引 en
×

分享给微信好友或者朋友圈

使用微信“扫一扫”功能。

车-简支梁桥耦合振动系统中全局最大动力响应研究*

  • 任剑莹1,2

    机 构：

    1. 石家庄铁道大学 省部共建交通工程结构力学行为与系统安全国家重点实验室,石家庄 050043

    2. 石家庄铁道大学 工程力学系,河北省石家庄 050043

    ×
  • ，付小莲3

    机 构：

    3. 中铁九桥工程有限公司,江西省,九江 332004

    ×
  • ，李韶华1

    机 构：

    1. 石家庄铁道大学 省部共建交通工程结构力学行为与系统安全国家重点实验室,石家庄 050043

    ×
  • ，刘旌1

    机 构：

    1. 石家庄铁道大学 省部共建交通工程结构力学行为与系统安全国家重点实验室,石家庄 050043

    ×

1. 石家庄铁道大学 省部共建交通工程结构力学行为与系统安全国家重点实验室,石家庄 050043；
2. 石家庄铁道大学 工程力学系,河北省石家庄 050043；
3. 中铁九桥工程有限公司,江西省,九江 332004；

The Global Maximum Dynamic Responses of Vehicle-Simply Supported Bridge Coupling System *

  • Ren Jianying1,2

    Affiliation：

    1. State Key Laboratory of Mechanical Behavior and System Safety of Traffic Engineering Structures, Shijiazhuang Tiedao University, Shijiazhuang 050043 ,China

    2. Department of Engineering Mechanics, Shijiazhuang Tiedao University, Shijiazhuang 050043 ,China

    ×
  • ，Fu Xiaolian3

    Affiliation：

    3. China Railway Jiujiang Bridge Engineering Co.,Ltd, Jiujiang 332004 ,China

    ×
  • ，Li Shaohua1

    Affiliation：

    1. State Key Laboratory of Mechanical Behavior and System Safety of Traffic Engineering Structures, Shijiazhuang Tiedao University, Shijiazhuang 050043 ,China

    ×
  • ，Liu Jing1

    Affiliation：

    1. State Key Laboratory of Mechanical Behavior and System Safety of Traffic Engineering Structures, Shijiazhuang Tiedao University, Shijiazhuang 050043 ,China

    ×

1. State Key Laboratory of Mechanical Behavior and System Safety of Traffic Engineering Structures, Shijiazhuang Tiedao University, Shijiazhuang 050043 ,China；
2. Department of Engineering Mechanics, Shijiazhuang Tiedao University, Shijiazhuang 050043 ,China；
3. China Railway Jiujiang Bridge Engineering Co.,Ltd, Jiujiang 332004 ,China；

通讯作者:

