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Article(id=1268884385928478914, tenantId=1146029695717560320, journalId=1268266580820377661, issueId=1268884383122494171, articleNumber=null, orderNo=null, doi=10.3969/j.issn.1001-4632.2026.02.08, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=null, receivedDate=1763481600000, receivedDateStr=2025-11-19, revisedDate=1770566400000, revisedDateStr=2026-02-09, acceptedDate=null, acceptedDateStr=null, onlineDate=1780455212328, onlineDateStr=2026-06-03, pubDate=1772294400000, pubDateStr=2026-03-01, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1780455212328, onlineIssueDateStr=2026-06-03, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1780455212328, creator=13701087609, updateTime=1780455212328, updator=13701087609, issue=Issue{id=1268884383122494171, tenantId=1146029695717560320, journalId=1268266580820377661, year='2026', volume='47', issue='2', pageStart='1', pageEnd='255', issueExtLink='null', onlineDate='null', pubDate='null', beforeIssueId=null, nextIssueId=null, price=null, status=1, issueComplete=1, articleOrder=1, issueType=1, specialIssue=null, createTime=1780455211667, creator=13701087609, updateTime=1780455310713, updator=13701087609, preIssue=null, nextIssue=null, ext={EN=IssueExt(id=1268884798719300557, tenantId=1146029695717560320, journalId=1268266580820377661, issueId=1268884383122494171, language=EN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=), CN=IssueExt(id=1268884798723494862, tenantId=1146029695717560320, journalId=1268266580820377661, issueId=1268884383122494171, language=CN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=)}, issueFiles=null}, startPage=87, endPage=95, ext={EN=ArticleExt(id=1268884386368880836, articleId=1268884385928478914, tenantId=1146029695717560320, journalId=1268266580820377661, language=EN, title=Periodic Track Irregularities on Bridges and Vehicle Response Characteristics for 400 km · h-1 High-Speed Railways, columnId=null, journalTitle=China Railway Science, columnName=null, runingTitle=null, highlight=null, articleAbstract=

With the development of high-speed railways towards 400 km · h-1 and higher speed levels, train operation safety and ride comfort impose more stringent requirements on track regularity. Focusing on track regularity of simply-supported bridges with common spans widely used in high-speed railways, a refined track-bridge finite element model is established to reveal the inherent mechanism of periodic track irregularities induced by creep camber of bridge girders. Furthermore, an analysis element for periodic track irregularities on bridges suitable for dynamic simulation is proposed. Based on the established vehicle-track-bridge coupled dynamic model for higher-speed railways, the influence of periodic track irregularities on the carbody response of trains running at 400 km · h-1 is investigated in depth. The results show that an increase in girder creep deformation directly leads to increased rail deformation, with a significant linear correlation between their amplitudes, and the peak rail deformation is always slightly lower than that of girder creep. The proposed calculation element for periodic track irregularities exhibits better consistency with the waveform variation of measured track irregularities. Under the excitation of periodic irregularities, obvious spectral peaks appear at the harmonic frequencies corresponding to a 32 m wavelength in the carbody response spectrum, with the maximum peak occurring at the second harmonic, indicating that the carbody is more sensitive to the excitation of 16 m wavelength, resulting in a double-peak characteristic of the carbody dynamic response within the 32 m wavelength range. The findings provide theoretical support for track condition assessment and track regularity control of 400 km · h-1 high-speed railways.

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随着高速铁路向400 km · h-1及更高速度等级迈进，列车运行安全与乘坐舒适性对轨道平顺性提出了更严苛的要求。针对高速铁路常用跨度简支梁桥上轨道平顺性问题，通过构建精细化轨道-桥梁结构有限元模型，阐明梁体徐变上拱引发轨道周期性不平顺的内在机制，进一步提出适用于动力学仿真的桥上轨道周期性不平顺分析单元，并基于建立的更高速度等级车辆-轨道-桥梁耦合动力学模型，深入研究轨道周期性不平顺对400 km · h-1运行列车车体响应的影响。结果表明：桥梁徐变变形的增大会直接引起钢轨变形的加剧，二者幅值呈现较为显著的线性相关性，且钢轨变形的峰值始终略低于桥梁徐变的幅值；提出的轨道周期性不平顺计算单元与实测轨道不平顺的波形变化具有更高的一致性；周期性不平顺作用下，车体响应频谱在32 m波长的各倍频处出现明显峰值，最大谱峰出现在2倍频处，即车体对16 m波长的激励更为敏感，导致车体动力响应在32 m波长范围内呈现双峰值特征。研究结论为400 km · h-1高速铁路的线路状态评估与轨道平顺性控制提供理论支撑。

