structure [J]. Acta Physica Sinica, 2017, 66(24): 145-153.
[5] 杨坤,杨明月,崔世明,等. 大尺寸薄膜型声学超材料复合结构低频宽带隔声性能研究[J]. 振动与冲击. 2022, 41 (22): 14-22.
YANG Kun, YANG Ming-yue,CUI Shi-ming, et al. Study on low frequency broadband sound insulation performance of large-size thin-film acoustic metamaterial composite structures [J]. Journal of vibration and shock. 2022, 41 (22): 14-22.
[6] Zigoneanu L, Popa B, Cummer S A. Three-dimensional broadband omnidirectional acoustic ground cloak[J]. Nature Materials, 2014, 13(4): 352-355.
[7] Liu C, Xia B, Yu D. The spiral-labyrinthine acoustic metamaterial by coiling up space[J]. Physics Letters A, 2017, 381(36): 3112-3118.
[8] Man X, Luo Z, Liu J, et al. Hilbert fractal acoustic metamaterials with negative mass density and bulk modulus on subwavelength scale[J]. Materials & Design, 2019, 180: 107911.
[9] 吴光华，柯艺波，张林，等. 基于Peano分形的亚波长尺度声学超材料[J]. 振动与冲击. 2022, 41(23): 230-240.
WU Guang-hua,KE Yi-Bo,Zhang Lin, et al. Sub-wavelength scale acoustic metamaterial based on Peano fractal[J]. Journal of vibration and shock. 2022, 41(23): 230-240.
[10] Kadic M, Bückmann T, Schittny R, et al. Pentamode metamaterials with independently tailored bulk modulus and mass density[J]. Physical Review Applied, 2014, 2(5): 54007.
[11] Park J J, Lee K J, Wright O B, et al. Giant acoustic concentration by extraordinary transmission in zero-mass metamaterials[J]. Physical Review Letters, 2013, 110(24): 244302.
[12] Gu Y, Cheng Y, Wang J, et al. Controlling sound transmission with density-near-zero acoustic membrane network[J]. Journal of Applied Physics, 2015, 118(2).
[13] Liang Z, Li J. Extreme acoustic metamaterial by coiling up space[J]. Physical Review Letters, 2012, 108(11): 114301.
[14] Xiang L, Wang G, Zhu C. Controlling sound transmission by space-coiling fractal acoustic metamaterials with broadband on the subwavelength scale[J]. Applied Acoustics, 2022, 188: 108585.
[15] Wu G, Ke Y, Zhang L, et al. Acoustic metamaterials with zero-index behaviors and sound attenuation[J]. Journal of Physics D: Applied Physics, 2022, 55(28): 285301.
[16] 杨智为，周涵. 基于分形几何思路的超材料结构设计: 综述[J]. 材料导报. 2020, 34(21): 21052-21060.
YANG Zhi-Wei，ZHOU Han. Design of metamaterial structures based on fractal geometry:a review [J]. Materials Reports, 2020, 34(21): 21052-21060.
[17] Song G Y, Huang B, Dong H Y, et al. Broadband Focusing Acoustic Lens Based on Fractal Metamaterials[J]. Scientific Reports, 2016, 6(1).
[18] 夏百战，刘亭亭，郑圣洁，等. 基于Hilbert分形的亚波长空间盘绕型声学超材料[J]. 中国科学（技术科学）. 2017, 47 (6): 639-645.
XIA Bai-zhan，LIU Ting-ting，ZHENG Sheng-jie, et al. Coiling up space acoustic metamaterial with Hilbert fractal in a subwavelength scale [J]. Scientia Sinica(Technologica) ,2017, 47 (6): 639-645.
[19] Song G Y, Cheng Q, Huang B, et al. Broadband fractal acoustic metamaterials for low-frequency sound attenuation[J]. Applied Physics Letters[J], 2016, 109(13): 131901.
[20] Fokin V, Ambati M, Sun C, et al. Method for retrieving effective properties of locally resonant acoustic metamaterials[J]. Physical Review. B, Condensed Matter and Materials Physics, 2007, 76(14).
[21] Song B H, Bolton J S. A transfer-matrix approach for estimating the characteristic impedance and wave numbers of limp and rigid porous materials[J]. The Journal of the Acoustical Society of America, 2000, 107(3): 1131-1152.