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Article(id=1241784311729422557, tenantId=1146029695717560320, journalId=1241715181215068175, issueId=1241784304989175988, articleNumber=null, orderNo=null, doi=10.6052/1672-6553-2025-037, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=null, receivedDate=1743436800000, receivedDateStr=2025-04-01, revisedDate=1744646400000, revisedDateStr=2025-04-15, acceptedDate=null, acceptedDateStr=null, onlineDate=1773994051153, onlineDateStr=2026-03-20, pubDate=null, pubDateStr=null, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1773994051153, onlineIssueDateStr=2026-03-20, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1773994051153, creator=13701087609, updateTime=1773994051153, updator=13701087609, issue=Issue{id=1241784304989175988, tenantId=1146029695717560320, journalId=1241715181215068175, year='2025', volume='23', issue='10', pageStart='1', pageEnd='96', issueExtLink='null', onlineDate='null', pubDate='null', beforeIssueId=null, nextIssueId=null, price=null, status=1, issueComplete=1, articleOrder=1, issueType=-1, specialIssue=null, createTime=1773994049546, creator=13701087609, updateTime=1773994239413, updator=13701087609, preIssue=null, nextIssue=null, ext={EN=IssueExt(id=1241785101412012589, tenantId=1146029695717560320, journalId=1241715181215068175, issueId=1241784304989175988, language=EN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=), CN=IssueExt(id=1241785101412012590, tenantId=1146029695717560320, journalId=1241715181215068175, issueId=1241784304989175988, language=CN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=)}, issueFiles=null}, startPage=26, endPage=34, ext={EN=ArticleExt(id=1241784312484397294, articleId=1241784311729422557, tenantId=1146029695717560320, journalId=1241715181215068175, language=EN, title=Dynamic Modeling Method and Vehicle Responses of the Floating Bridge Considering the Stiffness of Connected Hinges and Supported Pontoons, columnId=1241784307421872311, journalTitle=Journal of Dynamics and Control, columnName=Research Articles, runingTitle=null, highlight=null, articleAbstract=

For a new type of multi-segment pontoon bridge with alternately supported floats in the span range, a theoretical model of the dynamic response is established which can simultaneously consider the roles of connection hinge stiffness and float support stiffness.In the model, the pontoon segments are regarded as Euler-Bernoulli beams with hinges at both ends, while the action of the floating body and the hydrostatic water is equivalent to the elastic support distributed along the length of the beams. The adjacent segments are connected by hinges with rotational stiffness.The relationship between the structural self-resonance characteristics and the moving vehicle load response with the above two stiffness parameters is investigated.The results show that the proposed method can effectively obtain the response sensitivity interval of the floating body support stiffness and the rotational stiffness of the connection hinges. As the rotational stiffness increases, the segment connection transitions from articulation to rigidity, and the relative angle of the two ends of the hinged joint in the modal state is changed from the “sharp angle” mutation form to the smooth form. When the rotational stiffness is smaller, there is the vertical direction of the connection.When the rotational stiffness is small, significant vertical displacement extremes and corner mutations occurs on the connection；however once the stiffness reaches a certain value, the structural displacement and internal force envelope tends to be stable.

