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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