Train passing analysis on large-span railway suspension bridge based on ANSYS-MATLAB co-simulation
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摘要: 针对大跨铁路悬索桥结构复杂、几何非线性显著的特点开展行车动力分析，提出了一种ANSYS与MATLAB实时交互、联合仿真的列车-轨道-桥梁耦合振动分析方法; 在ANSYS内建立悬索桥和轨道结构精细有限元模型，在MATLAB内基于多刚体动力学理论组装车辆质量、阻尼和刚度矩阵，并将轨道结构动力微分方程系数矩阵导至MATLAB中; 分别建立悬索桥子系统、轨道-车辆子系统的动力微分方程，然后基于异步长策略，以大时间步长在ANSYS内考虑主缆几何刚度，并通过更新结构刚度矩阵来求解悬索桥子系统振动响应，以小时间步长在MATLAB内考虑轮轨空间接触关系，并通过施加轨道不平顺来求解轨道-车辆子系统动力响应，2种计算软件通过实时交换数据实现子系统之间的耦合求解; 通过分析某单跨铁路简支梁桥的实测数据验证了该方法的正确性，并利用该联合仿真方法对主跨为660 m的某铁路悬索桥进行了行车动力计算。分析结果表明：随着车速的提高，桥梁动力响应增大，行车安全性与平稳性趋于恶化; 在车速不大于180 km·h-1的工况下，该悬索桥能够满足行车安全性要求; 在列车动力荷载作用下，不考虑悬索桥几何刚度会导致跨中竖向位移产生7.4%的计算误差; 考虑几何刚度、不更新桥梁刚度矩阵导致的桥梁与列车响应计算误差均不超过1%，能够满足工程计算精度需求。可见，提出的联合仿真方法可用于大跨柔性铁路桥梁的行车动力分析。
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关键词:
- 桥梁工程 /
- 大跨铁路悬索桥 /
- ANSYS-MATLAB联合仿真 /
- 列车-轨道-桥梁耦合振动 /
- 几何非线性 /
- 异步长
Abstract: To study the driving dynamics of large-span railway suspension bridges with complex structures and significant geometric nonlinearity, a train-track-bridge coupled vibration analysis method was introduced based on the real-time interacting ANSYS-MATLAB co-simulation. The refined finite element models of suspension bridge and track structure were established in ANSYS. The mass, damping, and stiffness matrices of train were assembled in MATLAB according to the multi-rigid-body dynamics theory, and the dynamic differential equation coefficient matrices of track structure were exported to MATLAB. The dynamic differential equations of suspension bridge subsystem and track-train subsystem were established separately. Then, based on the multi-time-step strategy, the vibration responses of suspension bridge subsystem were calculated by considering the geometric stiffness of main cables and updating the stiffness matrices of structure in ANSYS with coarse time steps. The dynamic responses of track-train subsystem were calculated by considering the wheel-rail spatial contact relationship and applying track irregularities in MATLAB with fine time steps. The coupling solution between subsystems was realized via the real-time data exchange between ANSYS and MATLAB. The method was verified by analyzing the test data of a railway simply supported beam bridge with single span. The co-simulation method was applied to a 660 m-long railway suspension bridge to analyze the driving dynamics. Analysis result shows that the dynamic responses of bridge tend to increase and the driving safety and stability tend to deteriorate as the speed of train increases. The suspension bridge design can fulfil the safety requirements when the train speed does not exceed 180 km·h-1. Under the train dynamic loads, neglecting the geometric stiffness of suspension bridge results in an calculation error of 7.4% in the midspan vertical displacement. Considering the geometric stiffness without updating the bridge stiffness matrix leads to a calculation error less than 1% for the bridge and train responses. The results satisfy the required calculation accuracy. Therefore, the proposed co-simulation method can be used to analyze the driving dynamics of large-span flexible railway bridges. 4 tabs, 14 figs, 31 refs. -