, correspAuthors=Zhuangpeng Yi, authorNote=null, correspAuthorsNote=null, copyrightStatement=null, copyrightOwner=null, extLink=null, articleAbsUrl=null, sourceXml=null, magXml=null, pdfUrl=null, pdf=null, pdfFileSize=null, pdfExtLink=null, richHtmlUrl=null, mobilePdfUrl=null, reviewReport=null, pdfFirstPage=null, abstractGraph=null, abstractGraphContent=null, abstractVideo=null, citation=null, cebUrl=null, magXmlContent=null, mapNumber=null, authorCompany=null, fund=null, authors=null, authorsList=Zhuangpeng Yi, Hongzhi Zhu, Yujie Li, Liyu Xiao, Youyi Zeng, Quan Pan), CN=ArticleExt(id=1241784325444796958, articleId=1241784311729422557, tenantId=1146029695717560320, journalId=1241715181215068175, language=CN, title=浮桥考虑连接铰/浮体刚度的动力建模方法与车辆荷载响应, columnId=1241784307690307771, journalTitle=动力学与控制学报, columnName=研究论文, runingTitle=null, highlight=null, articleAbstract=

针对跨度范围内浮体交替支撑的新型多节段浮桥，建立了可同时考虑连接铰刚度和浮体支撑刚度作用的动力响应理论模型.模型中，浮桥节段视为Euler-Bernoulli梁，两端为铰支，浮体与静水的作用等效为沿梁长分布的弹性支撑，相邻节段间通过具有转动刚度的铰连接.研究了结构自振特性及移动车辆荷载响应与上述两个刚度参数之间的关系.结果表明：该方法可获取浮体支撑刚度及连接铰转动刚度的响应敏感区间；随着转动刚度的增加，节段连接由铰接向刚性过渡，模态中铰接处两端相对转角由“尖角”突变形式向平滑形式转变；当转动刚度较小时，连接处存在竖向位移极值和转角突变，而增至特定值后结构位移、内力包络图趋于平稳.

, correspAuthors=易壮鹏, authorNote=null, correspAuthorsNote=
† E-mail:
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浮桥考虑连接铰/浮体刚度的动力建模方法与车辆荷载响应
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易壮鹏 1, 2, † , 朱鸿志 1, 2 , 李宇杰 1, 2 , 肖利宇 1, 2 , 曾有艺 1, 2 , 潘权 1, 2
动力学与控制学报 | 研究论文 2025,23(10): 26-34
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动力学与控制学报 | 研究论文 2025, 23(10): 26-34
浮桥考虑连接铰/浮体刚度的动力建模方法与车辆荷载响应
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易壮鹏1, 2, † , 朱鸿志1, 2, 李宇杰1, 2, 肖利宇1, 2, 曾有艺1, 2, 潘权1, 2
作者信息
  • 1.长沙理工大学　土木工程学院，长沙　410114
  • 2.长沙理工大学　桥梁工程安全控制教育部重点实验室，长沙　410114

通讯作者:

Dynamic Modeling Method and Vehicle Responses of the Floating Bridge Considering the Stiffness of Connected Hinges and Supported Pontoons
Zhuangpeng Yi1, 2, † , Hongzhi Zhu1, 2, Yujie Li1, 2, Liyu Xiao1, 2, Youyi Zeng1, 2, Quan Pan1, 2
Affiliations
  • 1. School of Civil Engineering, Changsha University of Science and Technology, Changsha　410114, China
  • 2. Key Laboratory of Bridge Engineering Safety Control by Department of Education, Changsha University of Science and Technology, Changsha　410114,China
doi: 10.6052/1672-6553-2025-037
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摘要
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针对跨度范围内浮体交替支撑的新型多节段浮桥，建立了可同时考虑连接铰刚度和浮体支撑刚度作用的动力响应理论模型.模型中，浮桥节段视为Euler-Bernoulli梁，两端为铰支，浮体与静水的作用等效为沿梁长分布的弹性支撑，相邻节段间通过具有转动刚度的铰连接.研究了结构自振特性及移动车辆荷载响应与上述两个刚度参数之间的关系.结果表明：该方法可获取浮体支撑刚度及连接铰转动刚度的响应敏感区间；随着转动刚度的增加，节段连接由铰接向刚性过渡，模态中铰接处两端相对转角由“尖角”突变形式向平滑形式转变；当转动刚度较小时，连接处存在竖向位移极值和转角突变，而增至特定值后结构位移、内力包络图趋于平稳.

