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Article(id=1203753459448259554, tenantId=1146029695717560320, journalId=1146123166801305609, issueId=1203753457208504777, articleNumber=null, orderNo=null, doi=10.12404/j.issn.1671-1815.2308581, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=research-article, receivedDate=1698854400000, receivedDateStr=2023-11-02, revisedDate=1729094400000, revisedDateStr=2024-10-17, acceptedDate=null, acceptedDateStr=null, onlineDate=1764926789390, onlineDateStr=2025-12-05, pubDate=1737129600000, pubDateStr=2025-01-18, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1764926789390, onlineIssueDateStr=2025-12-05, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1764926789390, creator=13701087609, updateTime=1764926789390, updator=13701087609, issue=Issue{id=1203753457208504777, tenantId=1146029695717560320, journalId=1146123166801305609, year='2025', volume='25', issue='2', pageStart='439', pageEnd='878', issueExtLink='null', onlineDate='null', pubDate='null', beforeIssueId=null, nextIssueId=null, price=null, status=1, issueComplete=1, articleOrder=1, issueType=-1, specialIssue=null, createTime=1764926788856, creator=13701087609, updateTime=1764928745558, updator=13701087609, preIssue=null, nextIssue=null, ext={EN=IssueExt(id=1203761664261858014, tenantId=1146029695717560320, journalId=1146123166801305609, issueId=1203753457208504777, language=EN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=), CN=IssueExt(id=1203761664261858015, tenantId=1146029695717560320, journalId=1146123166801305609, issueId=1203753457208504777, language=CN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=)}, issueFiles=null}, startPage=795, endPage=805, ext={EN=ArticleExt(id=1203753459850912751, articleId=1203753459448259554, tenantId=1146029695717560320, journalId=1146123166801305609, language=EN, title=Pedestrian Response on Large-Span Single-Level Rail-Cum-Road Bridge Considering the Coupling Effect of Pedestrian-Road Vehicle-Train-Bridge System, columnId=1156262728772735295, journalTitle=Science Technology and Engineering, columnName=Papers·Traffics and Transportations, runingTitle=null, highlight=null, articleAbstract=

With the continuous integration of urban Bridges into a variety of traffic forms, various traffic vehicles and pedestrians interfere with each other, affecting the safety and comfort of pedestrians. To research the pedestrian response on single-level rail-cum-road bridges, a pedestrian-road vehicle-train-bridge coupling vibration model was established. The acceleration difference between the bridge panel and pedestrian SMD model was researched, and the influence of trains and road vehicle passing the bridge in different ways on pedestrians was calculated. The results show that, compared with bridge panel, the amplitude of acceleration fluctuation of pedestrian SMD model is smaller, but the walking pedestrian model may experience abrupt and significant acceleration peaks. Each moving subsystem in the coupling model has a speed-sensitive interval, in which the pedestrian acceleration increases significantly. The further vehicles are away from the bridge center, the greater the acceleration of pedestrians become. When train and road vehicle pass the bridge simultaneously, the peak acceleration of pedestrian caused by them will be superimposed, and the peak acceleration caused by road vehicles increases significantly due to the train.

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随着城市桥梁不断并入多种交通形式,各种交通工具与行人之间相互干扰,对行人行走的安全与舒适均产生影响。为研究公铁平层桥梁上的行人响应,建立了行人-汽车-列车-桥梁耦合振动模型。对比分析了桥面板加速度与行人SMD(spring-mass-damp)模型的差异,计算了列车、汽车以不同的方式通过桥梁时的行人响应。结果表明,相较于桥面板加速度,行人SMD模型加速度的波动幅度更小,但行走的行人模型会出现突变的远大于波动区间的加速度峰值。行人-汽车-列车系统中各子系统均存在速度敏感区间,该区间内行人加速度响应显著增加。汽车与列车离桥梁中心线越远,引起的行人加速度响应越大。列车与汽车同时行驶通过桥梁时,二者引起的行人的加速度峰值会相互叠加,列车对汽车引起的行人加速度的峰值提升显著。

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何佳骏(1994—),男,汉族,四川成都人,博士,工程师。研究方向:桥梁动力学。E-mail:。

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何佳骏(1994—),男,汉族,四川成都人,博士,工程师。研究方向:桥梁动力学。E-mail:。

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何佳骏(1994—),男,汉族,四川成都人,博士,工程师。研究方向:桥梁动力学。E-mail:。