图 7 简支梁桥跨中竖向位移
Figure 7. Midspan vertical displacement of simply supported beam bridge
图 10 典型工况中主梁跨中轨下桥面板动力响应时程
Figure 10. Dynamic responses time histories of bridge deck of midspan section below track under typical working conditions
图 11 工况3中跨主缆应力时程
Figure 11. Stress time history of midspan main cable in working condition 3
图 14 首节车第1轮对左侧轮轨力
Figure 14. Left wheel-rail forces of first wheel-set of first vehicle
表 1 悬索桥模态分析结果
Table 1. Modal analysis result of suspension bridge
表 2 工况设置
Table 2. Working condition setting
工况 车速/(km·h-1) 单/双线 是否考虑几何刚度 是否更新刚度矩阵 1 80 单 是 是 2 100 单 是 是 3 120 单 是 是 4 140 单 是 是 5 160 单 是 是 6 180 单 是 是 7 120 双 是 是 8 120 单 否 否 9 120 单 是 否 
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表 3 桥梁最大动力响应
Table 3. Maximum dynamic responses of bridge
工况 位移/mm 加速度/(m·s-2) 左跨1/2截面轨下桥面板 中跨1/4截面轨下桥面板 中跨1/2截面轨下桥面板 左跨1/2截面轨下桥面板 中跨1/4截面轨下桥面板 中跨1/2截面轨下桥面板 横向 竖向 横向 竖向 横向 竖向 横向 竖向 横向 竖向 横向 竖向 1 0.2 -4.2 0.4 86.7 0.5 121.2 0.021 2 0.285 4 0.013 2 0.311 7 0.013 2 0.378 0 2 0.2 -4.2 0.3 86.9 0.4 121.6 0.021 0 0.380 9 0.015 8 0.405 7 0.013 8 0.531 4 3 0.2 -4.2 0.3 87.1 0.4 121.8 0.026 7 0.509 0 0.019 2 0.636 0 0.019 1 0.704 0 4 0.2 -4.2 0.3 87.4 0.4 122.3 0.030 9 0.666 8 0.027 4 0.739 5 0.025 0 0.863 6 5 0.2 -4.2 0.3 87.9 0.3 122.5 0.035 9 0.845 0 0.030 9 0.931 0 0.030 2 1.087 1 6 0.2 -4.2 0.3 88.1 0.3 123.6 0.036 8 0.966 1 0.032 7 1.133 6 0.036 9 1.358 7 7 0.2 -4.8 0.2 138.2 0.1 239.4 0.028 7 0.508 7 0.044 4 1.074 1 0.031 0 0.514 9 8 0.2 -4.4 0.2 93.7 0.2 130.7 0.026 4 0.619 8 0.024 9 0.670 2 0.024 0 0.806 8 9 0.2 -4.2 0.2 86.6 0.3 121.0 0.025 6 0.618 2 0.024 6 0.651 0 0.023 2 0.760 7
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表 4 最大车辆动力响应
Table 4. Maximum dynamic responses of vehicles
工况 动车 拖车 加速度/(m·s-2) 脱轨系数 轮轴横向力/kN 轮重减载率 加速度/(m·s-2) 脱轨系数 轮轴横向力/kN 轮重减载率 横向 竖向 横向 竖向 1 0.180 1 0.161 0 0.104 0 11.148 0.199 8 0.199 4 0.180 8 0.110 4 10.809 0.221 3 2 0.207 3 0.194 6 0.114 0 13.644 0.128 5 0.233 6 0.221 8 0.120 7 12.869 0.133 1 3 0.236 0 0.227 8 0.130 1 14.980 0.165 6 0.260 5 0.257 1 0.134 2 14.390 0.163 6 4 0.258 1 0.259 7 0.138 1 14.850 0.206 9 0.288 5 0.293 4 0.145 8 14.919 0.199 5 5 0.272 8 0.288 1 0.136 2 15.481 0.273 6 0.312 8 0.328 2 0.148 3 15.264 0.246 8 6 0.282 6 0.314 2 0.161 5 16.851 0.307 4 0.327 4 0.361 3 0.178 8 16.934 0.268 0 7 0.235 9 0.252 4 0.131 2 15.130 0.165 8 0.260 6 0.280 5 0.134 9 14.513 0.159 8 8 0.236 0 0.229 3 0.130 2 14.448 0.165 8 0.260 6 0.259 8 0.134 2 14.772 0.163 9 9 0.235 9 0.227 6 0.129 9 14.980 0.166 4 0.260 5 0.257 0 0.134 0 14.388 0.164 6
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