局域共振二维声子晶体的低频带隙特性研究
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摘要
针对低频带隙难以打开的问题,本文提出一种局域共振二维声子晶体结构,采用有限元法计算其能带结构,分析其带隙的形成机理和影响因素,并在此基础上对结构进行优化设计。结果表明:该结构可在200 Hz以下的频率范围内打开宽度70. 56 Hz的完全带隙,起始频率低至39. 77 Hz。等效刚度k一定的情况下,带隙起始频率由芯体的密度决定,而截止频率主要由基体边框密度决定。优化后的结构能够打开更低更宽的带隙,且对振动波的衰减性能提升。该结构具有优越的低频带隙特性,在地铁减振隔振领域中具有潜在的应用前景。
A type of locally resonant two-dimensional phononic crystal structure was proposed to overcome the difficulty of opening the low-frequency band gap. By the finite element method,the band gap structure was calculated. The formation mechanism and influencing factors of the band gap were analyzed,and the structure was optimized on this basis. The results show that,the structure can open a complete band gap with a width of 70. 56 Hz in the frequency range below 200 Hz,and the starting frequency is as low as 39. 77 Hz. When the equivalent stiffness k is constant,the starting frequency is determined by the density of the core,while the cut-off frequency is mainly determined by the density of the matrix. The optimized structure can open lower and wider band gap and improve the attenuation performance of vibration wave. The structure has excellent low-frequency band gap characteristics and has potential application prospects in the field of subway vibration attenuation and isolation.
A type of locally resonant two-dimensional phononic crystal structure was proposed to overcome the difficulty of opening the low-frequency band gap. By the finite element method,the band gap structure was calculated. The formation mechanism and influencing factors of the band gap were analyzed,and the structure was optimized on this basis. The results show that,the structure can open a complete band gap with a width of 70. 56 Hz in the frequency range below 200 Hz,and the starting frequency is as low as 39. 77 Hz. When the equivalent stiffness k is constant,the starting frequency is determined by the density of the core,while the cut-off frequency is mainly determined by the density of the matrix. The optimized structure can open lower and wider band gap and improve the attenuation performance of vibration wave. The structure has excellent low-frequency band gap characteristics and has potential application prospects in the field of subway vibration attenuation and isolation.
引文
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[2]栗润德,张鸿儒,刘维宁.地铁引起的地面振动及其对精密仪器的影响[J].岩石力学与工程学报,2008,27(1):206-214.
[3] Heckl M,Hauck G,Wettschureck R. Structure-borne Sound and Vibration from Rail Traffic[J]. Journal of Sound and Vibration,1996,193(1):175-184.
[4]王田友,丁洁民,楼梦麟,等.地铁运行所致建筑物振动的传播规律分析[J].土木工程学报,2009,42(5):33-39.
[5]楼梦麟,贾宝印,陆秀丽,等.地铁振动下基础隔振效应的实测与分析[J].同济大学学报(自然科学版),2011,39(11):1622-1628.
[6]李克飞,刘维宁,刘卫丰,等.交通振动对邻近古建筑的动力影响测试分析[J].北京交通大学学报,2011,35(1):79-83.
[7] Sheng X,Jones C J C,Thompson D J. Ground Vibration Generated by a Harmonic Load Moving in a Circular Tunnel in a Layered Ground[J].Journal of Low Frequency Noise,Vibration and Active Control,2016,22(2):83-96.
[8] Kushwaha M S,Halevi P,Dobrzynski L,et al. Acoustic Band-structure of Periodic Elastic Composites[J]. Physical Review Letters,1993,71(13):2022-2025.
[9] Liu Z Y,Zhang X X,Mao Y W,et al. Locally Resonant Sonic Materials[J]. Science,2000,289(5485):1734-1736.
[10] Yu D,Liu Y,Wang G,et al. Flexural Vibration Band Gaps in Timoshenko Beams with Locally Resonant Structures[J]. Journal of Applied Physics,2006,100:12490112.
[11]郁殿龙.基于声子晶体理论的梁板类周期结构振动带隙特性研究[D].长沙:国防科学技术大学,2006.
[12] Yu K,Chen T,Wang X,et al. Large Band Gaps in Phononic Crystal Slabs with Rectangular Cylinder Inclusions Parallel to the Slab Surfaces[J]. Journal of Physics and Chemistry of Solids,2013,74(8):1146-1151.
[13] Li S,Chen T,Wang X,et al. Expansion of Lower-frequency Locally Resonant Band Gaps Using a Double-sided Stubbed Composite Phononic Crystals Plate with Composite Stubs[J]. Physics Letters A,2016,380(25-26):2167-2172.
[14]吴九汇,张思文,沈礼.螺旋局域共振单元声子晶体板结构的低频振动带隙特性研究[J].机械工程学报,2013,49(10):62-69.
[15]李建宝,汪越胜,张传增.二维声子晶体微腔能带结构的有限元分析与设计[J].人工晶体学报,2010,39(3):649-655.
[16] Gao N,Wu J H,Yu L. Research on Bandgaps in Two-dimensional Phononic Crystal with Two Resonators[J]. Ultrasonics,2015,56:287-293.
[17]祁鹏山,杜军,姜久龙,等.二维声子晶体的隔声机理及其特性[J].硅酸盐学报,2016,44(10):1458-1464.
[18]李德葆,陆秋海.工程振动试验分析[M].北京:清华大学出版社,2004.