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Engineering Mecha-nics, 2016, 33(4): 130-135., articleTitle=Wind tunnel test on aerodynamic characteristics of vehicle-bridge system for six-track double-deck steel-truss railway bridge, refAbstract=null)], funds=[Fund(id=1203787169035956480, tenantId=1146029695717560320, journalId=1146123166801305609, articleId=1203753459448259554, awardId=2021YFB3704404, language=CN, fundingSource=国家重点研发计划(2021YFB3704404), fundOrder=null, country=null)], companyList=[AuthorCompany(id=1203787155870036558, tenantId=1146029695717560320, journalId=1146123166801305609, articleId=1203753459448259554, xref=1, ext=[AuthorCompanyExt(id=1203787155882619471, tenantId=1146029695717560320, journalId=1146123166801305609, articleId=1203753459448259554, companyId=1203787155870036558, language=EN, country=null, province=null, city=null, postcode=null, companyName=null, departmentName=null, remark=1 Southwest Municipal Engineering Design and Research Institute of China, Chengdu 610299, China), AuthorCompanyExt(id=1203787155891008080, tenantId=1146029695717560320, journalId=1146123166801305609, articleId=1203753459448259554, companyId=1203787155870036558, language=CN, country=null, province=null, city=null, postcode=null, companyName=null, departmentName=null, remark=1 中国市政工程西南设计研究总院有限公司, 成都 610299)]), AuthorCompany(id=1203787156004254303, tenantId=1146029695717560320, journalId=1146123166801305609, articleId=1203753459448259554, xref=2, ext=[AuthorCompanyExt(id=1203787156008448607, tenantId=1146029695717560320, journalId=1146123166801305609, articleId=1203753459448259554, companyId=1203787156004254303, language=EN, country=null, province=null, city=null, postcode=null, companyName=null, departmentName=null, remark=2 China Railway Eryuan Engineering Group Co., Ltd., Chengdu 610031, China), AuthorCompanyExt(id=1203787156016837216, tenantId=1146029695717560320, journalId=1146123166801305609, articleId=1203753459448259554, companyId=1203787156004254303, language=CN, country=null, province=null, city=null, postcode=null, companyName=null, departmentName=null, remark=2 中铁二院工程集团有限责任公司, 成都 610031)])], figs=[ArticleFig(id=1203787160999670727, tenantId=1146029695717560320, journalId=1146123166801305609, articleId=1203753459448259554, language=EN, label=Fig.1, caption=SMD model of pedestrian, figureFileSmall=g2vneuFIXpmg97UDFBXv4g==, figureFileBig=WvLK+ROjrDLixy38SCSz1Q==, tableContent=null), ArticleFig(id=1203787161125499855, tenantId=1146029695717560320, journalId=1146123166801305609, articleId=1203753459448259554, language=CN, label=图1, caption=行人SMD模型图

mp为行人质量;mp1、mp2为行人上下部的质量;kp、cp分别为行人的竖向刚度和阻尼

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tenantId=1146029695717560320, journalId=1146123166801305609, articleId=1203753459448259554, language=CN, label=图16, caption=列车与汽车共同作用下的行人加速度频域分析, figureFileSmall=4RDMJ/cgyGafT5ClfFFI9g==, figureFileBig=AG52D3D2pGZ0N5b6CQ/plg==, tableContent=null), ArticleFig(id=1203787166318047422, tenantId=1146029695717560320, journalId=1146123166801305609, articleId=1203753459448259554, language=EN, label=Table 1, caption=

Dynamic characteristics of the bridge model

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阶次 自振频率/Hz 振型描述
1 0.264 3 3#塔纵弯+主梁对称竖弯-1
2 0.297 3 4#塔纵弯+主梁反对称竖弯-1
3 0.300 4 3#塔横弯
4 0.345 2 4#塔横弯
5 0.438 5 反对称竖弯-1+桥塔反向纵弯
8 0.632 6 主梁对称扭转-1
), ArticleFig(id=1203787166435487939, tenantId=1146029695717560320, journalId=1146123166801305609, articleId=1203753459448259554, language=CN, label=表1, caption=

桥梁自振特性

, figureFileSmall=null, figureFileBig=null, tableContent=
阶次 自振频率/Hz 振型描述
1 0.264 3 3#塔纵弯+主梁对称竖弯-1
2 0.297 3 4#塔纵弯+主梁反对称竖弯-1
3 0.300 4 3#塔横弯
4 0.345 2 4#塔横弯
5 0.438 5 反对称竖弯-1+桥塔反向纵弯
8 0.632 6 主梁对称扭转-1
), ArticleFig(id=1203787166624231628, tenantId=1146029695717560320, journalId=1146123166801305609, articleId=1203753459448259554, language=EN, label=Table 2, caption=

Comparison of VBWW and the proposed model

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厢式货车 集装箱车
VBWW 本文方法 VBWW 本文方法
跨中竖向/mm 1.646 1.632 11.206 11.112
跨中扭转/10-3rad 0.056 0.053 0.378 0.369
), ArticleFig(id=1203787166724894932, tenantId=1146029695717560320, journalId=1146123166801305609, articleId=1203753459448259554, language=CN, label=表2, caption=

VBWW与本文计算结果对比

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厢式货车 集装箱车
VBWW 本文方法 VBWW 本文方法
跨中竖向/mm 1.646 1.632 11.206 11.112
跨中扭转/10-3rad 0.056 0.053 0.378 0.369
), ArticleFig(id=1203787166842335449, tenantId=1146029695717560320, journalId=1146123166801305609, articleId=1203753459448259554, language=EN, label=Table 3, caption=

