Band Gap Characteristics of Vibration Isolators of Phononic Crystals under Floating Slab
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摘要: 为了提升浮置板轨道的减振效果，阻碍浮置板垂向振动能量向轨下基底的传播，提出了一种基于声子晶体局域共振机理的浮置板轨道隔振器. 运用有限元方法研究了声子晶体隔振器的局域共振带隙特性，并验证了带隙频率范围内声子晶体隔振器对振动的抑制作用；计算了声子晶体隔振器的垂向刚度，建立了三维声子晶体隔振器浮置板轨道有限元模型；计算了整体结构的力传递率与基础加速度响应，并与传统钢弹簧浮置板的计算结果进行了对比. 研究结果表明，声子晶体隔振器存在声子晶体局域共振带隙，对50～150 Hz频带内的振动有抑制作用；声子晶体隔振器与传统钢弹簧垂向静刚度相近，均为6.0 kN/mm；保留了钢弹簧浮置板轨道的低固有频率隔振性能，并且在50～120 Hz频带具有带隙抑制特性，在51 Hz附近力传递率可减小10 dB左右；基础加速度响应在51～150 Hz频带内明显小于普通钢弹簧浮置板轨道，其中51～60 Hz频带内基础加速度相比钢弹簧浮置板轨道减小30%左右. 因此声子晶体隔振器有助于提高浮置板轨道的减振性能.Abstract: In order to improve the vibration damping effect of the floating slab track and hinder the propagation of the vertical vibration energy of the floating slab to the rail base, a vibration isolator for the floating slab track based on the local resonance mechanism of phononic crystals is developed. The band gap characteristics of phononic crystals with local resonance for the isolator are studied by the finite element method, and its vibration damping effect in the band gap frequency range is verified. The vertical stiffness of the isolator is calculated, and the finite element model of the three-dimensional floating slab track with these isolators is established. The force transmissibility and the base acceleration response of the whole structure are calculated, and then compared with the results of the traditional steel spring floating slab. The results of this work show that the isolators have a band gap of phononic crystals with local resonance, which suppresses the vibration in the frequency band of 50−150 Hz. The vertical static stiffness of the isolators are similar to that of the traditional steel springs, i.e., 6.0 kN/mm. It retains the vibration isolation performance of the steel spring floating slab track in low natural frequency, and has band gap suppression characteristics in the frequency band of 50−120 Hz. The force transmissibility is reduced by about 10 dB at around 51 Hz. The base acceleration response in the 51−150 Hz is significantly smaller than that of the normal steel spring floating slab track, and the base acceleration response in the 51−60 Hz is reduced by about 30% compared to the steel spring floating slab track. Therefore, the developed isolator is able to improve the vibration damping performance of the floating slab track.
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Key words:
- vibration isolator /
- phononic crystals /
- band gap /
- floating slab track /
- vibration reduction
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图 1 声子晶体隔振器浮置板轨道结构示意
Figure 1. Schematic diagram of the floating slab track with vibration isolators of phononic crystals
图 5 振动方向为垂向的声子晶体隔振器能带结构
Figure 5. Band structure of isolators withvibration in the vertical direction
图 6 第一带隙起始频率共振模态和截止频率共振模态
Figure 6. Resonance modes at start frequency andcut-off frequeny of the first bandgap
图 7 声子晶体隔振器传输特性有限元计算模型
Figure 7. Finite element model fortransmission characteristics of isolators
图 13 下部基础振动加速度时频域计算结果
Figure 13. Frequency-domain results of the vibration acceleration for lower base
表 1 声子晶体隔振器元胞部分参数
Table 1. Some parameters related to vibtration isolators and its phononic crystal cell
项目 参数 取值/mm 参数 取值/mm 几何参数 a1 10 a2 10 a3 10 a4 70 b1 5 b2 10 b3 70 项目 部件 密度/（kg•m−3） 弹性模量/MPa 泊松比 阻尼损耗