李韶华,E-mail:lshsjz@163.com

中图分类号:O327;U441+.3

文献标识码:A

文章编号:1672-6553-2023-21(5)-060-009

DOI:10.6052/1672-6553-2022-057

参考文献 1
李韶华,王伟达.车辆动力学与控制研究进展 [J].动力学与控制学报,2021,19(3):1-4.LI S H,WANG W D.Research advance in vehicle dynamics and control [J].Journal of Dynamics and Control,2021,19(3):1-4.(in Chinese)
查找原文
参考文献 2
李小珍,张黎明,张洁.公路桥梁与车辆耦合振动研究现状与发展趋势 [J].工程力学,2008,25(3):230-240.LI X Z,ZHANG L M,ZHANG J.State-of-the-art review and trend of studies on coupling vibration for vehicle and highway bridge system [J].Engineering Mechanics,2008,25(3):230-240.(in Chinese)
查找原文
参考文献 3
YANG Y B,LIN C W.Vehicle-bridge interaction dynamics and potential applications [J].Journal of Sound and Vibration,2005,284:205-226.
查找原文
参考文献 4
李小珍,辛莉峰,王铭,等.车-桥耦合振动2019年度研究进展 [J].土木与环境工程学报(中英文),2020,42(5):126-138.LI X Z,XIN L F,WANG M,et al.State-of-the-art review of vehicle-bridge interactions in 2019 [J].Journal of Civil and Environmental Engineering,2020,42(5):126-138.(in Chinese)
查找原文
参考文献 5
邓露,何维,俞扬,等.公路车-桥耦合振动的理论和应用研究进展 [J].中国公路学报,2018,31(7):38-54.DENG L,HE W,YU Y,et al.Research progress in theory and applications of highway vehicle-bridge coupling vibration [J].China Journal of Highway and Transport,2018,31(7):38-54.(in Chinese)
查找原文
参考文献 6
刘星,李韶华,司春棣,等.曲线梁桥在车辆载荷下的动力响应研究 [J].动力学与控制学报,2020,18(2):50-58.LIU X,LI S H,SI C D,et al.Dynamic response of curved girder bridge under random vehicle loads [J].Journal of Dynamics and Control,2020,18(2):50-58.(in Chinese)
查找原文
参考文献 7
彭献,殷新锋,茆秋华.车-桥系统的振动分析及控制 [J].动力学与控制学报,2006,4(3):253-258.PENG X,YIN X F,MAO Q H.Vibration analysis and control of vehicle-bridge system [J].Journal of Dynamics and Control,2006,4(3):253-258.(in Chinese)
查找原文
参考文献 8
张建波,廖敬波,唐光武,等.考虑桥面随机不平顺的桥梁动态响应研究 [J].振动与冲击,2016,35(7):214-219.ZHANG J B,LIAO J B,TANG G W,et al.Research on dynamic response of bridge considering random irregularity of bridge deck [J].Vibration and Shock,2016,35(7):214-219.(in Chinese)
查找原文
参考文献 9
桂水荣,张政韬,陈水生,等.桥面不平引起车桥系统随机振动车速因素分析 [J].振动测试与诊断,2018,38(6):1223-1228,1296-1297.GUI S R,ZHANG Z T,CHEN S S,et al.Analysis of vehicle speed factors of random vibration caused by uneven bridge deck [J].Vibration Testing and Diagnosis,2018,38(6):1223-1228,1296-1297.(in Chinese)
查找原文
参考文献 10
ESMAILZADEH E,JALILI N.Vehicle-passenger-structure interaction of uniform bridges traversed by moving vehicles [J].Journal of Sound and Vibration,2003,260(4):611-635.
查找原文
参考文献 11
朱劲松,香超,祁海东.大跨度悬索桥冲击系数影响因素研究 [J].天津大学学报(自然科学与工程技术版),2019,52(4):413-422.ZHU J S,XIANG C,QI H D.Research on influencing factors of impact coefficient of long-span suspension bridge [J].Journal of Tianjin University(Science and Technology),2019,52(4):413-422.(in Chinese)
查找原文
参考文献 12
蒋培文,贺拴海,王凌波.车辆相互作用对连续梁车桥耦合振动影响分析 [J].合肥工业大学学报(自然科学版),2011,34(8):1222-1226,1236.JIANG P W,HE S H,WANG L B.Analysis of the effect of vehicle interaction on coupling vibration of continuous beam vehicle-bridge [J].Journal of Hefei University of Technology(Natural Science),2011,34(8):1222-1226,1236.(in Chinese)
查找原文
参考文献 13
蒋培文,贺拴海,宋一凡,等.简支梁车桥耦合振动及其影响因素 [J].长安大学学报(自然科学版),2013,33(1):59-66.JIANG P W,HE S H,SONG Y F,et al.Simple supported beam vehicle-bridge coupling vibration and its influencing factors [J].Journal of Changan University(Natural Science),2013,33(1):59-66.(in Chinese)
查找原文
参考文献 14
经薇,李松,李强,等.多车车桥耦合振动特性研究 [J].科学技术与工程,2017,17(6):111-116.JING W,LI S,LI Q,et al.Study on the coupling vibration characteristics of multi-vehicle axles [J].Science Technology and Engineering,2017,17(6):111-116.(in Chinese)
查找原文
参考文献 15
陈水生,李孟廷,桂水荣,等.多车激励公路简支梁车桥耦合振动响应分析 [J].武汉理工大学学报,2014,36(3):101-106.CHEN S S,LI M T,GUI S R,et al.Analysis of coupled vibration response of simple supported beam vehicle-bridge on highway with multi-car excitation [J].Journal of Wuhan University of Technology,2014,36(3):101-106.(in Chinese)
查找原文
参考文献 16
盛国刚,李传习,赵冰.多个移动车辆作用下简支梁的动力响应分析 [J].工程力学,2006(12):154-158,99.SHENG G G,LI C X,ZHAO B.Analysis of dynamic response of simply supported beams under the action of multiple moving vehicles [J].Engineering Mechanics,2006(12):154-158,99.(in Chinese)
查找原文
参考文献 17
YANG Y B,LEE Y C,CHANG K C.Effect of road surface roughness on extraction of bridge frequencies by moving vehicle[M].Mechanics and Model-Based Control of Advanced Engineering Systems.Springer,Vienna,2014:295-305.
查找原文
参考文献 18
YAU J D,YANG Y B,KUO S R.Impact response of high speed rail bridges and riding comfort of rail cars [J].Engineering Structures,1999,21(9):836-844.
查找原文
参考文献 19
王解军,张伟,吴卫祥.重型汽车荷载作用下简支梁桥的动力反应分析 [J].中南公路工程,2005,30(2):55-57.WANG J J,ZHANG W,WU W X.Dynamic response analysis of simply supported beam bridge under heavy vehicle load [J].Central South Highway Engineering,2005,30(2):55-57.(in Chinese)
查找原文
目录contents

    摘要

    本文采用四分之一车辆模型和等截面简支梁模型,建立了车-桥耦合振动计算模型,分析了车辆匀速驶过桥梁时,桥梁动挠度、动弯矩、动剪力的全局最大值及发生的位置.进一步分析计算了车速、车距和桥梁模态截断阶数对桥梁动挠度、动弯矩、动剪力全局最大值的影响.结果表明,车速对桥梁动挠度、动弯矩、动剪力全局最大值影响较大,全局最大动挠度和全局最大动弯矩均出现在跨中附近,车速不同位置也不同,而全局最大动剪力均出现在车辆下桥的梁端;两车同时上桥时,前后车车距越大,桥梁动挠度、动弯矩、动剪力全局最大值越小,当达到一定车距时,三者不再减小且与单车情况相同;为提高桥梁动挠度、动弯矩、动剪力全局最大值计算精度,桥梁模态截断阶数宜分别大于3阶、6阶、7阶.