Cases for different pedestrian velocity

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工况编号 行人速度/(m·s-1) 列车速度/(km·h-1)
1 1
2 1.5 300
3 2
), ArticleFig(id=1203787166942998751, tenantId=1146029695717560320, journalId=1146123166801305609, articleId=1203753459448259554, language=CN, label=表3, caption=

不同行人速度计算工况

, figureFileSmall=null, figureFileBig=null, tableContent=
工况编号 行人速度/(m·s-1) 列车速度/(km·h-1)
1 1
2 1.5 300
3 2
), ArticleFig(id=1203787167052050659, tenantId=1146029695717560320, journalId=1146123166801305609, articleId=1203753459448259554, language=EN, label=Table 4, caption=

Cases for different train velocity

, figureFileSmall=null, figureFileBig=null, tableContent=
工况编号 列车速度/(km·h-1) 行人速度/(m·s-1)
1 200
2 250 1.5
3 300
), ArticleFig(id=1203787167156908264, tenantId=1146029695717560320, journalId=1146123166801305609, articleId=1203753459448259554, language=CN, label=表4, caption=

不同列车速度计算工况

, figureFileSmall=null, figureFileBig=null, tableContent=
工况编号 列车速度/(km·h-1) 行人速度/(m·s-1)
1 200
2 250 1.5
3 300
), ArticleFig(id=1203787167278543088, tenantId=1146029695717560320, journalId=1146123166801305609, articleId=1203753459448259554, language=EN, label=Table 5, caption=

Cases for different train location

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工况编号 列车位置 备注
1 线路1
2 线路2 列车车速300 km/h;行人位于线路1同侧的人行道
3 线路4
), ArticleFig(id=1203787168436170995, tenantId=1146029695717560320, journalId=1146123166801305609, articleId=1203753459448259554, language=CN, label=表5, caption=

不同列车线路计算工况

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工况编号 列车位置 备注
1 线路1
2 线路2 列车车速300 km/h;行人位于线路1同侧的人行道
3 线路4
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Cases for different road vehicle velocity

, figureFileSmall=null, figureFileBig=null, tableContent=
工况编号 行人速度/(m·s-1) 汽车速度/(km·h-1) 汽车位置
1 1.5 60 车道1
2 1.5 80 车道1
3 1.5 100 车道1
4 1.5 120 车道1
), ArticleFig(id=1203787168671052023, tenantId=1146029695717560320, journalId=1146123166801305609, articleId=1203753459448259554, language=CN, label=表6, caption=

不同汽车速度的计算工况

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工况编号 行人速度/(m·s-1) 汽车速度/(km·h-1) 汽车位置
1 1.5 60 车道1
2 1.5 80 车道1
3 1.5 100 车道1
4 1.5 120 车道1
), ArticleFig(id=1203787168767521019, tenantId=1146029695717560320, journalId=1146123166801305609, articleId=1203753459448259554, language=EN, label=Table 7, caption=

Cases for different road vehicle location

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工况编号 汽车车道 车速/(km·h-1)
1 车道1 100
2 车道2 100
3 车道3 100
), ArticleFig(id=1203787168855601403, tenantId=1146029695717560320, journalId=1146123166801305609, articleId=1203753459448259554, language=CN, label=表7, caption=

不同汽车位置计算工况

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工况编号 汽车车道 车速/(km·h-1)
1 车道1 100
2 车道2 100
3 车道3 100
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考虑行人-汽车-列车-桥耦合振动的大跨度公铁平层桥梁行人响应分析
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何佳骏 1 , 李苇 1 , 黄旭 1 , 董联杰 1 , 郭维 1 , 徐昕宇 2
科学技术与工程 | 论文·交通运输 2025,25(2): 795-805
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科学技术与工程 | 论文·交通运输 2025, 25(2): 795-805
考虑行人-汽车-列车-桥耦合振动的大跨度公铁平层桥梁行人响应分析
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何佳骏1 , 李苇1, 黄旭1, 董联杰1, 郭维1, 徐昕宇2
作者信息
  • 1 中国市政工程西南设计研究总院有限公司, 成都 610299
  • 2 中铁二院工程集团有限责任公司, 成都 610031