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闫子权（1985—），男，河北宁晋人，研究员，博士。E-mail：
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马登科（1995—），男，浙江绍兴人，助理研究员，博士。E-mail：

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马登科（1995—），男，浙江绍兴人，助理研究员，博士。E-mail：

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马登科（1995—），男，浙江绍兴人，助理研究员，博士。E-mail：

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项目最大横向加速度/（m · s-2）最大垂向加速度/（m · s-2）最大横向位移/mm最大垂向位移/mm
相对误差4.4%5.4%5.2%5.2%
仿真结果1.3502.7800.1150.378
实测数据1.2902.6300.1210.399
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仿真结果与实测数据对比验证

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项目最大横向加速度/（m · s-2）最大垂向加速度/（m · s-2）最大横向位移/mm最大垂向位移/mm
相对误差4.4%5.4%5.2%5.2%
仿真结果1.3502.7800.1150.378
实测数据1.2902.6300.1210.399
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徐变变形幅值/mm桥梁中心钢轨变形/mm桥梁边缘钢轨变形/mm钢轨与路基沉降差/mm
10.990.020.01
54.930.100.07
109.860.190.14
1514.790.290.21
2019.710.390.29
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不同桥梁徐变幅值下的钢轨变形

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徐变变形幅值/mm桥梁中心钢轨变形/mm桥梁边缘钢轨变形/mm钢轨与路基沉降差/mm
10.990.020.01
54.930.100.07
109.860.190.14
1514.790.290.21
2019.710.390.29
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400 km · h-1高速铁路桥上轨道周期性不平顺与车辆响应特征
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马登科 1, 2 , 闫子权 1, 2 , 江成 1, 2 , 肖俊恒 3 , 梁晨 1, 2
中国铁道科学 | 2026,47(2): 87-95
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中国铁道科学 | 2026, 47(2): 87-95
400 km · h-1高速铁路桥上轨道周期性不平顺与车辆响应特征
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马登科1, 2 , 闫子权1, 2 , 江成1, 2, 肖俊恒3, 梁晨1, 2
作者信息
  • 1．中国铁道科学研究院集团有限公司 铁道建筑研究所，北京100081
  • 2．中国铁道科学研究院集团有限公司 高速铁路轨道系统全国重点实验室，北京100081
  • 3．北京铁科首钢轨道技术股份有限公司，北京102206

    • 马登科（1995—），男，浙江绍兴人，助理研究员，博士。E-mail：

通讯作者:

闫子权（1985—），男，河北宁晋人，研究员，博士。E-mail：
Periodic Track Irregularities on Bridges and Vehicle Response Characteristics for 400 km · h-1 High-Speed Railways
Dengke MA1, 2 , Ziquan YAN1, 2 , Cheng JIANG1, 2, Junheng XIAO3, Chen LIANG1, 2
Affiliations
  • 1.Railway Engineering Research Institute, China Academy of Railway Sciences Corporation Limited, Beijing100081, China
  • 2.State Key Laboratory for Track System of High-Speed Railway, China Academy of Railway Sciences Corporation Limited, Beijing100081, China
  • 3.Beijing Tieke Shougang Railway-Tech Co., Ltd., Beijing102206, China
出版时间: 2026-03-01 doi: 10.3969/j.issn.1001-4632.2026.02.08
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摘要
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随着高速铁路向400 km · h-1及更高速度等级迈进，列车运行安全与乘坐舒适性对轨道平顺性提出了更严苛的要求。针对高速铁路常用跨度简支梁桥上轨道平顺性问题，通过构建精细化轨道-桥梁结构有限元模型，阐明梁体徐变上拱引发轨道周期性不平顺的内在机制，进一步提出适用于动力学仿真的桥上轨道周期性不平顺分析单元，并基于建立的更高速度等级车辆-轨道-桥梁耦合动力学模型，深入研究轨道周期性不平顺对400 km · h-1运行列车车体响应的影响。结果表明：桥梁徐变变形的增大会直接引起钢轨变形的加剧，二者幅值呈现较为显著的线性相关性，且钢轨变形的峰值始终略低于桥梁徐变的幅值；提出的轨道周期性不平顺计算单元与实测轨道不平顺的波形变化具有更高的一致性；周期性不平顺作用下，车体响应频谱在32 m波长的各倍频处出现明显峰值，最大谱峰出现在2倍频处，即车体对16 m波长的激励更为敏感，导致车体动力响应在32 m波长范围内呈现双峰值特征。研究结论为400 km · h-1高速铁路的线路状态评估与轨道平顺性控制提供理论支撑。

