颗粒材料中声波的超传递现象
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摘要
对给定频率,激励幅值达到某临界幅值时系统突然发生较大能量响应的现象,称为非线性超传递现象;针对周期球颗粒链的超传递现象进行了研究。运用数值分析的方法,研究颗粒链的频谱响应,发现根据颗粒链是否发生超传递现象,可以将频率谱分为下禁带、通带和上禁带三部分;而进一步研究发现不同的频率范围内声波在颗粒材料中产生的响应截然不同,间接说明了频率区域划分的合理性。在此基础上,又对声波在颗粒材料中的非对称传递进行了研究,发现激励声波频率在通带时,可以通过改变激励声波的幅值实现声波在颗粒材料中的单向传递。
At a given frequency, a system may occur sudden large energy flow when the harmonic driving reaches a threshold amplitude. This appearance is called nonlinear supra-transmission. In the paper, the nonlinear supra-transmission in periodic granular chain was studied. In studying the spectral responses of granular chain by numerical analysis, the whole frequency band can be divided into three parts, namely, the lower forbidden band, pass band and upper forbidden band. Besides, the responses in the three parts are entirely different. This manifestation further demonstrates our partitioning is feasible. The acoustic asymmetric propagation in particulate materials was also inrestigated. It is found that realize the one-way transmission of acoustic wave in granular materials can be realized by changing the acoustic amplitude.
At a given frequency, a system may occur sudden large energy flow when the harmonic driving reaches a threshold amplitude. This appearance is called nonlinear supra-transmission. In the paper, the nonlinear supra-transmission in periodic granular chain was studied. In studying the spectral responses of granular chain by numerical analysis, the whole frequency band can be divided into three parts, namely, the lower forbidden band, pass band and upper forbidden band. Besides, the responses in the three parts are entirely different. This manifestation further demonstrates our partitioning is feasible. The acoustic asymmetric propagation in particulate materials was also inrestigated. It is found that realize the one-way transmission of acoustic wave in granular materials can be realized by changing the acoustic amplitude.
引文
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[ 2 ] CHANG C W,OKAWA D,MAJUMDAR A,et al.Solid-state thermal rectifier[J].Science,2006,314(5802):1121-1124.
[ 3 ] KOBAYASHI W,TERAOKA Y,TERASAKI I.An oxide thermal rectifier[J].Applied Physics Letters,2009,95(17):143501.
[ 4 ] HUANG X,LAI Y,HANG Z H,et al.Dirac cones induced by accidental degeneracy in photonic crystals and zero-refractive-index materials[J].Nature Materials,2011,10(8):582.
[ 5 ] 梁彬,袁樱,程建春.声单向操控研究进展[J].物理学报,2015,64(9):26-36.LIANG Bin,YUAN Ying,CHENG Jianchun.Recent advances in acoustic one-way manipulation[J].Acta Physica Sinica,2015,64(9):26-36.
[ 6 ] LIANG B,GUO X S,TU J,et al.An acoustic rectifier[J].Nature Materials,2010,9(12):989-992.
[ 7 ] FLEURY R,SOUNAS D L,SIECK C F,et al.Sound isolation and giant linear nonreciprocity in a compact acoustic circulator[J].Science,2014,343(6170):516-519.
[ 8 ] JOO H O,HOE W K,PYUNG S M,et al.Inverted bi-prism phononic crystals for one-sided elastic wave transmission applications[J].Applied Physics Letters,2012,100(21):213503.
[ 9 ] AHMET C,OLGUN A K,BULENT U.Refraction-type sonic crystal junction diode[J].Applied Physics Letters,2012,100(11):111905.
[10] ZHU X,ZOU X,LIANG B,et al.One-way mode transmission in one-dimensional phononic crystal plates[J].Journal of Applied Physics,2010,108(12):121102.
[11] NARISETTI R K,LEAMY M J,RUZZENE M.A perturbation approach for predicting wave propagation in one-dimensional nonlinear periodic structures[J].Journal of Vibration & Acoustics,2010,132(3):031001.
[12] BOECHLER N,YANG J,THEOCHARIS G,et al.Tunable vibrational band gaps in one-dimensional diatomic granular crystals with three-particle unit cells[J].Journal of Applied Physics,2011,109(7):241.
[13] BOECHLER N,THEOCHARIS G,DARAIO C.Bifurcation-based acoustic switching and rectification[J].Nature Materials,2011,10(9):665-668.
[14] MAN Y,BOECHLER N,THEOCHARIS G,et al.Defect modes in one-dimensional granular crystals[J].Physical Review E Statistical Nonlinear & Soft Matter Physics,2011,85(3 Pt 2):037601.
[15] BURGOYNE H A,DARAIO C.Elastic-plastic wave propagation in uniform and periodic granular chains[J].Journal of Applied Mechanics,2015,82(8):483-496.
[16] JOSEPH L,GEORGIOS T,CHIARA D.Nonlinear resonances and energy transfer in finite granular chains[J].Physical Review E,2015,91(2):023208.
[17] GENIET F,LEON J.Energy transmission in the forbidden band gap of a nonlinear chain[J].Physical Review Letters,2002,89(13):134102.
[18] HERBOLD E B,KIM J,NESTERENKO V F,et al.Pulse propagation in a linear and nonlinear diatomic periodic chain:effects of acoustic frequency band-gap[J].Acta Mechanica,2009,205(1):85-103.
[19] LEON J,GENIET F.Nonlinear supratransmission[J].Journal of Physics:Condensed Matter,2003,15(17):2933.
[20] KHOMERIKI R.Nonlinear band gap transmission in optical waveguide arrays[J].Physical Review Letters,2004,92(6):063905.
[21] KHOMERIKI R,LEPRI S,RUFFO S.Nonlinear supratransmission and bistability in the Fermi-Pasta-Ulam model[J].Physical Review B,2004,70(2):066626.
[22] HERTZ H.Ueber die Berührung fester elastischer K?rper[J].Journal Für Die Reine Und Angewandte Mathematik,2006,1882(92):156-171.
[23] NADKARNI N,DARAIO C,KOCHMANN D M.Dynamics of periodic mechanical structures containing bistable elastic elements:from elastic to solitary wave propagation[J].Physical Review E Statistical Nonlinear & Soft Matter Physics,2014,90(2):023204.
[24] MOTCHEYO A B T,TCHAWOUA C,SIEWE M S,et al.Supratransmission phenomenon in a discrete electrical lattice with nonlinear dispersion[J].Communications in Nonlinear Science & Numerical Simulation,2013,18(4):946-952.