散射体旋转角对二维声子晶体带隙结构影响分析
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摘要
为探讨散射体旋转作用对于弹性波在声子晶体中的传播特性产生的影响,采用平面波展开法将散射体与晶格轴线夹角因素引入结构函数,研究了在不同填充率下,伴随着旋转角的变化,正方形、椭圆形、正六边形散射体禁带出现的位置及宽度变化情况。研究结果表明:散射体旋转角度对二维声子晶体带隙结构具有显著影响,并且散射体旋转角对正六边形、正方形散射体的影响明显大于对于椭圆形散射体的影响;然而,无论散射体取为何种形状,旋转角度对声子晶体产生禁带的位置(禁带中间频率)影响并不明显。
In order to investigate the influence of rotation of scatterers on the propagation characteristic of elastic waves in phononic crystals,the plane wave expansion method is utilized in this paper. The factor of rotation angle between scatterers and lattice axis is introduced into the structure function to explore the change of position as well as the width of the band gap structure for square,ellipse and hexagon scatterers corresponding to the change of rotation angle and filling fractions. The results demonstrated that the rotation angle of scatterers has significant impact on the band gap structure of two dimensional phononic crystals. In the meantime,such impact on the hexagon and square scatterers is more obvious than the elliptical scatterers. However,no matter what the shape of the scatterer is,the influence of rotation angle on the band gap position( mid-gap) of phononic crystals is not obvious.
In order to investigate the influence of rotation of scatterers on the propagation characteristic of elastic waves in phononic crystals,the plane wave expansion method is utilized in this paper. The factor of rotation angle between scatterers and lattice axis is introduced into the structure function to explore the change of position as well as the width of the band gap structure for square,ellipse and hexagon scatterers corresponding to the change of rotation angle and filling fractions. The results demonstrated that the rotation angle of scatterers has significant impact on the band gap structure of two dimensional phononic crystals. In the meantime,such impact on the hexagon and square scatterers is more obvious than the elliptical scatterers. However,no matter what the shape of the scatterer is,the influence of rotation angle on the band gap position( mid-gap) of phononic crystals is not obvious.
引文
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[17]赵言诚.二维声子晶体结构设计及其特性研究[D].哈尔滨:哈尔滨工程大学,2006:15-34.ZHAO Yancheng.Two dimensional phononic crystal design and its characteristics investigations[D].Harbin:Harbin Engineering University,2006:15-34.
[2]温激鸿,韩小云,王刚,等.声子晶体研究概述[J].功能材料,2003,34(4):1-3.WEN Jihong,HAN Xiaoyun,WANG Gang,et al.Review of phononic crystals research[J].Journal of Functional Materials,2003,34(4):1-3.
[3]SIGALAS M M,ECONOMOU E N.Elastic and acoustic wave band structure[J].Journal of Sound and Vibration,1992,158(2):377-382.
[4]KUSHWAHA M S,HALEVI P,ROUHANI B D.Acoustic band structure of periodic elastic composite[J].Phys Rev Lett,1993,71(1):2022-2025.
[5]MARTINEZ R S,SANCHO J,SANCHEZ J V,et al.Sound attenuation by sculpture[J].Nature,1995,378(1):241-248.
[6]KUSHWAHA M S,HALEVI P,MARTNEZ G.Theory of acoustic band structure of periodic elastic composites[J].Phys Rev B,1994,49(4):2313-2321.
[7]MESEGURE F,HOLGADO M.Rayleigh-wave attenation by a semi-infinite two-dimensional elastic-band-gap crystal[J].Physical Review B,1999,59(19):12169-12172.
[8]VASSEUR J O,DRYMIER P A,CHENNI B,et al.Experimental and theoretical evidence for the existence of absolute acoustic band gaps in two-dimensional solid phononic crystals[J].Physical Review Letters,2001,86(1):3021-3024.
[9]BERTODI K,BOYCE M C.Mechanically triggered transformation of phononic band gap in periodic elastomeric structures[J],Physical Review B,2008(77):052105.
[10]MULIN T,DESCHANEL S,BERTODI K,et al.Pattern transformation triggered by deformation[J].Phsical.Review Letter,2007(99):084301.
[11]BERTODI K,BOYCE M C.Wave propagation and instabilities in monolithic and periodically structured elastomeric materials undergoing large deformation[J].Phsical Review,2008(78):184107.
[12]YAN L,ZHAO H P,WANG X Y.Influence of scatterer’s tropism on the band gaps of two dimension phononic crystal[J].Technical Acoustics,2006,25(6):608-612.
[13]WU F G,LIU Z Y,LIU Y Y.Acoustic band gaps created by rotating square rods in a two dimensional lattice[J].Phys Rev E,2002,66:046628.
[14]温熙森,温激鸿.声子晶体[M].北京:国防工业出版社,2009:61-68.
[15]王毅泽.磁电弹性声带隙材料中的弹性波传播与局部化研究[D].哈尔滨:哈尔滨工业大学,2009:18-32.WANG Yize.Elastic wave propagation and localization in magnetoelectroelastic band gap materials and structures[D].Harbin:Harbin Institute of Technology,2009:18-32.
[16]WANG R Z,WANG X H,GU B Y,et al.Effects of shapes and orientations of scatterers and lattice symmetries on the photonic band gap in two-dimensional photonic crystals[J].J Appl Phys,2001,90(9):4307-4313.
[17]赵言诚.二维声子晶体结构设计及其特性研究[D].哈尔滨:哈尔滨工程大学,2006:15-34.ZHAO Yancheng.Two dimensional phononic crystal design and its characteristics investigations[D].Harbin:Harbin Engineering University,2006:15-34.