400 km · h-1高速铁路  /  桥梁徐变  /  轨道周期性不平顺  /  车辆-轨道-桥梁耦合动力学模型  /  动力响应

With the development of high-speed railways towards 400 km · h-1 and higher speed levels, train operation safety and ride comfort impose more stringent requirements on track regularity. Focusing on track regularity of simply-supported bridges with common spans widely used in high-speed railways, a refined track-bridge finite element model is established to reveal the inherent mechanism of periodic track irregularities induced by creep camber of bridge girders. Furthermore, an analysis element for periodic track irregularities on bridges suitable for dynamic simulation is proposed. Based on the established vehicle-track-bridge coupled dynamic model for higher-speed railways, the influence of periodic track irregularities on the carbody response of trains running at 400 km · h-1 is investigated in depth. The results show that an increase in girder creep deformation directly leads to increased rail deformation, with a significant linear correlation between their amplitudes, and the peak rail deformation is always slightly lower than that of girder creep. The proposed calculation element for periodic track irregularities exhibits better consistency with the waveform variation of measured track irregularities. Under the excitation of periodic irregularities, obvious spectral peaks appear at the harmonic frequencies corresponding to a 32 m wavelength in the carbody response spectrum, with the maximum peak occurring at the second harmonic, indicating that the carbody is more sensitive to the excitation of 16 m wavelength, resulting in a double-peak characteristic of the carbody dynamic response within the 32 m wavelength range. The findings provide theoretical support for track condition assessment and track regularity control of 400 km · h-1 high-speed railways.