    Abstract

    In this paper, a quarter vehicle model and a uniform cross-section simply supported beam model are used to establish a vehicle-bridge coupling system. The global maximum values and its location on the bridge of dynamic deflection, dynamic bending moment and dynamic shear force are analyzed when the vehicle travelling through the bridge at a constant speed. The effects of vehicle speed, distance between front and rear vehicles, and bridge modal truncation order on the global maximum value are further analyzed and calculated. The results show that the vehicle speed has a greater impact on the global maximum value of dynamic deflection, dynamic bending moment, and dynamic shear force of the bridge. Both the global maximum dynamic deflection and the global maximum dynamic bending moment appear in the mid-span range, the locations are different with different vehicle speeds. The global maximum dynamic shear force appears at the beam end of the vehicle exiting the bridge. when two vehicles are on the bridge at the same time, the greater the distance between the front and rear vehicles, the smaller the global maximum value of dynamic deflection, dynamic bending moment, and dynamic shear force of the bridge. When a certain distance is reached, the global maximum values are no longer reduced and are the same as the case of a single vehicle. In order to improve the calculation accuracy of the dynamic deflection, dynamic bending moment, and dynamic shear force of the bridge, the bridge modal truncation order should be greater than 3 orders, 6 orders and 7 orders, respectively.

  • 引言

  • 为了提升车辆的动力性、稳定性、平顺性和安全性，车辆动力学与控制已经成为近年来相关学者研究的重点[1]并取得了一定研究成果.而车辆行驶的过程中通过桥梁时，会引起桥梁振动，桥梁的振动反过来会影响车辆的振动，这种车-桥之间相互影响的振动，称为车-桥耦合振动[2].车、桥之间的耦合振动会加剧对桥梁结构的损伤和破坏，也会影响车辆的安全性和舒适性.因此，车-桥耦合振动[3-6]问题长期以来也一直被国内外学者和工程师广泛关注.在众多的研究中发现，车速对车-桥耦合系统中桥梁的跨中动挠度、动应力、动弯矩等响应影响较大，且车速越快，越易激发桥梁的高阶模态; 桥面不平顺对桥梁结构的冲击系数影响较大[7-13].还有学者指出在多车同时驶过桥梁时的车-桥耦合振动系统中[14-16]，车辆行驶间距接近桥梁单孔跨径时产生的冲击系数均较大，桥面不平整度对动弯矩、动剪力的影响较大，整座桥梁最大动挠度发生在跨中附近，并且当车辆位于跨中附近时出现最大动挠度.

  • 目前的研究大多集中于对桥梁跨中动态响应进行分析，而实际上桥梁各点的振动响应有较大差别.因此，本文拟建立车-桥耦合系统振动方程，计算桥梁各点动态响应，及不同车速下桥梁动挠度、动弯矩、动剪力全局最大值及最大值发生的位置，分析车速、车距、模态截断阶数对桥梁动力响应的影响情况.计算结果可为车-桥耦合振动问题的数值计算及实际桥梁的安全运营提供理论依据.

  • 1 车-桥耦合系统计算模型

  • 图1所示为考虑桥面不平顺的车-桥耦合系统模型，车辆简化为二自由度四分之一车模型，桥梁为简支梁.梁的跨度为l; 梁的单位长度质量为m; 梁截面抗弯刚度为EI; 梁竖向动挠度为w（x，t）; 桥面不平顺函数为r（t）=0.001sin（2πvt/10）; m1，m2表示轮胎质量和车体质量; k1，k2表示悬架刚度和轮胎刚度; c1，c2表示悬架阻尼系数和轮胎阻尼系数; z1，z2表示轮胎动位移和车体动位移.