浮桥结构  /  浮体交替支撑  /  连接铰转动刚度  /  频率与模态  /  移动荷载列响应

For a new type of multi-segment pontoon bridge with alternately supported floats in the span range, a theoretical model of the dynamic response is established which can simultaneously consider the roles of connection hinge stiffness and float support stiffness.In the model, the pontoon segments are regarded as Euler-Bernoulli beams with hinges at both ends, while the action of the floating body and the hydrostatic water is equivalent to the elastic support distributed along the length of the beams. The adjacent segments are connected by hinges with rotational stiffness.The relationship between the structural self-resonance characteristics and the moving vehicle load response with the above two stiffness parameters is investigated.The results show that the proposed method can effectively obtain the response sensitivity interval of the floating body support stiffness and the rotational stiffness of the connection hinges. As the rotational stiffness increases, the segment connection transitions from articulation to rigidity, and the relative angle of the two ends of the hinged joint in the modal state is changed from the “sharp angle” mutation form to the smooth form. When the rotational stiffness is smaller, there is the vertical direction of the connection.When the rotational stiffness is small, significant vertical displacement extremes and corner mutations occurs on the connection；however once the stiffness reaches a certain value, the structural displacement and internal force envelope tends to be stable.

floating bridge structure  /  pontoon alternating support  /  rotational stiffness of connecting hinge  /  frequency and mode  /  responses by moving vehicles
易壮鹏, 朱鸿志, 李宇杰, 肖利宇, 曾有艺, 潘权. 浮桥考虑连接铰/浮体刚度的动力建模方法与车辆荷载响应. 动力学与控制学报, 2025 , 23 (10) : 26 -34 . DOI: 10.6052/1672-6553-2025-037
Zhuangpeng Yi, Hongzhi Zhu, Yujie Li, Liyu Xiao, Youyi Zeng, Quan Pan. Dynamic Modeling Method and Vehicle Responses of the Floating Bridge Considering the Stiffness of Connected Hinges and Supported Pontoons[J]. Journal of Dynamics and Control, 2025 , 23 (10) : 26 -34 . DOI: 10.6052/1672-6553-2025-037
正文
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引言
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浮桥是一种重要的桥型[1,2]，在军事交通领域及民用建设中发挥了重要的作用.风、浪[3]、流等环境荷载和车辆[4]等功能荷载，以及上述两种荷载共同作用下[5]浮桥结构的动力响应规律，对应的建模方法、浮体节段连接方式及各类边界处理技术，一直以来都是国内外学者关注的重点.
对于中小跨径的浮桥而言，通常由多节段拼组而成，相邻节段间的连接方式有多种[2]且连接设置的刚度对结构动力性能影响显著.同时在对浮桥节段连接方式的研究过程中，结构的整体模型建立是研究的基础，一个精准的动力学模型是获取浮桥在外荷载下结构响应的重要前提.全跨弹性基础梁[1]或弹簧铰连接弹性基础梁节段[6]是浮桥结构计算时常用的力学模型.林铸明和陈徐均[6]推导了移动荷载下浮桥结构弹性基础的连续梁和铰接梁力学模型，比较了二者的异同及适用范围；陈徐均等[7]基于两类模型的位移等效处理，求解出由弹性铰连接的多浮体模型中弹性铰的转动刚度.Raftoyiannis等[8]在将浮桥节段等效为刚体的基础上研究了节段之间铰接时浮桥在波浪及移动荷载下的动态响应.钱长照等[9]利用模态叠加原理，考虑弹性支撑刚度对弹性支撑梁的影响，研究了结构在移动车辆荷载作用下的动力响应.张军和贺方倩[10]同时考虑铰接梁式浮桥节段的刚体运动和弹性变形，运用模态展开法研究了浮桥结构在移动荷载作用下的运动响应.詹豪等[11]建立了考虑连接接头半刚性的带式浮桥抗弯弹簧铰梁模型，通过传递矩阵法研究了半刚性接头与刚接、铰接接头之间的区别与联系.计淞等[12]建立了桥节间通过缆绳和防撞垫连接的柔性连接浮桥水动力模型，发现连接缆绳刚度是移动载荷作用下浮桥运动响应的重要控制参数.孙奇等[13]将浮桥简化为弹性地基梁，研究了单个移动荷载作用下的动态响应.黄恒等[14]在进行多节段浮体弹性基础梁理论建模和浮桥动力响应计算时，根据浮桥实际水线面的改变计入了浮体支撑刚度的变化.以上研究均表明，在对浮桥进行动力响应研究过程中动力建模主要将节段等效为弹性基础梁/弹性支撑梁并考虑相邻节段间不同连接方式的影响.而所关注的浮桥多为跨度范围内连续支撑的结构，浮体之间通过特定方式连接在一起，浮体之间较少采用分开的方式布置.因此相同类型梁节段采用浮体交替支撑且梁节段之间采用弹簧铰拼接，将形成一种新型的浮桥结构.同时，关于连接方式的研究均是将连接处构件的刚度值等效为一确定值，而少有研究去分析连接处构件刚度变化对结构动力特性的影响.该类结构与已有文献涉及的浮桥模型存在显著差异，不能直接进行移动荷载响应的求解，已有弹性基础梁模型[6,15]和节段连接方式可为其建模提供借鉴.
