Journal of Shanghai Jiao Tong University

Journal of Shanghai Jiaotong University >

2021 , Vol. 55 >Issue 11: 1453 - 1458

DOI: https://doi.org/10.16183/j.cnki.jsjtu.2020.242

Dirac Cone Characteristics of Hexachiral Phononic Crystal

Expand
  • 1. State Key Laboratory of Ocean Engineering, Shanghai Jiao Tong University, Shanghai 200240, China
    2. Key Laboratory of Marine Intelligent Equipment and System of the Ministry of Education, Shanghai Jiao Tong University, Shanghai 200240, China
    3. Shanghai Second Militaryx Representative Office, Nanjing Military Representative Office of the Ministry of Army Equipment, Shanghai 200082, China

Received date: 2020-07-29

  Online published: 2021-12-03

Fold

Abstract

The band structure properties of phononic crystal is important to evaluate the vibration and noise reduction of acoustic metamaterials. Taking the 2D hexachiral phononic crystal as an example, the band structure and Dirac cone properties were investigated by numerical analysis, and the four-fold accidental degenerate Dirac point was obtained in the center of Brillouin zone. By adjusting the design parameters of ligament structure, a double Dirac cone was broken and a novel directional band gap was formed. The influence of geometric parameters on the directional band gaps width was investigated, and the band structure inversion problem was further discussed. This research can provide support for the application of hexachiral phononic crystal in elastic wave manipulation and acoustic topological insulator.

Key words： phononic crystal; band structure; Dirac cone; linear dispersion; directional band gap

Cite this article

CHEN Luyun, WANG Jian, CUI Yifeng, KONG Hui . Dirac Cone Characteristics of Hexachiral Phononic Crystal[J]. Journal of Shanghai Jiaotong University, 2021 , 55(11) : 1453 -1458 . DOI: 10.16183/j.cnki.jsjtu.2020.242

