基于非光滑系统的局域共振声子晶体结构动态特性研究

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振动与冲击 ›› 2021, Vol. 40 ›› Issue (22) : 28-34.

论文

何超，高海峰，徐慧东，李志强

作者信息 +

Dynamic characteristics of phononic crystals with locally resonant structures based on non-smooth system

HE Chao，GAO Haifeng，XU Huidong，LI Zhiqiang

Author information +

文章历史 +

摘要

基于扭转振动结构，研究了非线性局域共振声子晶体的动态特性及含非光滑碰撞系统单胞对混沌带隙产生的作用机理。非线性局域振子由安装于轴上的圆盘、轴承、线性弹簧、碰撞杆构成。一方面，在特定频率范围内，各个单胞产生共振同时与轴体之间扭转波相互耦合作用，可以在低频范围内能打开多条线性共振带隙。另一方面，基于碰撞机构的非光滑系统会给振子带来非线性动力学特性，在低频范围产生混沌带隙。首先采用传递矩阵法计算一维声子晶体扭转振动在线性范围内的能带结构，并与实验结果进行对照验证。然后通过分析单胞的非线性动力学行为阐明系统出现混沌带隙的频率范围，并通过实验进行了验证。研究结果表明，该结构不仅在线性特性下在多个频率范围内有明显抑振效果，其混沌特性也可以使结构在更低频范围实现减振特性。

Abstract

The dynamic characteristics of nonlinear locally resonant phononic crystals and the mechanism of chaotic band gaps induced by the unit cell with the non-smooth collision system was analyzed based on the torsional vibration structure. The nonlinear local oscillator was composed of a disk mounted on the shaft, a bearing, linear springs, and colliding rods. On the one hand, the coupling of local resonance of unit cells and the torsional wave in the shaft leads to low frequency bandgaps in certain ranges. On the other hand, the non-smooth system resulted from the collision mechanism provides the unit cells with nonlinear dynamic properties and chaotic bandgaps in the low-frequency range are observed. Firstly, the band structure of the proposed one-dimensional phononic crystals with linear vibration was calculated by using transfer matrix method, and the computed results was verified with the experimental study. Then the correlation between the chaotic bandgaps and the nonlinear dynamic behavior of the unit cell was clarified through experimental verification. The results show that the structure has obvious vibration suppression effects at multiple frequency ranges with linear characteristics, and the chaotic property results in the vibration suppression in lower frequency ranges.

导出引用

何超，高海峰，徐慧东，李志强. 基于非光滑系统的局域共振声子晶体结构动态特性研究[J]. 振动与冲击, 2021, 40(22): 28-34

HE Chao，GAO Haifeng，XU Huidong，LI Zhiqiang. Dynamic characteristics of phononic crystals with locally resonant structures based on non-smooth system[J]. Journal of Vibration and Shock, 2021, 40(22): 28-34

参考文献

[1] Ewing W M, Jardetzky W S, Press F. Elastic Waves in Layered Media[J]. GFF,1958,80(1):128-129.
[2] Kushwaha M S, Halevi P, Dobrzynsi L, et al. Acoustic band structure of periodic elastic composites[J]. Physical Review Letters. 1993,71(13):2022-2025.
[3] Martinez-Sala R, Sancho J, Meseguer F, et al. Sound attenuation by sculpture[J]. Nature,1995,378(16):241.
[4] Liu Z Y, Zhang X, Mao Y et al. Locally resonant sonic materials[J]. Science, 2000, 289: 1734-1736
[5] Wang G, Liu Y Z, Wen J H and Yu D L. Formation mechanism of the low-frequency locally resonant band gaps in the two-dimensional ternary phononic crystals[J]. Chinese Physics.2006, 15(2): 407-411
[6] 吴昱东,李人宪,丁渭平,等.基于局域共振声子带隙的扭转减振器设计方法[J].振动与冲击,2018,37(09):180-184.
WU Yudong，LI Renxian，DING Weiping，et al． Design method of torsion damper based on local resonant phononic bandgaps［J］．Vibration and Impact，2018,37(09):180-184．
[7] Chuang K C, Wang D F, Fang X, et al. Applying bandgap defect modes to crack detection in beams using periodic concentrated masses[J]. Journal of Sound and Vibration,2020,477.
[8] Gharibi H, Bahrami A, Phononic crystals for sensing FAMEs with demultiplexed frequencies[J]. Journal of Molecular Liquids,2020,305.
[9] Fermi E, Pasta J and Ulam S. Studies of Nonlinear Problems: LA-1940 [R].1955-05-01.
[10] Gallavotti G. The Fermi-Pasta-Ulam Problem[J]. Lecture Notes in Physics, 2008, 728(9):1017.
[11] Fang X, Wen J, Yin J, et al. Broadband and tunable one-dimensional strongly nonlinear acoustic metamaterials: Theoretical study[J]. Physical Review E, 2016, 94(5):052206.
[12] Fang X, Wen J, Yin J, et al. Wave propagation in nonlinear metamaterial multi-atomic chains based on homotopy method[J]. Aip Advances,2016,6(12):121706.
[13] Fang X, Wen J, Bonello B, et al. Wave propagation in one-dimensional nonlinear acoustic metamaterials[J]. New Journal of Physics, 2017.
[14] Fang X, Wen J, Bonello B, et al. Ultra-low and ultra-broad-band nonlinear acoustic metamaterials[J]. Nature Communications, 2017, 8(1):1288.
[15] Fang X, Wen J, Yu D, et al. Bridging coupling bandgaps in nonlinear acoustic metamaterials[J]. Physical Review Applied,2018.
[16] Fang X, Wen J, Yu D, et al. Wave propagation in infinite nonlinear acoustic metamaterial beam by considering the third harmonic generation[J]. Applied Physics ,2018.
[17] Narisetti R K, Ruzzene M, Leamy M J, Study of wave propagation in strongly nonlinear periodic lattices using a harmonic balance approach[J]. Wave Motion, 2012, 49(2): 394–410.
[18] Donahue C M, Anzel P W J, Bonanomi L, et al. Experimental realization of a nonlinear acoustic lens with a tunable focus[J]. Applied Physics Letters, 2013, 104(1):909.
[19] Ciampa F, Mankar A, Marini A. Phononic Crystal Waveguide Transducers for Nonlinear Elastic Wave Sensing[J]. Scientific Reports,2017,7(2).
[20] Khobragade S, Granja C D S, Sandström N, et al. Direct detection of whole bacteria using a nonlinear acoustic resonator[J]. Sensors and Actuators: B. Chemical,2020,316.
[20] 温熙森. 声子晶体[M]. 北京：国防工业出版社, 2009.
WEN Xisen. Phononic Crystals [M]. Beijing: National Defense Industry Press, 2009.
[21] Yu D L, Liu Y Z, Wang G, et al. Low frequency torsional vibration gaps in the shaft with locally resonant structures[J]. Physics Letters A, 2006,348(3-6):410 -415.
[22] Gao H F, Matsumoto T, Takahashi T, et al. Analysis of acoustic transmission for one directional periodic bounded structure in 2D by BEM [J]. Transactions of Japan Society for Computational Methods in Engineering,2012,12:12-121212