基于上述背景，以跨度范围内浮体交替支撑的多段浮桥为对象，将浮体作用效应等效为沿梁长的竖向支撑刚度，将相邻节段之间的连接处理为具有一定转动约束刚度的铰，建立移动车辆荷载列作用下的理论模型.分析结构自振特性、移动荷载响应与连接铰转动刚度、浮体支撑刚度的关联规律.
1　理论模型
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1.1　问题描述
本文考虑的浮桥结构在跨度范围内由多段模块式节段组成，为A类和B类，其中A类由浮体支撑，B类与A类采用具有一定转动刚度的弹性铰直接连接或与端部连接，在跨度范围内交替布置，图1给出了浮桥的结构模型与理论计算模型示意图.为建立同时考虑连接铰刚度和浮体刚度影响的动力模型并分析车辆荷载作用下结构响应，引入如下基本假定：（1）只考虑静水条件下浮桥结构的车辆荷载影响，不考虑波浪等环境荷载的影响；（2）两类梁节段均简化为几何、材料参数沿跨度范围内不发生变化的等截面Euler-Bernoulli梁；（3）A类节段与浮体连接在一起共同受力，浮体与静水对该类节段的作用等效为纵向均匀弹性支撑梁；（4）浮桥结构两端部边界条件为铰接.
图1(b)所示的理论模型中，O-xy为以结构左端点O为原点的直角坐标系，x、y分别表示纵向、竖向.Kri（i=1~n）为相邻节段间弹性铰的转动连接刚度，n指代弹性铰数目，对应节段数目为n+1.Kf为A类节段等效为纵向均匀弹性支撑梁之后的竖向刚度.Di（i=0~n+1）为坐标系O-xy内弹性铰位置、两个端部的水平坐标，浮桥总长L=Dn+1-D0，第i（i=1~n+1）个节段位于坐标区间[Di-1，Di]内，vp为移动汽车荷载的行驶速度.考虑m台车辆荷载的作用，每台车等效为图1(b)所示的3个集中力.在前述假定的基础上，图1所示第i个节段的动力学微分方程[16]可写为
式中Vi表示第i节段的竖向位移，t为时间，mt为单位长度质量，c是阻尼系数，E为弹性模量，I为截面惯性矩，A为截面面积，Ph为车辆荷载轴重，δ为Dirac-Delta函数，xh=vp t-Lh-Di-1，Lh为第h个轴重Ph与P1之间考虑车辆速度、安全间距之后的距离.由式（1）及图1可知在i（i=1~n+1）个节段中，当i为奇数时，式（1）表示竖向无弹性支撑的B类节段的动力方程；当i为偶数时，式（1）表示带竖向均匀线刚度Kf的A类节段的动力方程.
