Analysis of the Vertical Dynamic Response of the Carbody When the Subway Vehicle Runs on the Bridge

doi:10.3901/JME.260199

Abstract

Abstract: The coupled vibration behavior of vehicles and bridges has an important influence on the running safety and ride comfort of the vehicle. A vector form intrinsic finite-element method is used to establish the train-track-bridge coupling vibration model of a subway express line in China. The model considers the track and bridge as Euler beams, but the carbody, bogie frames, and wheelsets are treated as rigid bodies. The accuracy of the model is verified by using the vibration test data of the vehicle. The model is used to analyze the influencing factors of the dynamic response of the caybody when it runs on the bridge. The results show that the carbody generates obvious pitch resonance when it runs on the bridge at a speed of 114 km/h. The acceleration amplitudes of the left front and right rear floors of the carbody are the same, but the vibration phase of the left front and right rear floors is basically opposite. Varying the operating speed of the vehicle and increasing the damping coefficient of the secondary suspension can reduce the acceleration response of the carbody's pitch resonance. The operating speed of pitching resonance increases with increasing the bridge span, but the corresponding passing frequencies are all around 0.943 Hz. Compared to the bridge span of 30 m, the maximum pitch acceleration of the carbody is significantly reduced when the vehicle passes through the bridge with spans of 24 m and 36 m.

Key words: vector form intrinsic finite element, vehicle-track-bridge dynamic interaction, vertical response, pitch resonance

CLC Number:

U211

QIN Qingyang, TAO Gongquan, WEN Zefeng, REN Yu. Analysis of the Vertical Dynamic Response of the Carbody When the Subway Vehicle Runs on the Bridge[J]. Journal of Mechanical Engineering, 2025, 62(6): 359-369.

