二维十字排列椭圆孔声子晶体带隙研究
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摘要
采用有限元及实验方法,研究二维十字排列椭圆孔声子晶体中弹性波传播的带隙以及人为引入的夹杂对带隙的调控.当声子晶体薄板沿板厚方向均匀施加面内激励时,将激发面内的动力响应,对应于平面应力状态.基于逆向思维,针对二维十字排列椭圆孔声子晶体薄板,建立平面有限元模型,计算该模型沿晶格ΓX方向的波动传输特性,分析孔洞长短轴之比、孔隙率和线缺陷等因素对带隙及弹性波传播特性的影响.制作与计算模型同尺寸的声子晶体试样进行传输特性实验,测试结果与有限元仿真结果吻合.结果表明,带隙的宽度随着椭圆孔长短轴比例的增加而增大,可以通过引入合适的线缺陷来反向调控声子晶体的带隙.
The band gaps of elastic wave in two-dimensional phononic crystals with criss-crossed elliptical holes and the tunability of band gaps induced by the artificially introduced inclusions were analyzed through finite element method and experimental method. When the in-plane excitation is uniformly applied along the thickness of a thin phononic crystal plate, the dynamic response of the plate can be approximated as a plane-stress problem. Thin phononic plates with elliptical holes arrayed in a criss-cross pattern were analyzed with a two-dimensional finite element model based on the contrarian thinking in order to calculate the wave transmission along the ΓX direction of the reciprocal lattice. The effects of the ratio of major axis to minor axis, the porosity of holes, and the artificially introduced line defects on the band gaps and the wave propagation characteristics were systematically analyzed. The testing samples with the same dimensions as the numerical models were produced to conduct the transmission experiments. The numerical results accorded well with the experimental results. Results show that the width of band gap enlarges with the increasing of the ratio of major axis to minor axis, and the band gap can be reversely controlled by the insertion of line defects.
The band gaps of elastic wave in two-dimensional phononic crystals with criss-crossed elliptical holes and the tunability of band gaps induced by the artificially introduced inclusions were analyzed through finite element method and experimental method. When the in-plane excitation is uniformly applied along the thickness of a thin phononic crystal plate, the dynamic response of the plate can be approximated as a plane-stress problem. Thin phononic plates with elliptical holes arrayed in a criss-cross pattern were analyzed with a two-dimensional finite element model based on the contrarian thinking in order to calculate the wave transmission along the ΓX direction of the reciprocal lattice. The effects of the ratio of major axis to minor axis, the porosity of holes, and the artificially introduced line defects on the band gaps and the wave propagation characteristics were systematically analyzed. The testing samples with the same dimensions as the numerical models were produced to conduct the transmission experiments. The numerical results accorded well with the experimental results. Results show that the width of band gap enlarges with the increasing of the ratio of major axis to minor axis, and the band gap can be reversely controlled by the insertion of line defects.
引文
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[17]李建宝.声子晶体带隙调控的数值与实验研究[D].北京:北京交通大学,2011.LI Jian-bao.Numerical and experimental investigation on band gap engineering of phononic crystals[D].Beijing:Beijing Jiaotong University,2011.
[18]BERTOLDI K,BOYCE M C.Mechanically triggered transformations of phononic band gaps in periodic elastomeric structures[J].Physical Review B,2008,77(5):439-446.
[19]LANDAU L D,LIFSHITZ E M.Theory of elasticity[M].Berlin:Springer,1959.
[20]温熙森,温激鸿,郁殿龙,等.声子晶体[M].北京:国防工业出版社,2009.
[21]HUANG Y L,GAO N,CHEN W Q,et al.Extension compression-controlled complete band gaps in 2DChiral square-lattice-like structures[J].Acta Mechanica Solida Sinica,2018,31(1):51-65.
[2]KUSHWAHA M S,HALEVI P,MARTíNEZ G,et al.Theory of acoustic band structure of periodic elastic composites[J].Physical Review B,1994,49(4):2313-2322.
[3]MOHAMMADI S,EFTEKHAR A A,KHELIF A,et al.Complete phononic bandgaps and bandgap maps in two-dimensional silicon phononic crystal plates[J].Electronics Letters,2007,43(16):898-899.
[4]REINKE C M,SU M F,OLSSON R H,et al.Realization of optimal bandgaps in solid-solid,solid-air,and hybrid solid-air-solid phononic crystal slabs[J].Applied Physics Letters,2011,98(6):055405.
[5]WANG Y F,WANG Y S,SU X X.Large bandgaps of two-dimensional phononic crystals with cross-like holes[J].Journal of Applied Physics,2011,110(11):2059.
[6]DOWLING J P.Sonic band structure in fluids with periodic density variations[J].Journal of the Acoustical Society of America,1992,91(5):2539-2543.
[7]SIGALAS M M,SOUKOULIS C M.Elastic-wave propagation through disordered and/or absorptive layered systems[J].Physical Review B,1995,51(5):2780.
[8]AO X,CHAN C T.Complex band structures and effective medium descriptions of periodic acoustic composite systems[J].Physical Review B,2009,80(23):308-310.
[9]LIU Z,CHAN C T,SHENG P,et al.Elastic wave scattering by periodic structures of spherical objects:theory and experiment[J].Physical Review B,2000,62(4):2446-2457.
[10]GARCIA-PABLOS D,SIGALAS M,FR M D E,et al.Theory and experiments on elastic band gaps[J].Physical Review Letters,2000,84(19):4349.
[11]SIGALAS M M,GARCíA N.Theoretical study of three dimensional elastic band gaps with the finitedifference time-domain method[J].Journal of Applied Physics,2000,87(6):3122-3125.
[12]MEAD D J.A general theory of harmonic wave propagation in linear periodic systems with multiple coupling[J].Journal of Sound and Vibration,1973,27(2):235-260.
[13]LANGLET P,HLADKY‐HENNION A,DECARPIGNY J.Analysis of the propagation of plane acoustic waves in passive periodic materials using the finite element method[J].Journal of the Acoustical Society of America,1995,98(5):2792-2800.
[14]黄屹澜,高楠,鲍荣浩,等.周期结构后屈曲新算法及其应用[J].计算力学学报,2016,33(4):509-515.HUANG Yi-lan,GAO Nan,BAO Rong-hao,et al.Anovel algorithm for post-buckling analysis of periodic structures and its application[J].Chinese Journal of Computational Mechanics,2016,33(4):509-515.
[15]MARTíNEZSALA R,SANCHO J,SáNCHEZ J V,et al.Sound attenuation by sculpture[J].Nature,1995,378(6554):241.
[16]YANG C L,ZHAO S D,WANG Y S.Experimental evidence of large complete bandgaps in zig-zag lattice structures[J].Ultrasonics,2017,74:99-105.
[17]李建宝.声子晶体带隙调控的数值与实验研究[D].北京:北京交通大学,2011.LI Jian-bao.Numerical and experimental investigation on band gap engineering of phononic crystals[D].Beijing:Beijing Jiaotong University,2011.
[18]BERTOLDI K,BOYCE M C.Mechanically triggered transformations of phononic band gaps in periodic elastomeric structures[J].Physical Review B,2008,77(5):439-446.
[19]LANDAU L D,LIFSHITZ E M.Theory of elasticity[M].Berlin:Springer,1959.
[20]温熙森,温激鸿,郁殿龙,等.声子晶体[M].北京:国防工业出版社,2009.
[21]HUANG Y L,GAO N,CHEN W Q,et al.Extension compression-controlled complete band gaps in 2DChiral square-lattice-like structures[J].Acta Mechanica Solida Sinica,2018,31(1):51-65.