将与节段位移Vi（x，t）对应的转角、弯矩和剪力分别用Ri（x，t）、Mi（x，t）和Qi（x，t）表示，根据基本假定（4）结构两端边界条件可表述为
接下来，引入无量纲变量
式中为截面的转动半径，将式（3）中无量纲变量代入式（1）中可得梁段在区间[Di-1，Di]内的无量纲形式的动力方程
1.2　固有频率与模态
与式（4）对应的结构自由振动方程为
其解可表示为
上式中及后续变量的下标i、j分别表示结构节段数和模态阶次，为第j阶模态的影响值，ωj为结构第j阶振动频率，表示第j阶整体振动模态中第i个节段的分量，i表示虚数单位，将式（6）代入式（5）可得模态通解
式（7）中的两种表达式分别表示i为奇数（B类节段）和偶数（A类节段）的情形，且，Aij1~Aij4为模态系数.
式（7）根据相邻梁段间的平衡关系[12]与边界条件方程可得相邻梁段间的模态系数关系和边界条件矩阵方程
其中Θij是相邻梁段间的4×4阶连接矩阵，BjL和BjR为2×4阶边界连接矩阵.Θij可以写为
其中，当表征节段数的变量i分别为奇数和偶数时，上述式中的简化系数分别用不同的表达式替代.
整理相邻梁间的连接矩阵方程和边界矩阵方程，可得到全结构在全局坐标系下的特征方程：
由于式（10）中有非零解，因此需满足|Z|=0，据此可求得结构的各阶频率值.同时可得到模态向量系数，根据式（8）所求得的模态系数向量和式（7）所示的模态函数可得到梁段的各阶模态，将各阶模态进行标准化和归一化处理有如下关系：
式中δjk表示Kronecker delta函数.
1.3　车辆荷载作用下的动力响应
式（4）中动力响应方程的解可写成
其中qj（τ）是第j阶模态的广义正则坐标，将上式代入式（4）中进行Galerkin积分[17]并结合式（11）中的正交关系可得到关于qj（τ）的常微分方程：
其中和分别表示非线性项和外移动荷载项，截取前N阶模态影响后其表达式为
2　算例分析与讨论
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选取浮桥算例的基本设计参数如下：浮桥总长度L=100 m，桥面宽度为一个车道宽，等截面浮桥单位质量mt=2550 kg·m-1，截面抗弯刚度EI=4.2×109 N·m2，截面轴向刚度EA=6.72×1010 N，水密度ρw=1000 kg·m-3.汽车行驶速度vp=15 km·h-1，3个轴重等效后的集中力分别为60 kN、120 kN和120 kN，车辆之间安全行驶间距40 m，每辆汽车长为8 m.将宽度b作为变化参数来控制浮体竖向弹性刚度Kf的大小[7]，本文所关注的浮体结构宽度b∈[8，26]m，为Kf=ρgb∈[7.84×104，2.55×105]N·m-2，与之对应根据式（3）中kf=Kf L 4/EI可确定无量纲刚度kf的变化区间为[1.87×103，6.07×103]，以5段模块式节段为例，在宽度b的变化范围内浮体吃水深度变化区间为[0.060，0.277]m.假定两类节段的长度均相等，且各节段间转动铰的刚度均相同，考虑kr由零增至无穷大过程中结构的力学性能.
2.1　浮桥结构的自振特性
图2给出了浮桥结构分别采用3、5、7个节段数且跨中A类节kf取4×103时频率随节段间连接铰刚度kr变化的分布规律，其中横坐标采用对数表述用以描述尽可能大的kr范围，纵坐标的频率为式（10）中|Z|=0所得特征方程的解.由图2可知，与节段数目相同的每一组频率呈现特定的规律，其中该组频率的最大值与kr无关而其余值均随kr的变化而改变.其原因在于，当采用铰支边界条件时，由|Z|=0所得特征方程可以表述为
上式中第二项sin[liηsj]=0对应的解与kr无关，可表示为i 2（n+1）2π2，其中i=1，2，3…为整数，（n+1）为浮桥节段数，这与文献[18]中相同边界悬浮隧道结构的频率分布规律一致.在kr由零增至无穷大时，也即相邻节段间连接方式从理想铰接过渡到刚性连接的变化过程中，这些频率均随kr的增大而增大，其中kr∈[10-1，102]为变化的敏感区间，在此区间内频率值增长显著.在敏感区间之外，当kr增或减至某一值时频率值基本不再变化，并分别趋近于图2中用三角形和菱形图标表示的转动铰采用理想铰接和刚性连接对应的频率值.基于kr的这种影响规律，4组典型kr值（100、101、102、103）将被用于后续结构响应分析.