    • 何佳骏(1994—),男,汉族,四川成都人,博士,工程师。研究方向:桥梁动力学。E-mail:。

Pedestrian Response on Large-Span Single-Level Rail-Cum-Road Bridge Considering the Coupling Effect of Pedestrian-Road Vehicle-Train-Bridge System
Jia-jun HE1 , Wei LI1, Xu HUANG1, Lian-jie DONG1, Wei GUO1, Xin-yu XU2
Affiliations
  • 1 Southwest Municipal Engineering Design and Research Institute of China, Chengdu 610299, China
  • 2 China Railway Eryuan Engineering Group Co., Ltd., Chengdu 610031, China
出版时间: 2025-01-18 doi: 10.12404/j.issn.1671-1815.2308581
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摘要
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随着城市桥梁不断并入多种交通形式,各种交通工具与行人之间相互干扰,对行人行走的安全与舒适均产生影响。为研究公铁平层桥梁上的行人响应,建立了行人-汽车-列车-桥梁耦合振动模型。对比分析了桥面板加速度与行人SMD(spring-mass-damp)模型的差异,计算了列车、汽车以不同的方式通过桥梁时的行人响应。结果表明,相较于桥面板加速度,行人SMD模型加速度的波动幅度更小,但行走的行人模型会出现突变的远大于波动区间的加速度峰值。行人-汽车-列车系统中各子系统均存在速度敏感区间,该区间内行人加速度响应显著增加。汽车与列车离桥梁中心线越远,引起的行人加速度响应越大。列车与汽车同时行驶通过桥梁时,二者引起的行人的加速度峰值会相互叠加,列车对汽车引起的行人加速度的峰值提升显著。

公铁平层桥梁  /  行人-桥耦合振动  /  车-桥耦合振动  /  动力分析  /  行人响应

With the continuous integration of urban Bridges into a variety of traffic forms, various traffic vehicles and pedestrians interfere with each other, affecting the safety and comfort of pedestrians. To research the pedestrian response on single-level rail-cum-road bridges, a pedestrian-road vehicle-train-bridge coupling vibration model was established. The acceleration difference between the bridge panel and pedestrian SMD model was researched, and the influence of trains and road vehicle passing the bridge in different ways on pedestrians was calculated. The results show that, compared with bridge panel, the amplitude of acceleration fluctuation of pedestrian SMD model is smaller, but the walking pedestrian model may experience abrupt and significant acceleration peaks. Each moving subsystem in the coupling model has a speed-sensitive interval, in which the pedestrian acceleration increases significantly. The further vehicles are away from the bridge center, the greater the acceleration of pedestrians become. When train and road vehicle pass the bridge simultaneously, the peak acceleration of pedestrian caused by them will be superimposed, and the peak acceleration caused by road vehicles increases significantly due to the train.