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References

[1] WANG T L. Ramp/bridge interface in railway prestressed concrete bridge[J]. Journal of Structural Engineering，1990，116(6)：1648-1659.
[2] SONG M K，CHOI C K. Analysis of high-speed vehicle-bridge interactions by a simplified 3-D model[J]. Structural Engineering and Mechanics，2002，13(5)：505-532.
[3] 李小珍，马文彬，强士中. 车桥系统耦合振动分析的数值解法[J]. 振动与冲击，2002，21(3)：21-25. LI Xiaozhen，MA Wenbin，QIANG Shizhong. Coupling vibration analysis of vehicle-bridge system by iterative solution method[J]. Journal of Vibration and Shock，2002，21(3)：21-25.
[4] SONG M K，NOH H C，CHOI C K. A new three-dimensional finite element analysis model of high-speed train-bridge interactions[J]. Engineering Structures，2003，25(13)：1611-1626.
[5] 娄平，曾庆元. 车辆-轨道-桥梁系统竖向运动方程的建立[J]. 铁道学报，2004，26(5)：71-80. LOU Ping，ZENG Qingyuan. Formulation of equations of vertical motion for vehicle-track-bridge system[J]. Journal of the China Railway Society，2004，26(5)：71-80.
[6] LUO P. Vertical dynamic responses of a simply supported bridge subjected to a moving train with two-wheelset vehicles using modal analysis method[J]. International Journal for Numerical Method in Engineering，2005，64(9)：1207-1235.
[7] 翟婉明，蔡成标，王开云. 高速列车-轨道-桥梁动态相互作用原理及模型[J]. 土木工程学报，2005，38(11)：132-137. ZHAI Wanming，CAI Chengbiao，WANG Kaiyun. Mechanism and model of high-speed train-track-bridge dynamic interaction[J]. China Civil Engineering Journal，2005，38(11)：132-137.
[8] 昌超，肖乾，王亚朋. 高速列车车轮型面磨耗对轨道、桥梁振动特性影响分析[J]. 振动与冲击，2019，38(13)：185-196. CHANG Chao，XIAO Qian，WANG Yapeng. Effects of high-speed train’s wheel wear on vibration characteristics of track and bridge[J]. Journal of Vibration and Shock，2019，38(13)：185-196.
[9] 武隽，司慧龙，董凯，等. 多线地铁列车-高架桥耦合系统动力分析[J]. 振动、测试与诊断，2023，43(2)：263-270. WU Jun，SI Huilong，DONG Kai，et al. Train-bridge coupling dynamic analysis of muti-line subway viaduct[J]. Journal of Vibration，Measurement & Diagnosis，2023，43(2)：263-270.
[10] 翟婉明. 非线性结构动力分析的Newmark预测-校正积分模式[J]. 计算力学学报，1990，7(2)：51-58. ZHAI Wanming. The predictor-corrector scheme based on the Newmarks integration algorithm for nonlinear structural dynamic analysis[J]. Chinese Journal of Computational Mechanics，1990，7(2)：51-58.
[11] 吴定俊，李奇，陈艾荣. 车桥耦合振动迭代求解数值稳定问题[J]. 力学季刊，2007，28(3)：405-411. WU Dingjun，LI Qi，CHEN Airong. Numerical stability iteration scheme for solution of vehicle-bridge coupling vibration[J]. Chinese Quarterly of Mechanics，2007，28(3)：405-411.
[12] 毛国辉，王小松，郑鸿飞. 车-桥耦合振动的联合方程分析方法[J]. 重庆交通大学学报(自然科学版)，2013，32(1)：1-4. MAO Guohui，WANG Xiaosong，ZHENG Hongfei. Analytical method for joint equation of vehicle-bridge coupling vibration[J]. Journal of Chongqing Jiaotong University(Natural Science)，2013，32(1)：1-4.
[13] TING E C，SHIH C，WANG Y K. Fundamentals of a vector from intrinsic finite element：Part Ⅰ. Basic procedure and a plane frame element[J]. Journal of Mechanics，2004，20(2)：113-122.
[14] TING E C，SHIH C，WANG Y K. Fundamentals of a vector from intrinsic finite element：Part Ⅱ. Plane solid elements[J]. Journal of Mechanics，2004，20(2)：123-132.
[15] TING E C，SHIH C，WANG Y K. Fundamentals of a vector from intrinsic finite element：Part Ⅲ. Convected material frame and examples[J]. Journal of Mechanics，2004，20(2)：133-143.
[16] 罗尧治，郑延丰，杨超，等. 结构复杂行为分析的有限质点法研究综述[J]. 工程力学，2014，31(8)：1-7. LUO Yaozhi，ZHENG Yanfeng，YANG Chao，et al. Review of the finite particle method for complex behaviors of structures[J]. Engineering Mechanics，2014，31(8)：1-7.
[17] DUAN Y F，HE K，ZHANG H M，et al. Entire-process simulation of earthquake-induced collapse of a mockup cable-stayed bridge by vector form intrinsic finite element(VFIFE) method[J]. Advances in Structural Engineering，2014，17(3)：347-360.
[18] 郑延丰，罗尧治. 基于有限质点法的多尺度精细化分析[J]. 工程力学，2016，33(9)：21-29. ZHENG Yanfeng，LUO Yaozhi. Multi-scale fine analysis based on the finite particle method[J]. Engineering Mechanics，2016，33(9)：21-29.
[19] 林贤宏，罗尧治，唐敬哲，等. 考虑剪切和扭转变形的有限质点法纤维梁单元研究[J]. 工程力学，2022，39(5)：34-43. LIN Xianhong，LUO Yaozhi，TANG Jingzhe，et al. A fiber beam element for the finite particle method considering shear and torsion deformation[J]. Engineer Mechanics，2022，39(5)：34-43.