因子材料参数 基体外壳 2 700 70 000 0.30 0 钢散射体 7 810 216 000 0.30 0 橡胶垫层 1 300 13 0.47 0.50 软材料包
覆层1 300 6 0.47 0.05 
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表 3 仰拱部件计算参数
Table 3. Calculation parameters of invert components
参数 数值 尺寸（长/宽/高）/m 5.000/3.200/0.165 弹性模量/GPa 35 下部支撑刚度/（N•m−1） 5×1010 密度/（kg•m−3） 2 500 泊松比 0.20
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夏禾,曹艳梅. 轨道交通引起的环境振动问题[J]. 铁道科学与工程学报,2004,1(1): 44-51. doi: 10.3969/j.issn.1672-7029.2004.01.008XIA He, CAO Yanmei. Environmental vibration caused by rail transit[J]. Journal of Railway Science and Engineering, 2004, 1(1): 44-51. doi: 10.3969/j.issn.1672-7029.2004.01.008 闫维明,聂晗,任珉,等. 地铁交通引起地面振动的实测与分析[J]. 铁道科学与工程学报,2006,3(2): 1-5. doi: 10.3969/j.issn.1672-7029.2006.02.001YAN Weiming, NIE Wei, REN Wei, et al. Measurement and analysis of ground vibration caused by subway traffic[J]. Journal of Railway Science and Engineering, 2006, 3(2): 1-5. doi: 10.3969/j.issn.1672-7029.2006.02.001 British Standards Institution. Evaluation of human exposure tovibration in buildings (1 to 8 Hz): BS6472: 1992[S]. London: British Standards Institution, 1992. British Standards Institution. Guide to measurement and evaluation of human exposure to whole body mechanical vibration and repeated shock: BS6841: 1987[S]. London: British Standards Institution, 1987. 孙晓静,刘维宁,张宝才. 浮置板轨道结构在城市轨道交通减振降噪上的应用[J]. 中国安全科学学报,2005,15(8): 65-69. doi: 10.3969/j.issn.1003-3033.2005.08.016SUN Xiaojing, LIU Weining, ZHANG Baocai. Application of floating slab track structure in vibration reduction and noise reduction of urban rail transit[J]. Chinese Journal of Safety Science, 2005, 15(8): 65-69. doi: 10.3969/j.issn.1003-3033.2005.08.016 KUSHWAHA M S. Acoustic band structure of periodicelastic composites[J]. Physical Review Letter, 1993, 17: 2022-2025. KOO G H, PARK Y S. Vibration reduction by using periodic supports in a piping system[J]. Journal of Sound and Vibration, 1998, 210(1): 53-68. doi: 10.1006/jsvi.1997.1292 SHENG Ping, ZHANG X X, LIU Z, et al. Locally resonant sonic materials[J]. Science, 2003, 338(1/2/3/4): 201-205. YU Dianlong, LIU Yaozong, ZHAO Honggang, et al. Flexural vibration band gaps in Euler-Bernoulli beams with locally resonant structures with two degrees of freedom[J]. Physical Review B, 2006, 73(6): 064301-1-064301-5. 邢俊. 基于声子晶体的地铁轨道弹性垫层波阻单元设计研究[D]. 成都: 西南交通大学, 2017. 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. 袁俊. 地铁浮置板轨道结构减振研究[D]. 西安: 西安建筑科技大学, 2008. 程祖依. 弹性动力学基础[M]. 武汉: 中国地质大学出版社, 1989: 264-266 温激鸿,王刚,刘耀宗,等. 周期弹簧振子结构振动带隙及隔振特性研究[J]. 机械工程学报,2005,41(2): 205-209. doi: 10.3321/j.issn:0577-6686.2005.02.040WEN Jihong, WANG Gang, LIU Yaozong, et al. Study on vibration band gap and vibration isolation characteristics of periodic spring oscillator[J]. Journal of Mechanical Engineering, 2005, 41(2): 205-209. doi: 10.3321/j.issn:0577-6686.2005.02.040 肖伟. 声子晶体型周期复合结构禁带特性研究[D]. 武汉: 华中科技大学, 2007. 温激鸿. 声子晶体振动带隙及减振特性研究[D]. 长沙: 国防科学技术大学, 2005. 朱龙翔,王悦民,宗侣,等. 基于模态分析方法的管道导波频散曲线计算[J]. 海军工程大学学报,2014(6): 64-68.ZHU Longxiang, WANG Yuemin, ZONG Lü, et al. Calculation of dispersion curves of pipeline guide waves based on modal analysis method[J]. Journal of Naval University of Engineering, 2014(6): 64-68. 张宏亮. 隧道内钢弹簧浮置板轨道结构振动特性及其对环境影响的研究[D]. 北京: 北京交通大学, 2007. -
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