single-level rail-cum-road bridge  /  pedestrian-bridge coupling vibration  /  vehicle-bridge coupling vibration  /  dynamic analysis  /  pedestrian response
何佳骏, 李苇, 黄旭, 董联杰, 郭维, 徐昕宇. 考虑行人-汽车-列车-桥耦合振动的大跨度公铁平层桥梁行人响应分析. 科学技术与工程, 2025 , 25 (2) : 795 -805 . DOI: 10.12404/j.issn.1671-1815.2308581
Jia-jun HE, Wei LI, Xu HUANG, Lian-jie DONG, Wei GUO, Xin-yu XU. Pedestrian Response on Large-Span Single-Level Rail-Cum-Road Bridge Considering the Coupling Effect of Pedestrian-Road Vehicle-Train-Bridge System[J]. Science Technology and Engineering, 2025 , 25 (2) : 795 -805 . DOI: 10.12404/j.issn.1671-1815.2308581
正文
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随着中国桥梁建设技术的进一步发展,城市桥梁不仅跨度逐步增大,往往还需要同时考虑列车、汽车以及行人的通行需求[1]。多种交通工具之间的动力干扰轻则会影响通行的舒适度,重则引起交通事故,威胁人民的生命财产安全。
对于行人而言,人行桥等结构在人群荷载下引起的振动较为容易导致行人的不适[2-4]。因此,重量更大,冲击作用更为明显的铁路以及公路车辆对行人舒适度的影响是不可忽视的。特别是对于公铁平层桥梁,其主梁宽度较大,人行道通常设置在桥梁截面两端,桥梁扭转引起的加速度效应更为明显。公铁两用桥梁通常用作跨江跨海桥梁,行人通行的需求相对薄弱。近几年城市桥梁中逐步引入公铁两用桥梁才开始加入人行道,因此相关的研究较少。
针对行人响应,近几年学者们主要从人致振动分析方法和不同桥梁的人致振动特性及控制两个方面对人行桥的人致振动进行研究。振动分析方法方面,陈舟[5]基于两自由度的行人模型编制了行人-桥耦合振动计算程序,考虑人群的质量、步频等参数的随机性,分析了人群对耦合振动的影响,并基于行人的加速度响应进行了舒适度评估。王彩峰[6]通过理论分析、数值仿真和实验测试等方法研究了动态行人-结构耦合系统的动力特性,以北京市KY人行桥为研究对象,讨论了多种人群工况下的振动响应。谢伟平等[7]基于建立的自激励人体模型,分析了人-桥竖向相互作用的变化规律及影响因素。陈得意[8]分析了行人行走方式、行走速度、行走步频等参数对人行桥结构加速度响应的影响,基于参数敏感性分析得出了对加速度影响最显著的参数,针对舒适度设计提供了建议。
针对不同类型桥梁的振动,罗晓群等[9]研究了一种单斜面索拱支承曲梁人行桥的人致振动响应特点,对比分析了调制质量阻尼器(tuning mass damping,TMD)布置前后桥梁的振动响应。周涛等[10]基于Midas与德国规范E03,分析了一斜腿刚构曲线连续梁桥的人致振动特性,进一步地,分析了TMD布置对于结构振动控制的效果。张彦玲等[11]研究了人行悬索桥上不同的吊杆形式对于桥梁自振特性和人致振动响应的影响,并进行了舒适度评估。周健华等[12]以一斜拱曲梁人行景观桥为背景,系统开展了人致振动舒适度研究和减振控制研究。
通过上述研究可以看出,中外学者已建立了较为成熟的行人-桥耦合分析模型,并将其推广到各种特殊结构形式桥梁的计算中,但讨论的重点还是行人-桥梁的耦合效应对行人舒适度的影响。随着公铁两用桥梁引入人行道,列车以及公路车辆对于行人舒适度的影响是不可忽视的,相关的研究可以协助优化桥面布置,为振动控制提供参考。
现通过建立行人-汽车-列车-桥多系统耦合振动系统,讨论公铁平层桥梁上列车以及汽车对行人动力响应的影响。研究车辆速度、车辆位置对于行人最大加速度响应的影响,分析影响机理。
1 行人-汽车-列车-桥耦合振动模型
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1.1 动态行人SMD模型
人体SMD(spring-mass-damper)模型通常分为无质量支撑和有质量支撑两种[6],分别如图1所示。两种模型均只有单一的自由度,且在进行耦合分析时都有较为良好的性能。因此,本文研究选用相对简单的无质量支撑模型进行分析。
动态行人模型参数的获取十分困难,相关的研究结果也非常有限。大多数学者建立的SMD模型参数具有相似的统计分布,但分布参数存在一定的差别[13-14]。根据文献[14]提供的参数分布,采用蒙特卡洛抽样得到行人的质量为49.38 kg、刚度为605.82 N/m、阻尼为7 612.8 (N·s)/m。考虑到本文研究中讨论的是列车与汽车对行人的影响,为消除行人运动引起的随机荷载对计算结果的影响,在行人荷载中不考虑动载因子引起的谐波动载的影响。并且,由于本文研究尚未考虑人群荷载的影响,单个行人对于公路和铁路车辆的影响是有限的,不考虑该谐波动载因子对于计算结果的影响也是有限的。
1.2 汽车模型