  • 图1 车-桥耦合系统模型

  • Fig.1 Vehicle-bridge coupling system model

  • 车-桥耦合系统中车辆和梁的振动微分方程为:

  • m2z¨2+k2z2-z1+c2z˙2-z˙1=0
    (1)
  • m1z¨1+k2z1-z2+c2z˙1-z˙2+k1z1-w-r(t)+c1z˙1-w˙-r˙(t)]=0
    (2)
  • EI∂4w∂x4+m∂2w∂t2=-k1w+r(t)-z1+c1w˙+r˙(t)-z˙1+m1+m2gδ(x-vt)
    (3)

  • 令w（x，t）=∑i=1N φi（x）qi（t），其中N为模态截断阶数，本文中N取7，可得到车-桥耦合系统的振动方程为:

  • [M¯]U¨+[C¯]U˙+[K¯⌉U=[F]
    (4)

  • 其中:

  • U=z2, z1, q1, q2, ⋯, qNT

  		•

  • 式中:

  • Mi=∫0L mφi (x) φj (x) dx, i=j, (i, j=1, 2, ⋯, N) Ki=∫0L EIφ'''i (x) φj (x) dx, i=j, (i, j=1, 2, ⋯, N)

  • 式（4）中，[M¯]，[C¯]，[K¯]，[F]矩阵随车辆在桥梁上位置的变化而变化.本文运用Newmark-β法求解振动方程式（4）.

  • 2 车-桥耦合系统动力响应

  • 本节推导求解车-桥耦合系统振动方程的解析解[17]，将数值解与解析解进行对比，验证解的正确性.

  • 车辆作用下简支梁振动微分方程为:

  • q¨i(t)+ωn2qi(t)=2sin⁡iπvtL-m1+m2gmL+m1+m2k1m1mLqi(t)-ω(x,t)+m1+m2c1m1mLq˙i(t)-ω˙(x,t)-m1+m2k1m1mLr(t)-m1+m2c1m1m(t)r˙(t)
    (5)

  • 式中ωn为简支梁的固有频率:

  • ωn=i2π2L2EIm
    (6)

  • 式（5）可以简化为[18]:

  • q¨i(t)+ωn2qi(t)=2sin⁡iπvtL-m1+m2gmL
    (7)

  • 根据两端简支的等截面梁边界条件可得到简支梁的广义坐标:

  • qi(t)=Ai1-Bi2sin⁡iπvtL-Bisin⁡ωnt
    (8)

  • 式中:

  • Ai=-2m1+m2gL3π4EIBi=iπvLωn

  • 则简支梁动挠度的解析解为:

  • w(x,t)=∑i=1N Ai1-Bisin⁡iπxLsin⁡iπvtL-Bisin⁡ωnt
    (9)

  • 本文以湖南省某跨度为50m的预应力混凝土简支箱梁桥为例，桥梁抗弯刚度为EI=5.28×1011Nm2，单位长度质量为m=32840 kg/m.车辆参数选择重型车辆[19]:m1=190 kg，m2=10109 kg，k1=2060000N/m，c1=900Ns/m，k2=75000N/m，c2=30000Ns/m.

  • 分别采用解析和数值方法得到了桥梁跨中动挠度的时程曲线（如图2所示），表1列出了不同车速下跨中最大动挠度及相对偏差.

  • 图2 简支梁桥跨中动挠度时程曲线

  • Fig.2 Time-history curve of dynamic deflection in the middle span of a simply supported beam bridge

  • 由图2和表1可知，不同车速下跨中动挠度数值解与解析解变化趋势相同，得到的跨中动挠度最大值也基本一致，相对偏差小于3%，两种方法的分析结果吻合良好.

  • 表1 解析解与数值解所得桥梁跨中最大动挠度及相对偏差

  • Table1 Maximum dynamic deflection and relative deviation of bridge mid-span obtained from analytical and numerical solutions

  • 3 车-桥耦合系统动力响应的影响因素分析

  • 3.1 车速

  • 采用上述数值方法，分别计算了车速为5m/s、15m/s、25m/s时，简支梁跨中动挠度、动弯矩、动剪力，见图3~图5.结果表明，不同车速时，跨中动挠度、动弯矩、动剪力的变化趋势一致，随着车速的增加，以上动力响应的最大值逐渐增大.车辆在桥梁上行驶时，桥梁各个截面的动挠度、动弯矩和动剪力会在某一位置和某个瞬间达到最大值，且在车速不同时，最大值也不同.通过数值分析可以得到，不同车速下，桥梁所有截面的动挠度、动弯矩、动剪力全局最大值以及最大值所在位置.其中，桥梁动挠度、动弯矩、动剪力全局最大值定义为:

  • 图3 车速对简支梁桥跨中动挠度的影响

  • Fig.3 Mid-span dynamic deflection of bridges at different speeds

  • 图4 车速对简支梁桥跨中动弯矩的影响

  • Fig.4 Mid-span bending moment at different speeds

  • 图5 车速对简支梁桥跨中动剪力的影响

  • Fig.5 Mid-span shear force at different speeds

  • wmax=maxw(x,t),0≤x≤l,0≤t≤lv
    (10)
  • Mbmax=maxMb(x,t),0≤x≤l,0≤t≤lv
    (11)
  • Qbmax=maxQb(x,t),0≤x≤l,0≤t≤lv
    (12)

  • 其中，由材料力学知识可知，梁的弯矩、剪力与挠度的关系为:

  • Mb(x,t)=-EI∂2w(x,t)∂x2
    (13)
  • Qb(x,t)=-EI∂3w(x,t)∂x3
    (14)

  • 图6~图8为车速对桥梁动挠度、动弯矩、动剪力全局最大值及所在位置的影响情况.