[20] LIEN K H，CHIOU Y J，WANG R Z，et al. Nonlinear behavior of steel structures considering the cooling phase of a fire[J]. Journal of Constructional Steel Research，2009，65(8-9)：1776-1789.
[21] LIEN K H，CHIOU Y J，WANG R Z，et al. Vector form intrinsic finite element analysis of nonlinear behavior of steel structures exposed to fire[J]. Engineering Structures，2010，32(1)：80-92.
[22] 倪秋斌，段元峰，高博青. 采用向量式有限元的斜拉索振动控制仿真[J]. 振动工程学报，2014，27(2)：238-245. NI Qiubin，DUAN Yuanfeng，GAO Boqing. Vector form intrinsic finite element (VFIFE) based simulation on vibration control of stay cables[J]. Journal of Vibration Engineering，2014，27(2)：238-245.
[23] 段元峰，黄嘉思，邓南，等. 采用向量式有限元的拉索参数振动模拟[J]. 振动工程学报，2023，36(1)：188-195. DUAN Yuanfeng，HUANG Jiasi，DENG Nan，et al. Vector form intrinsic finite element based simulation on parametric vibration of cables[J]. Journal of Vibration Engineering，2023，36(1)：188-195.
[24] 郑延丰，杨超，刘磊，等. 基于有限质点法的含间隙铰平面机构动力分析[J]. 工程力学，2020，37(3)：8-17. ZHENG Yanfeng，YANG Chao，LIU Lei，et al. Dynamic analysis of planar mechanism with revolute joint clearance based on finite particle method[J]. Engineering Mechanics，2020，37(3)：8-17.
[25] 唐敬哲，汪伟，郑延丰，等. 基于并行有限质点法的界面断裂-接触行为分析[J]. 工程力学，2021，38(6)：24-35. TANG Jingzhe，WANG Wei，ZHENG Yanfeng，et al. Interface failure and contact analysis based on parallelized finite particle method[J]. Engineering Mechanics，2021，38(6)：24-35.
[26] 申莹莹. 基于向量式分析的轮轨滚动接触模拟[D]. 成都：西南交通大学，2012. SHEN Yingying. Numerical simulation of wheel-rail rolling contact based on the vector form analysis[D]. Chengdu：Southwest Jiaotong University，2012.
[27] 钟俊杰. 基于向量有限元的轮轨接触问题研究[D]. 成都：西南交通大学，2014. ZHONG Junjie. Analysis of wheel/rail contact based on vector form intrinsic finite element method[D]. Chengdu：Southwest Jiaotong University，2014.
[28] DUAN Y F，WANG S M，WANG R Z，et al. Vector form intrinsic finite-element analysis for train and bridge dynamic interaction[J]. Journal of Bridge Engineering，2017，23(1)：04017126.
[29] DUAN Y F，WANG S M，YAU J D. Vector form intrinsic finite element method for analysis of train-bridge interaction problems considering the coach-coupler effect[J]. International Journal of Structural Stability and Dynamics，2019，19(2)：1950014.
[30] 王素梅. 基于向量式有限元的风-车-轨-桥耦合系统动力分析[D]. 杭州：浙江大学，2018. WANG Sumei. Vector form intrinsic finite element method-based dynamic analysis of wind-train-rail-bridge interaction system[D]. Hangzhou：Zhejiang University，2018.
[31] 任尊松，刘志明. 高速动车组振动传递及频率分布规律[J]. 机械工程学报，2013，49(16)：1-7. REN Zunsong，LIU Zhiming. Vibration and frequency domain characteristics of high speed EMU[J]. Journal of Mechanical Engineering，2013，49(16)：1-7.
[32] 宫岛，周劲松，孙文静，等. 基于格林函数法的铁道车辆弹性车体垂向振动分析[J]. 机械工程学报，2013，49(12)：116-122. GONG Dao，ZHOU Jinsong，SUN Wenjing，et al. Vertical vibration analysis of flexible car body for railway vehicle based on green functions[J]. Journal of Mechanical Engineering，2013，49(12)：116-122.
[33] 徐宁，杨广雪，杨超. 车辆-轨道垂向耦合系统空间频域传递特性研究[J]. 机械工程学报，2023，59(24)：231-241. XU Ning，YANG Guangxue，YANG Chao. Spatial frequency domain transfer characteristics of vertical vehicle-track coupling system[J]. Journal of Mechanical Engineering，2023，59(24)：231-241.
[34] 汪群生，曾京，朱彬，等. 基于最优控制理论的高速列车车下悬吊系统半主动悬挂[J]. 机械工程学报，2020，56(4)：160-167. WANG Qunsheng，ZENG Jing，ZHU Bin，et al. Semi-active suspension applied on carbody underneath suspended system of high-speed railway based on optimal control theory[J]. Journal of Mechanical Engineering，2020，56(4)：160-167.
[35] 徐宁，李强，任尊松，等. 考虑一系悬挂局部细化的车辆垂向系统振动传递特性研究[J]. 机械工程学报，2021，57(10)：106-117. XU Ning，LI Qiang，REN Zunsong，et al. Study on the vibration transfer characteristics of vertical vehicle system considering local refinement of primary suspension[J]. Journal of Mechanical Engineering，2021，57(10)：106-117.
[36] 张鑫，池茂儒，罗赟，等. 二系垂向多功能减振器对铁道车辆动力学的影响研究[J]. 机械工程学报，2024，60(18)：258-265. ZHANG Xin，CHI Maoru，LUO Yun，et al. Research on the influence of secondary vertical multi-functional damper on railway vehicle dynamics[J]. Journal of Mechanical Engineering，2024，60(18)：258-265.