汽车种类繁多,轴重越大的车辆对桥梁冲击作用越明显,对行人的影响也越大[15]。因此,本文研究选取文献[15]中典型的四轴满载集装箱车作为汽车模型。车辆模型包含车体和轮胎两种刚体,各个刚体均具有3个方向的线自由度和3个方向的转动自由度,由于汽车行驶方向的振动对桥梁的竖向及横向振动几乎没有影响,因此忽略各刚体沿行驶方向的自由度以简化计算。此外,轮胎由于受到轮轴的约束,仅考虑竖向以及横向两个自由度。综上,车体共计21个自由度,如式(1)所示。车辆尺寸如图2所示,车辆动力学参数参考文献[15]。
U = Z v , Y v , φ v , θ v , φ v Z s 1 , Y s 1 , Z s 2 , Y s 2 , Z s 3 , Y s 3 , Z s 4 , Y s 4 Z s 5 , Y s 5 , Z s 6 , Y s 6 , Z s 7 , Y s 7 , Z s 8 , Y s 8
式(1)中:Z为竖向线自由度;Y为横向线自由度; φ为摇头; θ为点头; φ为侧滚;Zsi为第i个车轮的竖向自由度;Ysi为第i个车轮的横向自由度。
1.3 列车模型
桥梁的设计通行车辆为CRH3型列车。由于该桥梁截面较宽,横向刚度较大,且行人模型也仅考虑了竖向的自由度,故忽略列车模型的横向自由度以简化计算,列车自由度如式(2)所示。列车采用16节车厢编组。
U i = ( Z v i , θ v i , Z s 1 i , θ s 1 i , Z s 2 i , θ s 2 i ) , 　 i = 1,2 , …
式(2)中:Z为竖向自由度; θ为点头自由度。Zvi为第i个车厢的竖向自由度;Zs1i为第i个车厢第1个转向架的竖向自由度。
1.4 桥梁模型
选用宜宾临港长江大桥作为研究对象,该桥梁是一座大跨度公铁平层斜拉桥,共设置4线铁路以及双向6车道,人行道以及非机动车道布置在桥梁两端。桥梁宽度63.9 m,主跨跨度522 m,桥梁整体布置如图3所示,横截面布置如图4所示,为方便后续描述,从右向左对所有公路车道和列车线路进行编号。
通过有限元软件ANSYS建立桥梁的有限元模型。其中主梁、桥塔、桥墩采用Beam4单元,斜拉索采用Link8单元,二期恒载采用Mass21单元的形式加载到主梁节点。在此基础上,对桥梁进行了动力特性分析,前5阶频率以及第一阶扭转频率如表1所示。
1.5 求解方法
通过MATLAB软件调用ANSYS有限元模型导出的桥梁模型的质量与刚度矩阵,车辆以及行人的质量与刚度矩阵则基于D'Alembert原理计算。然后,通过分离迭代算法求解上述子系统的响应。对于行人、车辆同时在桥梁通行的工况而言,设定速度最快的运动子系统的求解步长为0.2 m,以兼顾计算精度和计算效率,程序计算过程如图5所示。
2 模型验证
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2.1 汽车-桥耦合振动分析
通过朱金[16]编制的风浪车桥程序VBWW(vehicle-bridge-wind-wave)来验证计算程序中的汽车-桥梁耦合振动模块。桥梁模型选用宜宾临港长江大桥,汽车模型采用一种厢式货车[17]和2.3节提及的集装箱车,汽车车速为100 km/h,路面等级为B级,汽车从车道1通过桥梁。对比了主梁跨中节点的最大竖向位移和桥梁扭转角,结果如表2所示。
由表2可见,本文程序的计算结果与VBWW的计算结果接近,本文的计算结果稍小,误差在5%以内,可以认为本文研究中汽车-桥耦合振动分析模块具有良好的计算精度。
2.2 列车-桥耦合振动分析
采用李永乐等[18]编制的风-列车-桥耦合振动分析软件BANSYS来验证计算程序中忽略横向自由度的列车模型的计算精度。桥梁模型采用宜宾临港长江大桥,列车选用16节编组的CRH3型列车,车辆以300 km/h车速从线路1通过桥梁,轨道不平顺采用德国低干扰谱。主跨跨中节点的竖向位移的时程对比如图6所示。
由图6可见,列车通过桥梁时,两个计算程序得到的跨中节点位移变化趋势接近,位移最大值的误差约为2%,可以认为本文计算程序的列车-桥耦合振动模块具有良好的计算精度。
3 计算结果分析
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3.1 行人模型的影响
部分规范在讨论行人舒适度时,通常以桥面板的加速度作为判别指标。因此,在进行工况计算之前,对比了行人模型与桥面板的加速度。考虑了列车位于线路1通过桥梁时的工况,选取了与列车同侧的人行道上行走行人的响应与主跨跨中节点作为对比,另外也添加了行人模型静止于主跨跨中的工况作为对照。列车与行人在主跨跨中相遇,列车速度300 km/h,3种工况的加速度对比如图7(a)所示,频域分析的结果对比如图7(b)所示。
由图7(a)可见,桥面板的加速度的波动幅度更大,行人模型的加速度变化幅度与之相比有一定衰减,这一现象是由于行人质量点与桥面板之间的弹簧和阻尼单元的作用。结合图7(b)可以看到,行人模型的弹簧阻尼单元削减了5~10 Hz频率区间内的能量,且对20 ~ 40 Hz频率区间内的峰值也有明显的削减作用,后者的峰值在行人开始运动后发生了进一步的衰减。值得注意的是,处于运动状态的行人模型出现了3个明显的峰值点,峰值点的大小显著高于加速度的波动区间。除峰值之外,行人模型在0~40 Hz频率区间内非峰值频率的能量明显高于桥面板,即,运动状态的行人在各个频率段均分布有能量,这可能是3个峰值点出现的原因。
进一步地,为了讨论运动行人模型出现的3个显著高于加速度波动区间的峰值,对表3中不同行人速度的工况进行了计算,得到的结果如图8所示。
由图8(a)可见,不同行人速度下均出现了明显高于正常波动区间的峰值。行人速度为1 m/s及2 m/s时峰值小于0.2 m/s2,行人速度为1.5 m/s的工况出现了大于0.4 m/s2的峰值。根据频域结果图8(b)可见,3个工况在低频区域(0~ 5 Hz)的峰值是十分接近的。最显著的区别在于峰值频率附近区域的能量分布,1.5 m/s行人速度的能量要高于其余两个工况,且在10~40 Hz区间内该工况的能量也稍高的。上述计算表明,行人模型的速度对于其吸收车桥系统振动的能量有影响。