  • 图6 不同车速下桥梁动挠度全局最大值及发生的位置

  • Fig.6 Global maximum deflection and location of the bridge’s dynamic deflection at different speeds

  • 由图6~图8可知，当车辆以20m/s行驶时，桥梁动挠度全局最大值最大，出现在跨中附近，距离上桥端为26m左右; 当车辆以17.5m/s行驶时，桥梁动弯矩全局最大值最大，出现的位置偏离跨中位置大约10m左右; 当车辆以17.5m/s行驶时，桥梁动剪力全局最大值最大，最大剪力始终出现在车辆下桥的位置.因此，车速不同，引起的桥梁动力响应的全局最大值不同，除了动剪力响应，其他响应发生的位置也有所不同.

  • 图7 不同车速下桥梁弯矩全局最大值及发生的位置

  • Fig.7 Global maximum value and location of bridge bending moment at different speeds

  • 图8 不同车速下桥梁剪力全局最大值及发生的位置

  • Fig.8 Global maximum value and location of bridge shear force at different speeds

  • 3.2 车距

  • 当两辆车同时上桥时，车辆参数与单车相同，前后车之间的车距分别为10m、20m、30m时，简支梁跨中动挠度、动弯矩、动剪力的时程曲线，如图9~图10所示.结果表明，随着车距的增加，桥梁跨中动挠度、动弯矩、动剪力逐渐减小.

  • 图9 不同车距下桥梁跨中动挠度

  • Fig.9 Mid-span dynamic deflection of bridge under different vehicle distances

  • 图10 不同车距下桥梁跨中动弯矩

  • Fig.10 Mid-span bending moment of bridge under different vehicle distances

  • 图11 不同车距下桥梁跨中动剪力

  • Fig.11 Mid-span shear force of bridge under different vehicle distances

  • 图12为两车同时上桥时，分别以车速5m/s、15m/s、25m/s，车距以5m为增量步长，从10m增加到60m通过桥梁，桥梁跨中动挠度、动弯矩、动剪力全局最大值变化规律.

  • 图12 不同车距下桥梁动挠度、弯矩、剪力全局最大值

  • Fig.12 Global maximum values of dynamic deflection, bending moment and shear force of bridges under different vehicle distances

  • 由图12可以看出，不同车速下车距越大，桥梁动挠度、动弯矩、动剪力全局最大值越小; 当达到临界车距时，三个最大值不再减小且与单车同车速下情况相同，说明达到临界车距后，两车对动力响应的全局最大值叠加影响消失.

  • 3.3 桥梁模态截断阶数

  • 进行数值计算时，分别截取简支梁第1阶模态、前6阶模态、前7阶模态、前8阶模态，计算桥梁的动力响应，如图13~图15所示，为车速15m/s，取不同模态截断阶数时，简支梁跨中动挠度、动弯矩、动剪力的时程曲线.结果表明，数值计算时，简支梁的模态截断阶数对跨中动挠度影响较小，若取低阶模态计算，跨中弯矩最大值计算结果偏大，跨中剪力最大值计算结果偏小.

  • 图13 模态截断阶数对桥梁跨中动挠度的影响

  • Fig.13 Mid-span dynamic deflection of bridge under different bridge modal truncation orders (MTO)

  • 图14 模态截断阶数对桥梁跨中动弯矩的影响

  • Fig.14 Mid-span bending moment of bridge under different bridge modal truncation orders (MTO)

  • 图15 模态截断阶数对桥梁跨中动剪力的影响

  • Fig.15 Mid-span shear force of bridge under different bridge modal truncation orders (MTO)

  • 图16~图18为车速为15m/s时，模态截断阶数对桥梁动挠度、动弯矩、动剪力全局最大值的影响.

  • 图16 不同桥梁模态截断阶数下桥梁动挠度全局最大值及位置

  • Fig.16 Global maximum deflection and location of deflection of bridge under different bridge modal truncation orders (MTO)

  • 图17 不同桥梁模态截断阶数下桥梁动弯矩全局最大值及位置

  • Fig.17 Global maximum value and location of bridge bending moment under different bridge modal truncation orders (MTO)

  • 由图16~图18可知，计算桥梁动挠度全局最大值时，桥梁模态截断阶数影响较小，随着截断阶数增大，动挠度全局最大值发生的位置稳定在26.8m处，为了提高桥梁动挠度计算精度，桥梁模态截断阶数应大于3阶; 计算桥梁动弯矩全局最大值时，桥梁模态截断阶数影响较大，若取低阶模态计算，计算结果偏小，动弯矩全局最大值发生的位置稳定在33.1m处，为提高精度，模态截断阶数应大于6阶; 计算桥梁动剪力全局最大值时，桥梁模态截断阶数影响较大，若取低阶模态计算，计算结果偏小，为提高精度，模态截断阶数应大于7阶，模态截断阶数对动剪力最大值发生的位置没有影响，始终在车辆下桥的梁端.