图3绘出了结构在kf=2×103，4×103，6×103和4组kr（100、101、102、103）组合下的前5阶模态图，它们由式（7）、式（8）和式（10）综合得到.由图3所示，第1~4阶受kf和kr的影响而第5阶则为kf和kr影响的标准正弦分布形式，这与式（15）中起决定作用的第二、三项及图2(b)中的频率值刚好对应.在受两类刚度影响的前4阶模态中，当kr较小时，模态在此处呈现尖角的突变形式；当kr较大时，节段之间连接铰两端转角差值较小，模态较平滑.这种转角随kr变化而变化的规律在kf越大和模态阶次越高时越明显，这显著地反映了kr由零增至无穷大时节段之间连接由铰接→半刚性连接→刚性连接的过程.
2.2　车辆荷载作用下的结构响应
为研究结构在移动车辆荷载列作用下的动力响应，参考现行规范《公路桥涵设计通用规范》（JTGD60-2015）和已有文献[10]关于浮桥车辆荷载的取值，选取6辆汽车以vp=15 km·h-1的速度按安全间距40 m行驶，形成一个由18个集中力组成的移动荷载列.图4给出三种kf下kr=102时5节段浮桥结构在移动汽车荷载列作用下关键位置的位移时程响应曲线.进行浮桥车辆荷载位移响应计算结果的收敛性分析时，通过比对关键点的响应幅值发现，式（14）中在模态截取阶数N取5时已收敛95%，N取10时已基本全部收敛，为满足计算精度要求并减少计算成本，选择N=15来获取响应的计算结果.同时，图4(a)、(b)还给出了kf=2×103、kr=102时，收敛之后理论解与基于ANSYS有限元（FEM）结果之间的对比，二者的相对差值均在5%之内，其中FEM中节段采用Beam单元模拟，转动铰和浮体刚度均采用Combine单元模拟.
由图4(a)、(c)、(e)中4个转动铰连接位置的位移响应曲线可知，整体上靠近边界的两个铰位置的位移响应小于中间两个铰位置的值.响应曲线的位移峰值均出现在某台车经过该转动铰的时刻，因而在位移曲线上存在6个与车辆对应的局部峰值.由图4(b)、(d)、(f)可知，A类节段中间位置的位移响应整体上大于处而小于处的无浮体支撑B类节段跨中响应值.随着kf的增大，两类铰（靠近边界的铰、中间铰）位置和两类节段（A类、B类）跨中位置的位移响应值均变小，且响应幅值变化呈靠近趋势.
浮桥节段间连接处两端的相对转角大小是该类结构的一个重要关注点，它与转动连接刚度kr密切相关，是行车平顺性和结构动力特性的重要考量指标.图5给出了5节段浮桥结构一个典型刚度参数（kf=4×103）下第二个铰两端的转角时程曲线，其中右上角的“L”和“R”分别指代左、右两端.对比图5中4个不同kr值对应的转角时程曲线，可以看出随着kr的增大铰两端的转角值越来越接近.当kr=100时，弹性铰左右两端转角之间出现“突变”，转角相对变化量大且方向相反；当kr=10时，弹性铰左右两端转角相对值变小；当kr增至102时，左右两端转角时程曲线非常接近；当kr增至103，即当弹性铰刚度足够大时，两端之间转角曲线差异已经很小，将保持稳定不再变化.