400 km · h-1 high-speed railway  /  Girder creep  /  Periodic track irregularity  /  Vehicle-track-bridge coupled dynamic model  /  Dynamic response
马登科, 闫子权, 江成, 肖俊恒, 梁晨. 400 km · h-1高速铁路桥上轨道周期性不平顺与车辆响应特征. 中国铁道科学, 2026 , 47 (2) : 87 -95 . DOI: 10.3969/j.issn.1001-4632.2026.02.08
Dengke MA, Ziquan YAN, Cheng JIANG, Junheng XIAO, Chen LIANG. Periodic Track Irregularities on Bridges and Vehicle Response Characteristics for 400 km · h-1 High-Speed Railways[J]. China Railway Science, 2026 , 47 (2) : 87 -95 . DOI: 10.3969/j.issn.1001-4632.2026.02.08
正文
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随着高速铁路技术的快速发展，列车运行速度的不断提升对轨道平顺性与车辆动力响应提出了更高要求。轨道不平顺作为影响列车运行安全与乘坐舒适性的关键因素，其形成机理及对车体动力学响应的影响始终是研究重点。特别是在400 km · h-1运行条件下，轨道几何状态的微小偏差即可诱发显著振动并影响列车运行安全，因此亟需系统揭示轨道不平顺的来源、演化规律与动力学效应，为更高速度等级线路的设计、施工与运维提供科学依据［1-5］。
为节约土地、提升线路线形的平顺性，我国高速铁路在线路建设中广泛采用以桥代路模式。在此背景下，我国形成了以24和32 m跨度桥梁结构及无砟轨道为主导的高速铁路线路基础设施关键技术体系。在长期服役过程中，混凝土收缩与徐变导致梁体上拱，进而在桥上形成具有跨径特征波长的周期性轨道不平顺［6-8］；桥梁下挠以及温度效应亦会进一步影响结构变形与轨道几何状态。
近年来，国内外学者围绕桥梁段轨道周期性不平顺的形成机理及影响开展了大量研究。Pombo等［9］采用多体动力学与轮轨耦合模型评估不平顺与线路几何对运行安全与轮轨力的影响，为周期性不平顺的动力效应评估提供了通用建模框架。黎国清等［10］基于轨检及仿真数据，揭示了32 m简支梁诱发的周期性高低不平顺形成机制及其对行车动力性能的影响规律。宋国华等［11］基于实测数据及动力学仿真模型，系统剖析了高速铁路简支梁桥上轨道周期性不平顺的形成机理，阐明了周期性高低不平顺对车体响应的影响规律。李东昇等［12］基于京沪高铁现场检测数据研究了桥上周期性不平顺随服役年限的变化规律。田新宇等［13］揭示了32 m波长桥上周期性不平顺与桥梁残余徐变上拱间的内在联系，并给出了残余徐变上拱的控制建议。徐旸等［14］进一步研究了有砟轨道梁端周期不平顺的形成机理，揭示环境温度与道床支承刚度变化的耦合效应。刘潇潇等［15］围绕高速铁路简支梁桥上轨道高低不平顺谱特征波长展开分析，指出特征波长与桥梁及轨道板结构密切相关。谭社会等［16］将大跨度桥上轨道线形的仿真结果与实测数据相结合，并综合考虑大桥温度变形、线路随机不平顺和线形拟合偏差等条件，提出了高速铁路大跨度桥上轨道不平顺调控方法。
在周期性不平顺表征与识别方面，杨飞等［17］通过修正高斯函数构造周期性不平顺并与随机不平顺叠加用于动力学分析；赵文博等［18］提出了基于小波变换与支持向量机的周期性不平顺识别方法，揭示了简支梁和轨道板周期性不平顺的特征波长；刁洪宝等［19］在长区段轨道周期不平顺的表征与量化方面取得新进展，其研究成果使得系统评估高速铁路轨道整体状态与横向对比分析不同轨下基础的影响成为可能；刘金朝［20］创新性地引入GEI指标，定量评价周期性轨道不平顺对车轨系统动力响应的影响，并在此基础上构建了一套自动诊断方法。
综上所述，现有研究虽揭示了桥梁徐变与周期性不平顺之间的基本关系，但针对更高速度条件下桥梁周期性不平顺的形成机理、轨道-桥梁结构耦合效应及其对车体动力响应的影响规律仍缺乏系统研究。以时速400 km高速铁路为背景，构建精细化轨道-桥梁结构有限元模型，阐明梁体徐变上拱导致的轨道周期性不平顺形成机理，并提出适用于动力学仿真的桥上轨道周期性不平顺计算单元；在此基础上，结合更高速度等级车辆-轨道-桥梁（车-线-桥）耦合动力分析模型，深入揭示轨道周期性不平顺对车体响应的影响规律及其与随机不平顺叠加下的频谱特性，为400 km · h-1高速铁路的线路状态评估与轨道平顺性控制提供理论支撑。