  • 图18 不同桥梁模态截断阶数下桥梁动剪力全局最大值及位置

  • Fig.18 Global maximum value and location of bridge shear force under different bridge modal truncation orders (MTO)

  • ４ 结论

  • 本文建立了考虑桥面不平顺的车-简支梁桥耦合系统模型，计算了车速、车距、桥梁模态截断阶数对桥梁动挠度、动弯矩、动剪力全局最大值及最大值发生的位置的影响.结果表明:

  • （1）车速对简支梁动挠度、动弯矩、动剪力全局最大值以及最大值发生的位置影响较大，三个最大值对应的特定车速不同.

  • （2）车距对简支梁动挠度、动弯矩、动剪力全局最大值影响较大.随着车距增大，两车对动力响应最大值的叠加效果逐渐削弱，当达到某个车距时，叠加效果消失，与单车过桥的情况相同.

  • （3）简支梁模态截断阶数对计算桥梁动挠度影响较小，对桥梁动弯矩和动剪力影响较大.因此，计算简支梁桥动挠度、动弯矩和动剪力时，其模态截断阶数宜分别大于3阶、6阶和7阶.

  • 参考文献

    • [1] 李韶华,王伟达.车辆动力学与控制研究进展 [J].动力学与控制学报,2021,19(3):1-4.LI S H,WANG W D.Research advance in vehicle dynamics and control [J].Journal of Dynamics and Control,2021,19(3):1-4.(in Chinese)

    • [2] 李小珍,张黎明,张洁.公路桥梁与车辆耦合振动研究现状与发展趋势 [J].工程力学,2008,25(3):230-240.LI X Z,ZHANG L M,ZHANG J.State-of-the-art review and trend of studies on coupling vibration for vehicle and highway bridge system [J].Engineering Mechanics,2008,25(3):230-240.(in Chinese)

    • [3] YANG Y B,LIN C W.Vehicle-bridge interaction dynamics and potential applications [J].Journal of Sound and Vibration,2005,284:205-226.

    • [4] 李小珍,辛莉峰,王铭,等.车-桥耦合振动2019年度研究进展 [J].土木与环境工程学报(中英文),2020,42(5):126-138.LI X Z,XIN L F,WANG M,et al.State-of-the-art review of vehicle-bridge interactions in 2019 [J].Journal of Civil and Environmental Engineering,2020,42(5):126-138.(in Chinese)

    • [5] 邓露,何维,俞扬,等.公路车-桥耦合振动的理论和应用研究进展 [J].中国公路学报,2018,31(7):38-54.DENG L,HE W,YU Y,et al.Research progress in theory and applications of highway vehicle-bridge coupling vibration [J].China Journal of Highway and Transport,2018,31(7):38-54.(in Chinese)

    • [6] 刘星,李韶华,司春棣,等.曲线梁桥在车辆载荷下的动力响应研究 [J].动力学与控制学报,2020,18(2):50-58.LIU X,LI S H,SI C D,et al.Dynamic response of curved girder bridge under random vehicle loads [J].Journal of Dynamics and Control,2020,18(2):50-58.(in Chinese)

    • [7] 彭献,殷新锋,茆秋华.车-桥系统的振动分析及控制 [J].动力学与控制学报,2006,4(3):253-258.PENG X,YIN X F,MAO Q H.Vibration analysis and control of vehicle-bridge system [J].Journal of Dynamics and Control,2006,4(3):253-258.(in Chinese)

    • [8] 张建波,廖敬波,唐光武,等.考虑桥面随机不平顺的桥梁动态响应研究 [J].振动与冲击,2016,35(7):214-219.ZHANG J B,LIAO J B,TANG G W,et al.Research on dynamic response of bridge considering random irregularity of bridge deck [J].Vibration and Shock,2016,35(7):214-219.(in Chinese)

    • [9] 桂水荣,张政韬,陈水生,等.桥面不平引起车桥系统随机振动车速因素分析 [J].振动测试与诊断,2018,38(6):1223-1228,1296-1297.GUI S R,ZHANG Z T,CHEN S S,et al.Analysis of vehicle speed factors of random vibration caused by uneven bridge deck [J].Vibration Testing and Diagnosis,2018,38(6):1223-1228,1296-1297.(in Chinese)

    • [10] ESMAILZADEH E,JALILI N.Vehicle-passenger-structure interaction of uniform bridges traversed by moving vehicles [J].Journal of Sound and Vibration,2003,260(4):611-635.