References

[1] 吴九汇, 马富银, 张思文, 等. 声学超材料在低频减振降噪中的应用评述[J]. 机械工程学报, 2016, 52(13):68-78.
[1] WU Jiuhui, MA Fuyin, ZHANG Siwen, et al. Application of acoustic metamaterials in low-frequency vibration and noise reduction[J]. Journal of Mecha-nical Engineering, 2016, 52(13):68-78.
[2] 阮居祺, 卢明辉, 陈延峰, 等. 基于弹性力学的超构材料[J]. 中国科学: 技术科学, 2014, 44(12):1261-1270.
[2] RUAN Juqi, LU Minghui, CHEN Yanfeng, et al. Metamaterial based on elastic mechanics[J]. Science China Technological Sciences, 2014, 44(12):1261-1270.
[3] 田源, 葛浩, 卢明辉, 等. 声学超构材料及其物理效应的研究进展[J]. 物理学报, 2019, 68(19):7-18.
[3] TIAN Yuan, GE Hao, LU Minghui, et al. Research advances in acoustic metamaterials[J]. Acta Physica Sinica, 2019, 68(19):7-18.
[4] BARAVELLI E, RUZZENE M. Internally resonat-ing lattices for bandgap generation and low-frequency vibration control[J]. Journal of Sound and Vibration, 2013, 332(25):6562-6579.
[5] LIU Z Y, ZHANG X X, MAO Y W, et al. Locally resonant sonic materials[J]. Physica B: Condensed Matter, 2000, 338(1/2/3/4):201-205.
[6] CUMMER S A, CHRISTENSEN J, ALÙ A. Controlling sound with acoustic metamaterials[J]. Nature Reviews Materials, 2016, 1(3):16001.
[7] JAMES R, WOODLEY S M, DYER C M, et al. Sonic bands, bandgaps, and defect states in layered structures—Theory and experiment[J]. The Journal of the Acoustical Society of America, 1995, 97(4):2041-2047.
[8] 梁孝东, 缪林昌, 尤佺, 等. 局域共振二维声子晶体的低频带隙特性研究[J]. 人工晶体学报, 2019, 48(7):1225-1232.
[8] LIANG Xiaodong, MIAO Linchang, YOU Quan, et al. Low-frequency band gap characteristics of locally resonant two-dimensional phononic crystal[J]. Journal of Synthetic Crystals, 2019, 48(7):1225-1232.
[9] 李妍. 光子晶体和声子晶体中由偶然简并所导致的 Dirac 锥形色散关系研究[D]. 广州: 华南理工大学, 2015.
[9] LI Yan. Research on the Dirac-cone dispersions induced by accidental degeneracy in photonic and phononic crystals[D]. Guangzhou: South China University of Technology, 2015.
[10] XIAO B, LAI K F, YU Y, et al. Exciting reflectionless unidirectional edge modes in a reciprocal photonic topological insulator medium[J]. Physical Review B, 2016, 94(19):195427.
[11] 范海燕, 夏百战. 三维声学超材料的高阶拓扑态[J]. 科学通报, 2020, 65(15):1411-1419.
[11] FAN Haiyan, XIA Baizhan. Higher-order topological states in a three-dimensional acoustic metamaterial[J]. Chinese Science Bulletin, 2020, 65(15):1411-1419.
[12] 王一鹤, 张志旺, 程营, 等. 声子晶体中的表面声波赝自旋模式和拓扑保护声传输[J]. 物理学报, 2019, 68(22):264-271.
[12] WANG Yihe, ZHANG Zhiwang, CHENG Ying, et al. Pseudospin modes of surface acoustic wave and topologically protected sound transmission in phono-nic crystal[J]. Acta Physica Sinica, 2019, 68(22):264-271.
[13] PENG Y G, QIN C Z, ZHAO D G, et al. Experimental demonstration of anomalous Floquet topological insulator for sound[J]. Nature Communications, 2016, 7:13368.
[14] HE C, NI X, GE H, et al. Acoustic topological insulator and robust one-way sound transport[J]. Nature Physics, 2016, 12(12):1124-1129.
[15] 裴东亮, 杨洮, 陈猛, 等. 基于复合蜂窝结构的宽带周期与非周期声拓扑绝缘体[J]. 物理学报, 2020, 69(2):153-161.
[15] PEI Dongliang, YANG Tao, CHEN Meng, et al. Broadband periodic and aperiodic acoustic topological insulator based on composite honeycomb structure[J]. Acta Physica Sinica, 2020, 69(2):153-161.
[16] 付子义, 王晨旭, 王立国, 等. 基于COMSOL的声子晶体带结构计算新方法[J]. 软件, 2018, 39(12):6-9.
[16] FU Ziyi, WANG Chenxu, WANG Liguo, et al. A new method for computation of phononic crystals band structure by COMSOL[J]. Computer Engineering & Software, 2018, 39(12):6-9.
[17] SPADONI A, RUZZENE M, GONELLA S, et al. Phononic properties of hexagonal chiral lattices[J]. Wave Motion, 2009, 46(7):435-450.
[18] HU L L, LUO Z R, YIN Q Y. Negative Poisson’s ratio effect of re-entrant anti-trichiral honeycombs under large deformation[J]. Thin-Walled Structures, 2019, 141:283-292.
[19] MOUSANEZHAD D, HAGHPANAH B, GHOSH R, et al. Elastic properties of chiral, anti-chiral, and hierarchical honeycombs: A simple energy-based approach[J]. Theoretical and Applied Mechanics Letters, 2016, 6(2):81-96.
[20] EBRAHIMI H, MOUSANEZHAD D, NAYEB-HASHEMI H, et al. 3D cellular metamaterials with planar anti-chiral topology[J]. Materials & Design, 2018, 145:226-231.
[21] XIA B Z, WANG G B, ZHENG S J. Robust edge states of planar phononic crystals beyond high-symmetry points of Brillouin zones[J]. Journal of the Mechanics and Physics of Solids, 2019, 124:471-488.
[22] BITTNER S, DIETZ B, MISKI-OGLU M, et al. Observation of a Dirac point in microwave experiments with a photonic crystal modeling graphene[J]. Physical Review B Condensed Matter, 2010, 82(1):1558-1564.
[23] BITTNER S, DIETZ B, MISKI-OGLU M, et al. Extremal transmission through a microwave photonic crystal and the observation of edge states in a rectangular Dirac billiard[J]. Physical Review B Condensed Matter, 2012, 85(6):652-660.
[24] DIEM M, KOSCHNY T, SOUKOULIS C M. Transmission in the vicinity of the Dirac point in hexa-gonal photonic crystals[J]. Physica B: Condensed Matter, 2010, 405(14):2990-2995.
[25] TORRENT D, MAYOU D, SÁNCHEZ-DEHESA J. Elastic analog of graphene: Dirac cones and edge states for flexural waves in thin plates[J]. Physical Review B Condensed Matter, 2013, 87(11):269-275.
[26] CHENG X J, JOUVAUD C, NI X, et al. Robust reconfigurable electromagnetic pathways within a photonic topological insulator[J]. Nature Materials, 2016, 15(5):542-548.
Options
Outlines

/

〈 〉