Coupled Train-Bridge Vibration and Dynamic Characteristics of Long-Span T-Shaped Rigid Frame Railway Bridge
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摘要: 为探究铁路大跨T形刚构桥车桥耦合振动特性与动力性能，以宜万铁路马水河大桥为工程背景，建立桥梁空间杆系有限元模型以及包含31个自由度的车辆模型，进行车桥耦合振动计算分析.通过动载试验测试桥梁的自振特性，并测试列车以不同速度通过桥跨和以一定速度在特定位置制动时桥跨结构的动应变、动位移以及加速度等动力响应.依据动载试验与车桥耦合振动计算综合分析马水河大桥的动力性能.研究结果表明：车桥耦合振动计算结果与实测结果吻合较好，桥梁结构动力响应满足规范限值，该桥具有良好的横向、竖向刚度与动力性能；实测桥跨结构及墩顶动力系数最大值为1.08，桥梁结构受行车及制动的动力作用不明显；列车的动力响应随车速的提高而增大，但均满足规范限值，具有良好的安全性与平稳性.Abstract: To study the characteristics of coupled train-bridge vibration and dynamic performance of a long-span T-shaped rigid frame railway bridge, taking the Mashuihe bridge on the Yichang-Wanzhou railway line as an example, a three-dimensional finite element model for coupled train-bridge vibrations was built, and each carriage of a train was modelled by a 31-degrees-of-freedom dynamic system. Field tests were conducted to determine the free vibration characteristics as well as the strain, displacement, and acceleration of the bridge structure under trains moving at different speeds and braking at a specified position from a set speed. Therefore, the dynamic responses of the Mashuihe bridge was studied comprehensively, both numerically and experimentally. The calculated results were in good agreement with the corresponding experimental results. The dynamic responses of the bridge satisfied the requirements of the code, and the bridge exhibited good lateral and vertical stiffness. The dynamic coefficients of the mid-span and the top of the pier was 1.08, which indicates that the impact of train braking has little effect on the bridge structure. The dynamic responses of the carriages increased with increasing speed, but also satisfied the requirements of the code. The carriages exhibited satisfactory safety and stability.
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图 4 马水河大桥动载试验测试截面布置示意图(单位:cm)
Figure 4. Positions of measured sections and arrangement of measuring points (unit: cm)
图 5 A-A测试截面竖向加速度时程曲线(单线80 km/h)
Figure 5. Time-history curve of measured vertical acceleration at section A-A under the train running on a single line at 80 km/h
图 6 B-B测试截面横向加速度时程曲线(单线80 km/h)
Figure 6. Time-history curve of measured transverse acceleration at section B-B under the train running on a single line at 80 km/h
图 7 A-A测试截面动挠度时程曲线(单线80 km/h)
Figure 7. Time-history curve of measured and calculated vertical deflection at section A-A under the train running on a single line at 80 km/h
图 8 B-B测试截面横向振幅时程曲线(单线80 km/h)
Figure 8. Time-history curve of measured and calculated lateral displacement at section B-B under the train running on a single line at 80 km/h
表 1 列车过桥时车辆响应
Table 1. Dynamic responses of carriages under the train running on the bridge
车速/(km·h-1) 工况 脱轨系数 轮重减载率 轮轴横向力/kN 加速度/(m·s-2) 平稳性指标 横向 竖向 横向 竖向 40 单线 0.24 0.34 27.89 0.59 0.20 2.08 1.44 双线 0.24 0.34 27.91 0.58 0.20 2.06 1.44 50 单线 0.25 0.36 30.31 1.04 0.52 2.49 1.90 双线 0.26 0.36 30.65 1.04 0.52 2.50 1.90 60 单线 0.26 0.37 30.36 1.50 0.85 2.82 2.20 双线 0.26 0.37 30.91 1.52 0.85 2.83 2.20 70 单线 0.26 0.39 31.70 1.42 1.31 2.81 2.50 双线 0.26 0.39 31.98 1.35 1.31 2.77 2.50 80 单线 0.26 0.39 32.93 1.46 2.20 2.87 2.91 双线 0.26 0.38 33.47 1.46 2.23 2.87 2.92 90 单线 0.30 0.39 38.15 1.81 2.59 3.10 3.05 双线 0.30 0.39 34.34 1.83 2.54 3.11 3.03 
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表 2 桥梁自振特性
Table 2. Free-vibration characteristics of the bridge
序号 实测频率/Hz 计算频率/Hz 振型 阻尼比 1 0.855 0.876 主桥一阶横向弯曲 0.029 2 1.392 1.415 主桥二阶横向弯曲 0.018 3 1.611 1.707 主桥一阶竖向弯曲 0.015 4 2.246 2.524 主桥二阶竖向弯曲 0.011
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表 3 控制截面处动力系数
Table 3. Dynamic coefficients of control sections
车速/
(km·h-1)工况 A-A B-B 上缘 下缘 上缘 下缘 实测 计算 实测 计算 实测 计算 实测 计算 20 单线 1.01 1.06 1.01 1.04 1.02 1.08 1.01 1.07 双线 1.01 1.08 1.01 1.08 1.01 1.11 1.00 1.05 40 单线 1.01 1.05 1.01 1.07 1.01 1.09 1.01 1.02 双线 1.01 1.10 1.01 1.09 1.01 1.05 1.01 1.10 制动 1.07 1.13 1.07 1.17 1.08 1.15 1.04 1.14 60 单线 1.04 1.09 1.01 1.06 1.02 1.10 1.01 1.08 双线 1.02 1.07 1.01 1.09 1.02 1.06 1.01 1.04 80 单线 1.02 1.08 1.02 1.10 1.02 1.12 1.01 1.06 双线 1.04 1.10 1.03 1.10 1.02 1.12 1.01 1.07
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表 4 控制截面处振动加速度
Table 4. Acceleration of control sections
m/s2 车速/
(km·h-1)工况 A-A B-B 横向 竖向 横向 竖向 实测 计算 实测 计算 实测 计算 实测 计算 20 单线 0.10 0.19 0.13 0.30 0.03 0.11 0.01 0.09 双线 0.10 0.22 0.21 0.35 0.03 0.15 0.01 0.05 40 单线 0.14 0.24 0.45 0.61 0.03 0.17 0.02 0.10 双线 0.18 0.26 0.36 0.57 0.03 0.14 0.03 0.13 制动 0.07 0.15 0.07 0.24 0.02 0.16 0.03 0.15 60 单线 0.26 0.38 0.43 0.67 0.04 0.20 0.02 0.15 双线 0.24 0.41 0.49 0.65 0.05 0.21 0.03 0.12 80 单线 0.23 0.37 0.46 0.74 0.04 0.27 0.04 0.17 双线 0.27 0.45 0.58 0.78 0.05 0.31 0.04 0.19
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表 5 控制截面处横向振幅及动挠度
Table 5. Lateral displacement and vertical deflection of control sections
mm 车速/
(km·h-1)工况 A-A B-B 横向振幅 动挠度 横向振幅 实测 计算 实测 计算 实测 计算 20 单线 0.28 0.61 — — 0.14 0.27 双线 0.31 0.57 39.4 56.3 0.10 0.25 40 单线 0.33 0.78 — — 0.17 0.35 双线 031 0.67 41.3 65.8 0.19 0.42 60 单线 0.44 0.84 — — 0.13 0.25 双线 0.47 0.91 43.7 70.2 0.18 0.68 80 单线 0.27 0.75 — — 0.12 0.31 双线 0.54 1.51 45.5 78.6 0.17 0.57
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