    • [11] 朱劲松,香超,祁海东.大跨度悬索桥冲击系数影响因素研究 [J].天津大学学报(自然科学与工程技术版),2019,52(4):413-422.ZHU J S,XIANG C,QI H D.Research on influencing factors of impact coefficient of long-span suspension bridge [J].Journal of Tianjin University(Science and Technology),2019,52(4):413-422.(in Chinese)

    • [12] 蒋培文,贺拴海,王凌波.车辆相互作用对连续梁车桥耦合振动影响分析 [J].合肥工业大学学报(自然科学版),2011,34(8):1222-1226,1236.JIANG P W,HE S H,WANG L B.Analysis of the effect of vehicle interaction on coupling vibration of continuous beam vehicle-bridge [J].Journal of Hefei University of Technology(Natural Science),2011,34(8):1222-1226,1236.(in Chinese)

    • [13] 蒋培文,贺拴海,宋一凡,等.简支梁车桥耦合振动及其影响因素 [J].长安大学学报(自然科学版),2013,33(1):59-66.JIANG P W,HE S H,SONG Y F,et al.Simple supported beam vehicle-bridge coupling vibration and its influencing factors [J].Journal of Changan University(Natural Science),2013,33(1):59-66.(in Chinese)

    • [14] 经薇,李松,李强,等.多车车桥耦合振动特性研究 [J].科学技术与工程,2017,17(6):111-116.JING W,LI S,LI Q,et al.Study on the coupling vibration characteristics of multi-vehicle axles [J].Science Technology and Engineering,2017,17(6):111-116.(in Chinese)

    • [15] 陈水生,李孟廷,桂水荣,等.多车激励公路简支梁车桥耦合振动响应分析 [J].武汉理工大学学报,2014,36(3):101-106.CHEN S S,LI M T,GUI S R,et al.Analysis of coupled vibration response of simple supported beam vehicle-bridge on highway with multi-car excitation [J].Journal of Wuhan University of Technology,2014,36(3):101-106.(in Chinese)

    • [16] 盛国刚,李传习,赵冰.多个移动车辆作用下简支梁的动力响应分析 [J].工程力学,2006(12):154-158,99.SHENG G G,LI C X,ZHAO B.Analysis of dynamic response of simply supported beams under the action of multiple moving vehicles [J].Engineering Mechanics,2006(12):154-158,99.(in Chinese)

    • [17] YANG Y B,LEE Y C,CHANG K C.Effect of road surface roughness on extraction of bridge frequencies by moving vehicle[M].Mechanics and Model-Based Control of Advanced Engineering Systems.Springer,Vienna,2014:295-305.

    • [18] YAU J D,YANG Y B,KUO S R.Impact response of high speed rail bridges and riding comfort of rail cars [J].Engineering Structures,1999,21(9):836-844.

    • [19] 王解军,张伟,吴卫祥.重型汽车荷载作用下简支梁桥的动力反应分析 [J].中南公路工程,2005,30(2):55-57.WANG J J,ZHANG W,WU W X.Dynamic response analysis of simply supported beam bridge under heavy vehicle load [J].Central South Highway Engineering,2005,30(2):55-57.(in Chinese)

  • 基本信息

    中图分类号: O327;U441+.3
    文献标识码: A
    DOI: 10.6052/1672-6553-2022-057
    文章编号: 1672-6553-2023-21(5)-060-009

    基金信息

    国家自然科学基金资助项目(11972238)；
    河北省自然科学基金资助项目(A2022210007, A2021210009, E2022210029)；
    河北省高等学校科学技术研究项目(ZD2022019)；
    National Natural Science Foundation of China (11972238)；
    Natural Science Foundation of Hebei Province, China (A2022210007, A2021210009, E2022210029)；
    Hebei Provincial Department of Education Project of China (ZD2022019)；

    引用信息

    稿件历史

    收稿日期: 2022-09-25

  • 参考文献

    • [1] 李韶华,王伟达.车辆动力学与控制研究进展 [J].动力学与控制学报,2021,19(3):1-4.LI S H,WANG W D.Research advance in vehicle dynamics and control [J].Journal of Dynamics and Control,2021,19(3):1-4.(in Chinese)

    • [2] 李小珍,张黎明,张洁.公路桥梁与车辆耦合振动研究现状与发展趋势 [J].工程力学,2008,25(3):230-240.LI X Z,ZHANG L M,ZHANG J.State-of-the-art review and trend of studies on coupling vibration for vehicle and highway bridge system [J].Engineering Mechanics,2008,25(3):230-240.(in Chinese)

    • [3] YANG Y B,LIN C W.Vehicle-bridge interaction dynamics and potential applications [J].Journal of Sound and Vibration,2005,284:205-226.

    • [4] 李小珍,辛莉峰,王铭,等.车-桥耦合振动2019年度研究进展 [J].土木与环境工程学报(中英文),2020,42(5):126-138.LI X Z,XIN L F,WANG M,et al.State-of-the-art review of vehicle-bridge interactions in 2019 [J].Journal of Civil and Environmental Engineering,2020,42(5):126-138.(in Chinese)

    • [5] 邓露,何维,俞扬,等.公路车-桥耦合振动的理论和应用研究进展 [J].中国公路学报,2018,31(7):38-54.DENG L,HE W,YU Y,et al.Research progress in theory and applications of highway vehicle-bridge coupling vibration [J].China Journal of Highway and Transport,2018,31(7):38-54.(in Chinese)

