Dynamic Characteristics and Parameter Selection of Two-Span Continuous Beam Bridges Under Superconducting Electrodynamic Suspension Train Loads
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摘要:
针对超导电动悬浮列车与连续梁桥耦合动力作用研究相对不足的问题，建立超导电动悬浮列车-双跨连续梁桥耦合动力学模型，分析桥梁跨径与列车编组对连续梁动力响应的影响规律，并基于动力系数开展连续梁桥的参数选取，在此基础上计算车桥耦合振动响应. 研究结果表明：桥梁动力响应受列车编组的影响程度取决于桥梁跨径与车辆定距的比值，比值接近1.5时，桥梁抑振效应明显，比值高于1.5时，虽存在一阶共振，但超谐共振响应小且对编组数量不敏感，比值低于1.5时，共振能量随编组增加显著累积，车桥匹配性差；基于动力系数限值的参数分析表明，双跨连续梁在超谐共振控制方面略优于同等跨径简支梁；在0～600 km/h速度范围内，连续梁允许采用更低的基频下限，意味着在满足动力学安全的前提下可降低结构刚度需求，提高经济性；在选定桥梁参数下的车桥耦合振动分析中，列车垂向平稳性指标均稳定在“优”级限值范围内，其中，中间车因满足抑振匹配条件，共振速度下动力响应变化极小.
Abstract:To address the relatively limited research on the coupled dynamic interaction between superconducting electrodynamic suspension trains and continuous beam bridges, a coupled dynamic model of a superconducting electrodynamic suspension train and a two-span continuous beam bridge was established. The effects of bridge span and train marshalling on the dynamic response of the continuous beam were analyzed, and the parameters of the continuous beam bridge were selected based on the dynamic amplification factor. On this basis, the coupled vibration responses of the train-bridge system were calculated. The results indicate that the influence of train marshalling on the dynamic response of the bridge depends on the ratio of the bridge span to the vehicle spacing. When the ratio approaches 1.5, a significant vibration suppression effect of the bridge is observed. When the ratio is higher than 1.5, although primary resonance occurs, the superharmonic resonance response is small and insensitive to the number of train marshalling. When the ratio is lower than 1.5, the resonance energy accumulates significantly with the increase in train marshalling, resulting in poor train-bridge matching. Parametric analysis based on the limit of the dynamic amplification factor shows that the two-span continuous beam is slightly superior to a simply supported beam with the same span in terms of superharmonic resonance control. Within the speed range of 0–600 km/h, the continuous beam allows for a lower limit of the fundamental frequency, indicating that structural stiffness requirements can be reduced while satisfying dynamic safety, thereby improving economic efficiency. In the coupled train-bridge vibration analysis under the selected bridge parameters, the Sperling ride index of all vehicles consistently remains within the “excellent” limit. Notably, because the intermediate vehicles satisfy the vibration suppression matching conditions, the change in dynamic response at the resonance speed is minimal.
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Key words:
- continuous beam /
- magnetic levitation train /
- dynamics /
- train-bridge coupling
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图 1 超导电动悬浮系统拓扑结构及等效电路
Figure 1. Topological structure and equivalent circuit of superconducting electrodynamic suspension system
图 2 悬浮力数值模拟预测值与文献实测值对比
Figure 2. Comparison of numerically predicted values of levitation force and measured values from literature
图 5 先行跨与后行跨动力响应差值对比
Figure 5. Comparison of dynamic response differences between leading span and trailing span
图 6 不同跨径下动力系数随β变化规律
Figure 6. Variation of dynamic amplification factor with β under different spans
图 7 不同编组下的桥梁动力响应
Figure 7. Dynamic responses of bridge under different train marshalling
图 8 连续梁、简支梁共振对应动力系数峰值
Figure 8. Peak values of dynamic amplification factor corresponding to resonance for continuous beam and simply supported beam
图 10 连续梁跨中加速度频域响应
Figure 10. Frequency-domain acceleration response at mid-span of continuous beam
表 1 桥梁跨度及侧壁单元长度
Table 1. Bridge span and side wall element length
跨径/m 20 24 28 30 侧壁梁长度/m 10 8、12 14 10 跨径/m 32 36 40 42 侧壁梁长度/m 8 6、12 8、10 14 
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表 2 桥梁材料属性
Table 2. Material properties of bridge
参数名称 弹性模量/Pa 密度/（kg•m−3） 阻尼比 数值 3.45 × 1010 2.5 × 103 0.02
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表 3 超导电动悬浮列车参数
Table 3. Parameters of superconducting electrodynamic suspension train
参数名称 数值 头、尾车车体质量/t 22、22 中间车车体质量/t 19.5 悬浮架质量/t 7.8 头、尾车悬浮架定距/m 21、21 中间车悬浮架定距/m 24 超导线圈极距/m 1.5 超导线圈磁动势/ kA 750 额定悬浮间隙/mm 45
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表 4 超导电动磁浮列车垂向模态及频率
Table 4. Vertical modal and frequencies of superconducting electrodynamic maglev train
模态 振动频率/Hz 头尾车点头、中间车浮沉 1.06、2.12 三车体点头 1.22、2.24 三车体浮沉 1.28 头尾车浮沉、中间车点头 1.99 构架点头 6.33、7.00、8.28 构架浮沉 7.51 超导磁体框架浮沉 7.73、7.91、7.95 超导磁体框架点头 8.09、8.30、8.44
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表 5 桥梁基频下限
Table 5. Lower limits of fundamental frequency of bridge
Hz 速度 600 km/h 范围内
动力系数峰值连续梁基频下限 简支梁基频下限 32 m 36 m 40 m 42 m 36 m 40 m 1.2 10.99 9.53 9.79 9.75 10.47 10.45 1.3 9.99 9.20 8.12 7.60 9.99 9.85 1.4 9.62 8.99 7.95 3.61 9.53 9.51 1.5 9.21 8.78 7.69 3.51 9.23 9.26 1.6 5.16 8.56 5.21 3.41 8.96 9.02 1.7 3.87 3.86 3.58 3.31 8.59 8.74 1.8 3.82 3.66 3.51 3.18 8.40 1.9 3.77 3.59 3.43 2.0 3.72 3.51 3.34
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