1　模型建立
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基于经典车辆-轨道耦合动力学理论［21］，采用自编程序实现车辆-轨道系统的建模，应用有限元软件构建精细化轨道-桥梁结构有限元模型，并通过二者联合仿真建立车辆-轨道-桥梁耦合动力学模型。
1.1　车辆-轨道动力学模型
车轨模型方面，通过引入考虑实测高速轮轨蠕滑特性的轮轨接触关系，建立适用于400 km · h-1运行工况的车辆-轨道空间动力学模型。其中，车辆模型和轨道模型分别基于多刚体动力学原理和有限单元理论构建，并通过轮轨接触关系形成耦合系统。轮轨接触模型方面，轮轨接触几何关系采用迹线法求解，轮轨法向力采用Hertz非线性接触理论求解，切向蠕滑力采用改进后的Polach蠕滑模型计算，并通过高速轮轨接触关系的实测数据对轮轨蠕滑模型特征参数进行修正［22］。
1.2　轨道-桥梁结构有限元模型
为深入分析高速铁路简支梁引起的轨道周期性不平顺影响特征，建立精细化轨道-桥梁结构有限元模型，如图1所示。该模型包含钢轨、扣件系统、承轨台、轨道板、自密实混凝土层、底座板及箱梁等结构，其中简支箱梁采用中国高速铁路32 m简支梁“通桥〔2016〕2322A”系列标准梁型，梁长32.6 m，梁间距0.1 m，模型计算长度为15跨。
无砟轨道-桥梁结构的层间连接方式对模型精度具有决定性影响。考虑到无砟轨道混凝土层在静载作用下连接紧密且相对滑动可忽略，采用Tie连接方式确保相邻表面变形协调，同时保留节点转动自由度，以更贴近实际工况。无砟轨道底座板与桥梁表面的连接刚度相对较低，在外力作用下可能出现离缝和滑移现象，因此采用硬接触约束法向变形以防止穿透，并结合考虑弹性滑移变形的库仑摩擦模型描述切向作用。这种层间连接设置能够准确模拟无砟轨道-桥梁各结构层的连接状态，有效反映层间状态演化与动态变形协调特性，适用于时速400 km及更高速度等级高速铁路线桥结构的仿真分析［23］。
1.3　模型验证
为验证所建轨道-桥梁结构有限元模型的计算精度，模拟某高速铁路的实际运营工况，并以350 km · h-1速度下桥梁跨中的动力响应作为对比指标，结果见表1。由表1可知：仿真计算结果与现场实测数据较为接近，桥梁跨中加速度和位移响应的相对误差基本控制在5%左右，最大相对误差仅为5.4%（在工程误差允许范围之内），充分验证了所构建有限元模型具有较高的预测精度与良好的计算可靠性。
进一步结合前文建立的考虑实测更高速度等级轮轨接触关系的车辆-轨道动力学模型，采用全过程交叉迭代法［24］分别求解车轨动力学模型和轨道-桥梁有限元模型，通过轮轨接触处力的平衡条件和位移协调条件控制迭代收敛，实现400 km · h-1高速铁路车辆-轨道-桥梁动力耦合系统的整体仿真计算。
2　简支梁引起的轨道周期性不平顺
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简支梁引起的轨道周期性不平顺主要是由桥梁徐变上拱造成的，因此仅对梁体徐变引起的轨道周期性不平顺展开分析。
2.1　梁体徐变变形模拟
采用正弦曲线拟合梁体徐变变形，并通过1阶可导的正弦曲线实现跨间平滑连接。梁体徐变变形的正弦模拟曲线表达式如下。
y=AsinπxL1                            0≤x≤L1L2AL1sinπ(x-L1)L2       L1≤x≤L1+L2
式中：y为桥梁徐变变形；x为线路里程；A为徐变变形幅值；L1为简支梁的计算跨径；L2为相邻跨简支梁相邻支座的中心距。
桥梁徐变变形幅值为10 mm的变形模拟曲线如图2所示。
2.2　轨道变形
基于所建立的轨道-桥梁结构有限元模型，对简支梁徐变上拱引起的轨道变形特征进行研究。将前述桥梁徐变变形曲线输入模型，设定徐变变形幅值在1~20 mm范围内，以1 mm为增量步长，逐级开展数值模拟分析。
桥梁徐变变形引起的钢轨垂向变形结果如图3所示。图3（a）为不同徐变幅值下钢轨垂向变形沿里程的变化曲线，可以看出钢轨变形随桥梁徐变幅值的增大而增大；图3（b）进一步表明，钢轨变形形态与桥梁徐变变形曲线基本吻合，且跨中位置的钢轨变形峰值略低于桥梁徐变上拱峰值，当桥梁徐变峰值为10 mm时，钢轨上拱峰值约为9.86 mm。