    • [6] 刘星,李韶华,司春棣,等.曲线梁桥在车辆载荷下的动力响应研究 [J].动力学与控制学报,2020,18(2):50-58.LIU X,LI S H,SI C D,et al.Dynamic response of curved girder bridge under random vehicle loads [J].Journal of Dynamics and Control,2020,18(2):50-58.(in Chinese)

    • [7] 彭献,殷新锋,茆秋华.车-桥系统的振动分析及控制 [J].动力学与控制学报,2006,4(3):253-258.PENG X,YIN X F,MAO Q H.Vibration analysis and control of vehicle-bridge system [J].Journal of Dynamics and Control,2006,4(3):253-258.(in Chinese)

    • [8] 张建波,廖敬波,唐光武,等.考虑桥面随机不平顺的桥梁动态响应研究 [J].振动与冲击,2016,35(7):214-219.ZHANG J B,LIAO J B,TANG G W,et al.Research on dynamic response of bridge considering random irregularity of bridge deck [J].Vibration and Shock,2016,35(7):214-219.(in Chinese)

    • [9] 桂水荣,张政韬,陈水生,等.桥面不平引起车桥系统随机振动车速因素分析 [J].振动测试与诊断,2018,38(6):1223-1228,1296-1297.GUI S R,ZHANG Z T,CHEN S S,et al.Analysis of vehicle speed factors of random vibration caused by uneven bridge deck [J].Vibration Testing and Diagnosis,2018,38(6):1223-1228,1296-1297.(in Chinese)

    • [10] ESMAILZADEH E,JALILI N.Vehicle-passenger-structure interaction of uniform bridges traversed by moving vehicles [J].Journal of Sound and Vibration,2003,260(4):611-635.

    • [11] 朱劲松,香超,祁海东.大跨度悬索桥冲击系数影响因素研究 [J].天津大学学报(自然科学与工程技术版),2019,52(4):413-422.ZHU J S,XIANG C,QI H D.Research on influencing factors of impact coefficient of long-span suspension bridge [J].Journal of Tianjin University(Science and Technology),2019,52(4):413-422.(in Chinese)

    • [12] 蒋培文,贺拴海,王凌波.车辆相互作用对连续梁车桥耦合振动影响分析 [J].合肥工业大学学报(自然科学版),2011,34(8):1222-1226,1236.JIANG P W,HE S H,WANG L B.Analysis of the effect of vehicle interaction on coupling vibration of continuous beam vehicle-bridge [J].Journal of Hefei University of Technology(Natural Science),2011,34(8):1222-1226,1236.(in Chinese)

    • [13] 蒋培文,贺拴海,宋一凡,等.简支梁车桥耦合振动及其影响因素 [J].长安大学学报(自然科学版),2013,33(1):59-66.JIANG P W,HE S H,SONG Y F,et al.Simple supported beam vehicle-bridge coupling vibration and its influencing factors [J].Journal of Changan University(Natural Science),2013,33(1):59-66.(in Chinese)

    • [14] 经薇,李松,李强,等.多车车桥耦合振动特性研究 [J].科学技术与工程,2017,17(6):111-116.JING W,LI S,LI Q,et al.Study on the coupling vibration characteristics of multi-vehicle axles [J].Science Technology and Engineering,2017,17(6):111-116.(in Chinese)

    • [15] 陈水生,李孟廷,桂水荣,等.多车激励公路简支梁车桥耦合振动响应分析 [J].武汉理工大学学报,2014,36(3):101-106.CHEN S S,LI M T,GUI S R,et al.Analysis of coupled vibration response of simple supported beam vehicle-bridge on highway with multi-car excitation [J].Journal of Wuhan University of Technology,2014,36(3):101-106.(in Chinese)

    • [16] 盛国刚,李传习,赵冰.多个移动车辆作用下简支梁的动力响应分析 [J].工程力学,2006(12):154-158,99.SHENG G G,LI C X,ZHAO B.Analysis of dynamic response of simply supported beams under the action of multiple moving vehicles [J].Engineering Mechanics,2006(12):154-158,99.(in Chinese)

    • [17] YANG Y B,LEE Y C,CHANG K C.Effect of road surface roughness on extraction of bridge frequencies by moving vehicle[M].Mechanics and Model-Based Control of Advanced Engineering Systems.Springer,Vienna,2014:295-305.

    • [18] YAU J D,YANG Y B,KUO S R.Impact response of high speed rail bridges and riding comfort of rail cars [J].Engineering Structures,1999,21(9):836-844.

    • [19] 王解军,张伟,吴卫祥.重型汽车荷载作用下简支梁桥的动力反应分析 [J].中南公路工程,2005,30(2):55-57.WANG J J,ZHANG W,WU W X.Dynamic response analysis of simply supported beam bridge under heavy vehicle load [J].Central South Highway Engineering,2005,30(2):55-57.(in Chinese)

    • 微信公众号二维码

    手机版网站二维码

    动力学与控制学报 ® 2024 版权所有
    技术支持：北京勤云科技发展有限公司