Vertical vibration control of curved track structure based on inertial enhancement effect
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摘要: 针对曲线轨道的垂向振动控制，基于惯性增强效应，引入了调谐质量阻尼惯容器(TMDI)和振幅放大型调谐质量阻尼器(AM-TMD)，以实现更佳的振动控制效果；将曲线轨道考虑为离散支承的曲线Timoshenko梁结构，采用能量泛函变分法建立了有限长曲线轨道分析模型；在曲线钢轨两端引入完美匹配层作为低反射边界条件，用于更好地模拟无限长轨道结构；通过与已有无限长离散支承曲线轨道动力响应计算结果的对比，验证了分析模型的准确性以及完美匹配层的有效性；分析了垂向固定谐荷载作用下，调谐质量阻尼器(TMD)、TMDI和AM-TMD对曲线轨道动力响应的影响，评估了TMD、TMDI和AM-TMD的减振性能；分析了振幅放大系数与TMD工作能力之间的关系，揭示了AM-TMD的工作机理。研究结果表明：TMDI的引入有效地弥补了传统TMD在实现宽频控制时的质量缺陷，与TMD相比，同参数的TMDI工作带宽拓宽约1.5倍，最大振动衰减提升了约5.5 dB；AM-TMD的实质在于利用振幅放大机构来同步增大TMD的有效质量、刚度和阻尼，进而全面提升TMD的工作能力，与TMD相比，同参数的AM-TMD工作带宽拓宽约2.0倍，最大振动衰减提升了约6.1 dB。可见，从宽频控制、高衰减率的角度考虑，TMDI、AM-TMD比TMD更具优势。Abstract: In view of vertical vibration control of curved tracks, tuned mass damper inerter (TMDI) and amplitude magnification tuned mass damper (AM-TMD) were introduced based on inertial enhancement effect to realize better vibration control effects. Curved track was considered as a curved Timoshenko beam structure with discrete supports, and the energy functional variational method was used to establish a finite length curved track analysis model. Perfectly matched layer was introduced at both ends of curved track as a low reflection boundary condition for better simulating the infinite length track structure. The accuracy of analysis model and the effectiveness of perfectly matched layer were verified through the comparison with the dynamic response calculation results of existing infinite length discrete supported curved tracks. The effects of tuned mass damper (TMD), TMDI, and AM-TMD on the dynamic response of curved tracks under the action of fixed vertical harmonic load were systematically analyzed, and the vibration damping performances of TMD, TMDI, and AM-TMD were compared and evaluated. The relationship between the amplitude magnification factor and the operational capability of TMD was analyzed, and the working mechanism of AM-TMD was revealed. Research results show that the introduction of TMDI can efficiently make up for the quality defects of traditional TMD in implementing broadband control. Compared with TMD, the operating bandwidth of TMDI with the same parameters is broadened by about 1.5 times, and the maximum vibration attenuation rate increases by about 5.5 dB. The essence of AM-TMD lies in applying an amplitude magnification mechanism to synchronously enhance the effective mass, stiffness, and damping of TMD, thereby comprehensively improving the operational capability of TMD. Compared with TMD, the operating bandwidth of AM-TMD with the same parameters is expanded by about 2.0 times, and the maximum vibration attenuation rate increases by about 6.1 dB. Therefore, TMDI and AM-TMD are more effective than TMD from the perspectives of broadband control and high attenuation rate.
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Key words:
- urban rail transit /
- curved track /
- vibration control /
- inertial enhancement effect /
- inerter /
- amplitude magnification
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图 6 曲线钢轨跨中垂向位移频响函数
Figure 6. Frequency response function of vertical displacement at mid-span of curved rail
图 8 TMD对曲线钢轨振动衰减率的影响
Figure 8. Influence of TMD on vibration decay rate of curved rail
图 9 TMD参数对曲线钢轨振动衰减率的影响
Figure 9. Influences of TMD parameters on vibration decay rate of curved rail
图 11 TMDI对曲线钢轨振动衰减率的影响
Figure 11. Influence of TMDI on vibration decay rate of curved rail
图 13 AM-TMD对曲线钢轨动力响应的影响
Figure 13. Influence of AM-TMD on dynamic response of curved rail
图 14 AM-TMD对曲线钢轨振动衰减率的影响
Figure 14. Influence of AM-TMD on vibration decay rate of curved rail
图 15 TMD、TMDI与AM-TMD减振性能综合对比分析
Figure 15. Comprehensive comparative analysis of vibration reduction performance between TMD, TMDI and AM-TMD
表 1 T60钢轨与DTVI2型扣件参数
Table 1. Parameters of T60 rail and DTVI2 fastener
参数 数值 A/m2 7.745×10-3 E/Pa 2.059×1011 G/Pa 7.919×1011 Iy/m4 3.217×10-5 I0/m4 3.714×10-5 J/m4 2.150×10-6 ηr 0.01 ρ/(kg·m-3) 7 830 R/m 300 κ 0.532 9 kw/(MN·m-1) 40 cw/(kN·s·m-1) 30 kr/(kN·m·rad-1) 225 cr/(N·m·s·rad-1) 160 ls/m 0.6 
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