图4进一步展示了15跨简支梁桥不同位置处钢轨变形峰值的分布情况。可以看出，受边界效应的影响，首尾跨段的变形峰值与中间跨段存在一定差异。后续分析将选取峰值相对稳定的中间跨钢轨变形作为研究基准。
图5展示了钢轨垂向变形峰值随桥梁徐变变形的变化曲线。由图可知，钢轨变形峰值随桥梁徐变幅值的增大近似呈线性增长，且钢轨变形峰值略低于桥梁徐变幅值。结合表2中不同桥梁徐变幅值下的数据变化规律，可以进一步明确二者之间的关系。同时可见，随着徐变变形幅值的增大，钢轨与路基之间的沉降差也逐渐增大。
至此，已明确简支梁桥徐变变形所引起的轨道不平顺的周期性变化规律。下文将重点分析适用于动力学仿真的轨道周期性不平顺仿真单元。
2.3　桥上轨道周期性不平顺仿真单元
目前，车轨动力学仿真计算中多直接采用正弦函数模拟周期性不平顺，这一做法存在一定的局限。杨飞等［17］提出采用高斯函数来表征各类轨道周期性不平顺。为验证本文基于有限元模型映射得到的轨道周期性不平顺波形的精确性，以高斯函数生成的结果作为参照，与实测轨道不平顺数据进行对比分析。
选取典型实测不平顺数据，消除基线漂移后统一调整幅值至相同基准，并对2种方法的计算结果进行对比分析，如图6所示。结果表明，虽然2种方法与实测不平顺在整体波长分布上具有一致性，但其变化特性存在显著差异。高斯函数拟合在接近峰值区域表现出显著的快速变化特性，导致不平顺幅度的急剧增减，这种集中的不平顺特征将对车辆产生更为剧烈的冲击作用，即可能导致车-轨耦合振动分析结果偏于保守。与高斯函数拟合方法相比，本文提出的轨道周期性不平顺计算单元与实测轨道不平顺波形变化具有更高的一致性。该方法能够更准确地反映轨道不平顺的演变规律，避免了高斯函数拟合在峰值区域产生的急剧变化特性，从而减少车-轨耦合振动分析中的保守性误差。
通过定量分析发现，图5所示不同徐变幅值条件下的钢轨变形曲线呈现良好的线性关系。基于此，选取幅值为1 mm的单个32 m波长轨道不平顺作为轨道周期性不平顺的基本计算单元，在仿真中，只需复制并乘以所需幅值即可得到所需的周期性轨道不平顺。
3　周期不平顺对车体响应影响
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3.1　周期性不平顺引起的响应
将桥梁徐变上拱导致的钢轨变形作为轨道不平顺输入至基于实测轮轨蠕滑特性的400 km · h-1高速铁路车-线-桥动力模型中，分析桥上轨道周期性不平顺对列车车辆动力学响应的影响。在400 km · h-1恒定运行条件下，对不同周期性不平顺幅值情形进行了对比仿真分析。
图7展示了不同周期性不平顺幅值条件下的车体响应特性。图7（a）为车体时程响应结果，从图中可以看出，车体响应呈现与轨道不平顺相对应的周期性变化规律，且在32 m的周期性里程范围内出现双峰值的现象。图7（b）为垂向振动加速度峰值与轨道不平顺幅值的变化规律，进一步表明随轨道周期性不平顺幅值的增加，车体响应呈现持续增长趋势，且不平顺幅值与车体响应之间存在显著的线性关系。
图8为不同幅值下的车体响应功率谱密度对比，从图中可以看出，谱峰值在32 m波长的倍频处显著，其中以2倍频（16 m）处的峰值最为突出，解释了图7（a）中车体响应在32 m波长范围内出现双峰值的现象。
图9为轨道周期性不平顺幅值为10 mm时不平顺与车体响应对比。结果表明，两者的波动特性呈现高度一致性。在轨道不平顺经历一个32 m桥梁跨度波长的过程中，垂向加速度表现出2个约16 m的特征波形。观察发现轨道不平顺波形相对于车体响应存在相位滞后现象，这主要归因于车辆前轮与轨道不平顺初次接触时，车体重心尚未到达对应的轨道不平顺位置。
3.2　叠加随机不平顺响应
为模拟真实的轨道状态，进一步将桥梁徐变上拱导致的钢轨变形与轨道随机不平顺进行耦合叠加，作为仿真输入条件进行动力学计算，研究周期性不平顺对车体动力响应的影响特性。其中，分别仅考虑随机不平顺，以及轨道随机不平顺叠加幅值为5，10和15 mm周期性不平顺的计算工况，得到不同周期性不平顺幅值下的车体垂向加速度响应如图10所示。分析表明车体响应呈现与轨道不平顺相对应的周期性变化特征，且响应峰值随周期性不平顺幅值的增加呈显著增大趋势。
图11为叠加不同周期性不平顺的车体响应功率谱密度对比，图12为轨道不平顺幅值为10 mm下的轨道不平顺与车体响应功率谱密度对比。从图中可以看出，响应谱呈现以32 m波长为基频的倍频特征。值得注意的是，虽然轨道不平顺在32 m波长处表现出最大谱峰，但车体响应的最大谱峰却出现在2倍频（16 m波长）处，表明车体对16 m波长的激励表现出更高的响应敏感性，该结论与未叠加随机不平顺时的分析结果保持一致。
3.3　垂向振动加速度与轨道不平顺对应关系
