声子晶体中波传播的自准直效应

摘要/Abstract

摘要： 本文针对不同介质形成的周期性阵列结构进行了不同频率的波传输计算,发现波在阵列声子晶体结构中的传输特性与光在光子晶体中的自准直类似,具有波传播的自准直效应。进一步计算发现,波在声子晶体中传输的自准直特性与外部介质和阵列结构的材料属性密切相关,也与阵列结构单胞中金属柱的截面几何特性相关。波传播的自准直效应产生的频率范围随模量比的增加出现先增加后减小的现象,并且随密度比的增加而减小。设置合理的模量比、密度比等材料性质和截面几何性质,能够实现对阵列结构自准直效应中的波传播频率范围的控制,其中,等频线是周期性结构阵列自准直效应的重要设计依据。

关键词: 声子晶体, 阵列结构, 波传输, 自准直, 等频线

Abstract: The wave transmission in different arrayed structures with different media and different frequency domain was calculated. It is found that the self-collimation effect of wave can be found in the designed arrayed structure phononic crystals being similar to the self-collimation of light in photonic crystals. Further computations show that the wave self-collimation can be related to the designed media and the material properties in the arrayed structures. Moreover, this phenomenon can be also affected by the geometrical property of the cross section of the metal pillar in the arrayed structures. The frequency domain for the self-collimation effect of wave increases initilally and then decreases with the increase of the specific modulus, and it is decreased with the increase of the specific density. The optimal designs on specific modulus, specific density and the geometrical properties are the key factors to realize the controlling of frequency domain of the wave self-collimation effect in the arrayed structures. Equi-frequency contour is the key criterion for the design of the self-collimation effect of wave in the periodic arrayed structures.

Key words: phononic crystal, arrayed structure, wave transmission, self-collimation, equi-frequency contour

中图分类号:

O735

张昭, 张磊, 郭江川, 李加瑞, 王艺飞. 声子晶体中波传播的自准直效应[J]. 人工晶体学报, 2021, 50(7): 1371-1377.

ZHANG Zhao, ZHANG Lei, GUO Jiangchuan, LI Jiarui, WANG Yifei. Self-Collimation Effect of Wave Propagation in Phononic Crystals[J]. JOURNAL OF SYNTHETIC CRYSTALS, 2021, 50(7): 1371-1377.

参考文献

[1] MALDOVAN M. Sound and heat revolutions in phononics[J]. Nature, 2013, 503(7475): 209-217.
[2] LIU Z, ZHANG X X, MAO Y W, et al. Locally resonant sonic materials[J]. Science, 2000, 289(5485): 1734-1736.
[3] HAN X K, ZHANG Z. Bandgap design of three-phase phononic crystal by topological optimization[J]. Wave Motion, 2020, 93: 102496.
[4] 郭兆枫,陈传敏,乔钏熙,等.超胞声子晶体板的轻量化设计与研究[J].人工晶体学报,2021,50(1):13-19.
GUO Z F, CHEN C M, QIAO C X, et al. Lightweight design and research of supercell phononic crystal plate[J]. Journal of Synthetic Crystals, 2021, 50(1): 13-19(in Chinese).
[5] 何宇漾.声子晶体结构板件在车内噪声控制中的应用研究[J].噪声与振动控制,2020,40(6):193-197.
HE Y Y. Application of phononic crystal plates in vehicle’s noise control[J]. Noise and Vibration Control, 2020, 40(6): 193-197(in Chinese).
[6] 李粮余.基于声子晶体理论进行轨道系统减振效果研究[J].铁道工程学报,2020,37(12):64-69.
LI L Y. Research on the vibration reduction effect of track system based on phononic crystal theory[J]. Journal of Railway Engineering Society, 2020, 37(12): 64-69(in Chinese).
[7] 耿志明,狄琛,方轲,等.人工晶体的微结构调控热输运研究[J].人工晶体学报,2020,49(9):1569-1582.
GENG Z M, DI C, FANG K, et al. Thermal transport study of engineered synthetic crystal microstructures[J]. Journal of Synthetic Crystals, 2020, 49(9): 1569-1582(in Chinese).
[8] HAN X K, ZHANG Z. Acoustic beam controlling in water by the design of phononic crystal[J]. Extreme Mechanics Letters, 2020, 34: 100602.
[9] YANG H, ZHANG X, ZHAO D G, et al. The self-collimation effect induced by non-Hermitian acoustic systems[J]. Applied Physics Letters, 2019, 114(13): 133503.
[10] PÉREZ-ARJONA I, SÁNCHEZ-MORCILLO V J, REDONDO J, et al. Theoretical prediction of the nondiffractive propagation of sonic waves through periodic acoustic media[J]. Physical Review B, 2007, 75: 014304.
[11] PARK J H, MA P S, KIM Y Y. Design of phononic crystals for self-collimation of elastic waves using topology optimization method[J]. Structural and Multidisciplinary Optimization, 2015, 51(6): 1199-1209.
[12] LI J, WU F G, ZHONG H L, et al. Acoustic beam splitting in two-dimensional phononic crystals using self-collimation effect[J]. Journal of Applied Physics, 2015, 118(14): 144903.
[13] TAN Y X, YU T B, YU M H, et al. Simultaneous beam guides of electromagnetic and acoustic waves in defect-free phoxonic crystals using self-collimation effect[J]. Applied Physics Express, 2019, 12(6): 062015.
[14] SHU Y Y, YU M H, YU T B, et al. Design of phoxonic virtual waveguides for both electromagnetic and elastic waves based on the self-collimation effect: an application to enhance acousto-optic interaction[J]. Optics Express, 2020, 28(17): 24813-24819.
[15] 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.
[16] WANG Y Z, PERRAS E, GOLUB M V, et al. Manipulation of the guided wave propagation in multilayered phononic plates by introducing interface delaminations[J]. European Journal of Mechanics - A/Solids, 2021, 88: 104266.
[17] GAO N, QU S C, SI L, et al. Broadband topological valley transport of elastic wave in reconfigurable phononic crystal plate[J]. Applied Physics Letters, 2021, 118(6): 063502.
[18] YANG S X, PAGE J H, LIU Z Y, et al. Focusing of sound in a 3D phononic crystal[J]. Physical Review Letters, 2004, 93(2): 024301.
[19] 张昭,冀广明,韩星凯.弯折臂格栅结构声子晶体带隙优化[J].人工晶体学报,2018,47(6):1226-1231.
ZHANG Z, JI G M, HAN X K. Optimization of band gaps in zig-zag lattice structures phononic crystals[J]. Journal of Synthetic Crystals, 2018, 47(6): 1226-1231(in Chinese).
[20] 张昭,韩星凯,苏开创.基于声子晶体带隙特性的薄板减振设计[J].人工晶体学报,2016,45(4):872-879.
ZHANG Z, HAN X K, SU K C. Vibration reduction design of thin plate based on band gap features of phononic crystals[J]. Journal of Synthetic Crystals, 2016, 45(4): 872-879(in Chinese).
[21] PATIL G U, MATLACK K H. Wave self-interactions in continuum phononic materials with periodic contact nonlinearity[J]. Wave Motion, 2021, 105: 102763.
[22] VAN DEN BOOM S J, VAN KEULEN F, ARAGÓN A M. Fully decoupling geometry from discretization in the Bloch-Floquet finite element analysis of phononic crystals[J]. Computer Methods in Applied Mechanics and Engineering, 2021, 382: 113848.