3.2 列车对行人舒适度的影响
3.2.1 列车速度的影响
为讨论列车速度对行人舒适度的影响,计算了表4中的工况。得到不同列车速度下行人响应如图9所示。所有工况列车与行人相遇的位置均为主跨跨中,相遇的方式为对向相遇。
由图9可见,列车通过桥梁对行人响应有明显的影响。对于行人位移,列车通过时行人发生了约-0.1 m的竖向位移,并在列车通过主跨之后竖向位移出现明显震荡,这是由于桥梁的自由振动引起的;对于行人速度,通行的列车产生了一正一负两个绝对值接近的极值,行人向下以及向上的速度是由于列车进入主跨和离开主跨引起的。两个极值出现的时间分别对应于列车车头和车尾行驶至主跨跨中的时刻,两个时刻列车的车厢在主跨上的长度相近,剩余长度的车厢分别位于左右的次边跨,由此推测该现象可能与主跨与边跨的协同振动有关;对于行人加速度,列车通过桥梁产生了3次显著高于加速度波动区间的峰值,对应的时刻分别为:①车头位于跨中附近;②列车尾部位于桥塔附近;③车尾位于主跨跨中附近。并且,列车通过行人位置时,引起了波动较为强烈的高频振动。
列车速度对行人响应的影响较为明显,随着列车速度增加,行人位移与速度的极值逐渐稳定,但出现了4.1节中叙述的突变加速度峰值。对于行人位移,由于列车速度越快,列车在主跨上的时间越短,位移极大值的持续时间越短,但由于对桥梁的冲击越强,极大值随速度的增加而增大;对于行人速度,其极值随车速的变化不明显,250 km/h与300 km/h工况的结果较为接近;对于加速度,列车的冲击作用随车速增加而发生明显变化,在较低的速度下(200 km/h、250 km/h)加速度的两个极值接近且首个加速度极值稍大,而在300 km/h车速下,行人的第二个加速度极值显著增大,接近0.4 m/s2。值得注意的是,列车经过桥梁后引起的振动在车速为250 km/h时最为明显,具有3个工况中最大的振幅,且在计算时长内未出现明显的衰减。
由图9可以看出,随着车速的增加,行人各项响应的极值也在增大。但列车速度对行人加速度的影响规律不明确,例如,当列车速度从200 km/h增加至250 km/h时,行人加速度最大值增幅0.001 1 m/s2;当列车速度从250 km/h增加至300 km/h时,行人最大加速度增幅0.293 5 m/s2。为进一步讨论列车速度对行人竖向振动频率的影响,增加了列车车速为225 km/h以及275 km/h的工况,并对各工况下行人的加速度时程进行了频域分析,得到的结果如图10所示。
由图10(a)可以看到,频域分析的结果可以分为4个阶段,标记为S1~S4。S1阶段具有最大的幅度,峰值幅度超过40 m/s2。S2阶段中各工况均具有3个峰值幅度,其所在的频率区间分别标记为S2-1,S2-2及S2-3,各工况的峰值幅度在10~20 m/s2。随着频率的增加,各车速的峰值差距越小。S3阶段各工况的幅度峰值更小,为3 m/s2左右。S4阶段几乎观测不到明显的峰值。整体而言,可以认为列车对行人产生影响的频率大约在10 Hz以内。
由图10(b)可以看到2个主要的峰值,即 f 1 - i以及 f 2 - i(其中i取值为1~5,分别表示车速从200~300 km/h的工况),各工况峰值幅度对应的频率也标记于图中。由图10(b)可知,随着车速增加,首个频率 f 1 - i峰值的幅度也在增大,该频率对应的是列车对主跨的冲击频率,因此车速越大,频率越高,该频率的能量越大。值得注意的是,第二个峰值的幅度并不随车速的增加而增加,250 km/h车速下峰值最大,幅度超过100 m/s2,对应的频率f2-3为0.267 4,该频率与桥梁主梁的一阶竖弯频率接近,桥梁主梁可以从列车冲击荷载中吸收更多的能量。这一现象也能解释在车速为250 km/h的工况下列车通过桥梁之后行人振动更为明显的现象。
3.2.2 列车线路的影响
列车通过时对行人的影响来自其引起的主梁弯扭效应对行人的影响的叠加。该叠加效应与列车和行人的位置均有关。本节讨论了不同的列车线路对行人的影响,计算工况如表5所示,行人响应如图11所示。
由图11可见,引起行人响应最大的为线路1。另外两条线路中,线路2引起的位移和速度响应更为明显,而线路4引起的加速度响应更为明显。这些现象均可由列车引起的桥梁竖弯和扭转的叠加效应来解释。与行人同侧的线路由于桥梁扭转和竖弯会对行人产生同向的竖向位移和速度,因此两者的位移和速度均大于线路4。值得注意的是,由于列车在驶入主跨之前位于次边跨,次边跨的下弯导致位于主跨的行人产生向上的位移。线路4的该位移稍大,这是由于列车位于线路4时,主跨的扭转也会产生向上的挠度。对于图11(c)的加速度响应而言,外侧线路(线路1、线路4)在5.3、7.8、10.6 s左右产生了大小接近方向相反的加速度。可以推断此处的加速度主要由桥梁扭转引起,但由于线路1列车产生的扭转与桥梁竖弯引起的加速度同向,故线路1产生的加速度更大。值得注意的是,列车通过桥梁后,3个工况下行人各项响应的震荡趋势接近,可以推断此时桥梁扭转产生的影响迅速消耗,响应的震荡主要由主梁竖弯引起。
3.3 汽车对行人舒适度的影响
相较于列车而言,汽车轴重较小,但公路车道距离桥梁中心线更远。由4.2节内容可知,距离行人更近的车辆引起的行人响应更为明显,因此汽车也可能会对行人舒适度产生影响。
3.3.1 汽车速度的影响
计算表6中的工况,以讨论汽车速度对于行人舒适度的影响,两者相遇位置为主跨跨中,计算结果如图12所示。