为分析车体垂向振动加速度与轨道不平顺的峰值分布特征，对两者在同一里程范围内的时程响应进行对比分析。图13为轨道周期性不平顺幅值为10 mm时的时程对比结果。可以看到，轨道不平顺与车体垂向加速度的峰值呈现显著的相关性。
进一步以单跨桥梁覆盖里程为统计单元，对两者的对应峰值进行统计分析，研究实际轨道不平顺条件下车体垂向加速度与轨道不平顺的峰值分布规律，结果如图14所示。分析发现，车体垂向加速度随叠加周期性不平顺幅值的增加呈现整体增长趋势，且在研究的轨道不平顺幅值范围内，垂向加速度与轨道不平顺峰值表现出良好的线性相关特性。
4　结论
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本文通过建立精细化轨道-桥梁结构有限元模型和车辆-轨道耦合动力学仿真模型，系统研究了桥梁徐变上拱诱发轨道周期性不平顺的内在机理，并深入探讨了400 km · h-1高速铁路桥上轨道周期性不平顺对列车运行动力性能的影响规律，主要结论如下。
（1）桥梁徐变变形的增大会直接引起钢轨变形的加剧，二者幅值呈现较为显著的线性相关性，且钢轨变形的峰值始终略低于桥梁徐变的幅值，这一规律为轨道不平顺的预测和控制提供了理论依据。
（2）与传统高斯函数拟合方法相比，本文提出的轨道周期性不平顺计算单元与实测轨道不平顺波形变化具有更高的一致性。该方法能够更准确地反映轨道不平顺的演变规律，避免了高斯函数拟合在峰值区域产生的急剧变化特性，从而减少车轨耦合振动分析中的保守性误差。
（3）在400 km · h-1运行条件下，轨道周期性不平顺会导致车体响应频谱在32 m波长的各倍频处出现明显峰值，最大谱峰出现在2倍频（16 m波长）处，即车体对16 m波长的激励更为敏感，导致车体动力响应在32 m波长范围内呈现双峰值特征。
（4）当周期性不平顺与随机不平顺叠加时，车体响应仍表现出以32 m波长为基频的倍频特征，且最大谱峰依然出现在16 m波长处。这表明在复合不平顺条件下周期性不平顺仍起主导作用，其影响不容忽视。
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2026年第47卷第2期
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doi: 10.3969/j.issn.1001-4632.2026.02.08
  • 接收时间：2025-11-19
  • 首发时间：2026-06-03
  • 出版时间：2026-03-01
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  • 收稿日期：2025-11-19
  • 修回日期：2026-02-09
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    1．中国铁道科学研究院集团有限公司 铁道建筑研究所，北京100081
    2．中国铁道科学研究院集团有限公司 高速铁路轨道系统全国重点实验室，北京100081
    3．北京铁科首钢轨道技术股份有限公司，北京102206

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闫子权（1985—），男，河北宁晋人，研究员，博士。E-mail：
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2种不同金属材料的力学参数
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Number of
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鹅膏菌科Amanitaceae 2 11 5.26 鹅膏菌属 Amanita 10 4.78
小菇科 Mycenaceae 2 12 5.74 丝盖伞属 Inocybe 5 2.39
多孔菌科 Polyporaceae 8 14 6.70 蜡蘑属 Laccaria 5 2.39
红菇科 Russulaceae 3 23 11.00 小皮伞属 Marasmius 6 2.87
小菇属 Mycena 11 5.26
光柄菇属 Pluteus 5 2.39
红菇属 Russula 17 8.13
栓菌属 Trametes 5 2.39
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