Train-induced environmental vibration analysis of large-chassis and multi-tower metro depots
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摘要: 为探究大底盘多塔地铁车辆段在列车振动荷载作用下的振动响应规律，采用精细化数值分析模型与高效率分析技术，基于子结构方法将振动的产生和传播拆分为2个子结构；基于半构架列车荷载简化计算方法推导出半车模型轮轨力解析表达式，建立了轨道-土体-建筑系统精细化有限元模型，将轮轨力荷载施加于有限元模型以求解系统动力响应，并通过多图形处理器(GPU)异构并行显式算法实现了高效率分析；以某地铁车辆段为研究对象，结合现场实测数据验证了数值模拟的准确性，通过对比不同算法对同一模型的求解时长，验证了多GPU异构并行显式算法的高效性；在此基础上，重点分析了振动在运用库及其上盖建筑中的传播规律。分析结果表明：在运用库内，列车运行产生的振动以中低频为主，源强的优势频段集中在10~50 Hz，峰值频率在30 Hz附近；库柱脚的振级随水平振源距的增加线性衰减，但由于边柱相对于其他柱受到结构整体的约束作用最小，库最外侧边柱上的振动响应有所增大；由于列车直接在结构底层的立柱间通行，振动传播路径短，衰减效果弱，上盖建筑的振动频谱丰富，楼板振动的优势频段集中在20.0~31.5 Hz；上盖建筑楼板在低频时呈现出整体振动的规律，跨中最大Z振级在靠近顶层时最大，楼板振动强度受其自振频率和源强频谱特性的共同影响，位于源强振动优势频段的范围越多，越容易产生共振。Abstract: To investigate the vibration response patterns at large-chassis and multiple-tower metro depots under the influence of train-induced vibration load, a refined numerical analysis model and efficient analysis techniques were employed. Based on the substructure method, the generation and propagation of vibrations were decomposed into two substructures. The analytical expression for wheel-rail forces in a half-train model was derived based on the simplified calculation method of half-bogie train load. A refined finite element model for the track-soil-building system was established. By applying the wheel-rail force load to the finite element model, the dynamic response of the system was solved, and the high-efficiency analysis was achieved through the multi-graphics processing unit (GPU)-heterogeneous parallel explicit algorithm. By taking a specific metro depot as the research subject, the accuracy of numerical simulation was validated with the on-site measurement data. The efficiency of multi-GPU heterogeneous parallel explicit algorithm was confirmed by comparing the solution times of different algorithms applied to the same model. On this basis, the propagation patterns of vibrations within the operation depot and over-track buildings were highlighted. Analysis results indicate that within the operation depot, the vibrations generated by train operation are predominantly characterized by medium to low frequencies. The dominant frequency band of the source strength concentrates on 10-50 Hz, with a peak frequency near 30 Hz. The vibration level at the column base of the operation depot decreases linearly with the increase in the horizontal distance from the vibration source. However, due to the slight constraint exerted by the structure on perimeter columns compared with others, the vibration response amplifies on the outmost perimeter columns of the operation depot. Given that trains pass directly between the supporting columns at the lowest structural level, the vibration propagation path is short with weak attenuation, leading to a richer vibration spectrum in over-track buildings, where the floor vibration advantageously concentrates on the frequency band of 20.0-31.5 Hz. A coherent vibration pattern of the over-track building floor is observed at low frequencies, with the maximum Z-vibration level at mid-span near the top floor. The floor vibration intensity is influenced by both its natural frequency and the spectral characteristics of source strength. Resonance is more likely to occur when the natural frequency of floor falls within the predominant vibration frequency band of source strength.
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图 12 运用库拾振点振动水平
Figure 12. Vibration levels of vibration pickup points in operation depot
图 14 楼板跨中竖向加速度峰值分布
Figure 14. Peak vertical acceleration distributions at mid-spans of floors
图 15 楼板跨中最大Z振级随楼层的分布
Figure 15. Distributions of maximum Z-vibration levels at mid-spans of floors
图 16 楼板分频振级随楼层的分布
Figure 16. Distributions of floor frequency division vibrations with floor
图 17 各层楼板分频振级放大量
Figure 17. Frequency division vibration level amplifications of each floor slab
表 1 轨道和建筑结构材料参数
Table 1. Material parameters of building structure and track
材料/部件 密度/(kg·m-3) 弹性模量/GPa 泊松比 C30 2 500 30 0.20 C40 2 500 32 0.20 C50 2 500 34 0.20 HRB400 7 800 200 0.25 Q235 7 800 206 0.25 Q345 7 800 206 0.25 钢轨 7 850 206 0.30 轨枕 2 500 30 0.20 轨道板 2 500 32 0.20 
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表 2 土体参数
Table 2. Parameters of soil
土层 厚度/m 密度/(kg·m-3) 弹性模量/MPa 泊松比 1 4.5 2 040 219 0.25 2 7.2 1 980 364 0.30 3 5.8 2 120 402 0.35 4 3.5 2 150 401 0.25 5 14.0 2 120 453 0.35
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表 3 车辆参数
Table 3. Parameters of vehicle
车辆部件 质量/kg 点头转动惯量/(kg·m2) 车厢 23 825 528 628 构架 4 610 2 936 轮对 1 654
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表 4 悬挂参数
Table 4. Parameters of suspension
悬挂 竖向刚度/(kN·m-1) 竖向阻尼/(N·s·m-1) 一系 1 260 10 626 二系 490 20 590
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表 5 计算效率对比
Table 5. Comparison of computional efficiencies
算法 精度 配置 数量 计算时长/min CPU显式并行 双精度 Intel(R) Xeon(R)
Gold 6246R CPU32核 19 110 GPU显式并行 双精度 NVIDLA GeForce RTX 3080 1个 3 900
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表 6 楼板前5阶自振频率
Table 6. First five natural frequencies of floors
阶数 自振频率/Hz 4号楼板 7号楼板 10号楼板 1 28.322 59.916 18.756 2 49.946 63.491 23.322 3 64.386 69.958 27.385 4 84.108 79.778 34.792 5 84.836 93.236 44.007
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