由图12可以看到汽车速度会对行人响应产生明显影响,车速从60 km/h增加至100 km/h时,行人的最大加速度从0.021 3增加至0.128 8。但100 km/h与120 km/h的工况行人加速度相同。为进一步分析该现象,补充了车速为70~150 km/h的工况,各工况下行人的加速度最大值如图13所示。
由图13可以看到,汽车速度在100~120 km/h之间时,行人加速度的最大值显著增加。行人加速度可分为3个档次:车速为60~70 km/h时,行人加速度最大值在0.02 m/s2左右;车速为80~90 km/h以及130~150 km/h时,行人最大加速度约为0.06 m/s;车速在100~120 km/h时,行人最大加速度在0.11~0.12。可以认为,由于行人-汽车-桥系统复杂的耦合效应,在某个车速敏感区间内,行人的最大加速度有显著增加。
3.3.2 汽车车道的影响
计算了表7中的工况以讨论汽车位于不同车道对行人的影响。行人位于汽车车道同侧的人行道,行人速度1.5 m/s,计算结果如图14所示。
由图14可见,各工况下行人加速度变化趋势接近,且在23.2~26.9 s存在明显的波动。越靠近外侧车道,汽车引起的加速度的最大值越大,最外侧车道比最内侧车道的加速度最大值增加了约40%。
3.4 列车与汽车同时作用的影响
本节考虑了列车与汽车同时通过桥梁时对行人响应的影响,根据上文对计算工况进行了设置。其中列车速度为300 km/h,位于线路1;汽车速度为100 km/h,位于车道1;行人速度为1.5 m/s,位于汽车和列车的同侧车道。三者在主跨跨中相遇,行人加速度响应如图15所示,汽车与列车分别与行人相遇的结果也展示在图15中。3个工况的频域分析结果对比如图16所示。
由图15可见,汽车与列车共同作用下行人的加速度共出现了3个峰值,分别标记为P1、P2和P3。结合汽车、列车分别与行人相遇的结果,可以认为P1由汽车引起,P2和P3由列车引起。值得注意的是,列车与汽车的耦合作用加强了各自峰值的大小:对于汽车而言,列车使P1的值从0.128 9增加至0.202 5,增幅约57%;汽车使P2的值从0.184 2增加至0.192 9,增幅约4.7%,使P3的值从0.411 6增加至0.413 2,增幅约0.3%。
由图16可以看出,列车与汽车同时作用的工况对于大于10 Hz的高频区间的影响十分有限,相对于列车、汽车分别与行人相遇的工况,主要是增大了1~3 Hz范围内的能量,这部分区间是行人振动频率的敏感区间,因此行人的加速度得到了进一步的增强。
4 结论
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基于建立的行人-汽车-列车-桥耦合振动模型,分析对比了行人SMD模型与桥面板的振动特点,讨论了列车与汽车通过桥梁时行人的响应,得到如下结论。
(1)相较于桥面板加速度,行人SMD模型的加速度波动稍小,但运动状态的行人模型会出现显著的加速度峰值。行人速度存在一定的敏感速度区间,该区间内行人的加速度峰值显著增加。
(2)高速列车会显著增加行人的加速度,200 km/h及250 km/h车速下行人最大加速度在0.1 m/s2左右,在300 km/h车速下行人最大加速度超过0.4 m/s2。列车引起的行人加速度的能量主要分布在0~10 Hz。
(3)列车在与行人同侧线路行驶时引起更大的行人位移与速度,在外侧线路行驶时引起行人更大的加速度响应。
(4)汽车速度为100~120 km/h为速度敏感区间,汽车在该速度区间内对行人加速度的影响显著增加。最外侧车道引起的最大行人加速度较最内侧车道增加约40%,引起的加速度最大值约为0.1 m/s2。
(5)列车与汽车引起的加速度峰值会相互叠加,从而引起更大的加速度响应。列车对汽车引起的峰值加速度提升更为明显,增幅超过50%。
基金
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  • 国家重点研发计划(2021YFB3704404)
文献
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doi: 10.12404/j.issn.1671-1815.2308581
  • 接收时间：2023-11-02
  • 首发时间：2025-12-05
  • 出版时间：2025-01-18
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  • 收稿日期：2023-11-02
  • 修回日期：2024-10-17
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国家重点研发计划(2021YFB3704404)
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    1 中国市政工程西南设计研究总院有限公司, 成都 610299
    2 中铁二院工程集团有限责任公司, 成都 610031
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2种不同金属材料的力学参数
科
Family		 属数
Number of
genus		 种数
Number of
species		 占总种数比例
Percentage of
total species (%)		 属
Genus		 种数
Number of
species		 占总种数比例
Percentage of total
species (%)
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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