2.3　车辆荷载作用下浮桥结构响应的包络区间
为从全局角度展示浮桥结构在不同连接铰刚度与浮体刚度时汽车荷载列引起的动力响应规律，图6分别给出了3组kf（2×103、4×103、6×103）和4组kr（100、101、102、103）组合下的5节段结构的位移、转角和弯矩的时程响应包络图，横坐标表示节点的位置，纵坐标变量的下标“max”和“min”分别指代响应时程曲线的最大和最小值.
图6(a)~(c)为位移响应包络图，对比不同kf和kr的包络曲线发现两类刚度值的增加均使竖向位移绝对值减小.当kr=100时，结构在相邻节段连接处竖向位移值较大且整体位移相对于其余较大kr值对应的位移值也偏大；当kr增至102和103时，节段间连接处的位移值变化减小，此时跨内不同位置位移值变化稳定，这是因为kr增大时连接铰更有效地传递荷载，相邻梁段之间相对位移差减小.
由图6(d)~(f)的转角包络图可以发现，当kr=100时在每一个铰位置左、右两端的转角存在显著差异，包络图在这些位置存在突变，这与图5(a)所反映的规律一致，这是因为此时节段之间连接铰的转动约束刚度较小，无法有效限制节段间的转角变形.而当kr增至102和103时，各连接铰位置两端的转角接近一致，整体线形变得平顺，这是因为转动刚度的增大增强了节段之间的约束，限制了节段之间的相对转动.此外，随着kf的增大，转角响应值逐渐减小至特定值.
对于图6(g)~(i)所示的弯矩响应包络图，不同kf对应的包络曲线整体上类似，极值较为接近；弯矩对kr的变化较敏感，kr增大时弯矩包络的极值减小，且kr为102、103时趋于稳定.通过对比可知，A类节段所在位置的弯矩值明显小于B类节段的弯矩值，其原因在于支撑浮体可以减小弯矩值，kf的存在对结构起到了约束作用.
3　结论
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建立了可考虑节段间转动铰连接刚度与跨内浮体支撑刚度的多节段浮桥理论模型，研究了各种刚度组合下结构的自振特性和移动车辆荷载列作用下的动力响应，主要结论有：
（1）所建模型与所提方法，经与有限元结果对比验证后，可求解一类浮桥考虑多刚度影响的频率、模态，并分析移动车辆荷载列引起的动力响应.
（2）节段间连接铰刚度kr基于频率、模态和车辆荷载列响应的敏感区间为[10-1，102].多节段浮桥结构频率随两类刚度的增大而增大；各阶模态节段间连接铰位置两端的相对转角由kr较小时的“尖角”突变形式逐渐向当kr较大时的平滑形式转变.这种变化规律显著地反映了kr由零增至无穷大时，节段间连接由铰接→半刚性连接→刚性连接的过程.
（3）两类节段（A类、B类）中间位置与节段之间连接铰位置的位移响应曲线上存在车辆经过该位置时的局部峰值，当kr较小时，结构的各类响应值的变化量较大，随着kr的增大，响应值变化逐渐稳定并保持不变.同时，两类刚度参数的增大均能抑制结构的动力响应.
基金
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  • 国家自然科学基金资助项目(52278139; 52278141)
  • 湖南省自然科学基金资助项目(2022JJ30612)
  • 长沙理工大学土木工程重点学科基金资助项目(18ZDXK05; 15ZDXK01)
文献
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2025年第23卷第10期
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文章信息
doi: 10.6052/1672-6553-2025-037
  • 接收时间：2025-04-01
  • 首发时间：2026-03-20
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出版历史
  • 收稿日期：2025-04-01
  • 修回日期：2025-04-15
基金
National Natural Science Foundation of China(52278139; 52278141)
国家自然科学基金资助项目(52278139; 52278141)
National Science Fund of Hunan Province(2022JJ30612)
湖南省自然科学基金资助项目(2022JJ30612)
Key Discipline Funds for Civil Engineering of Changsha University of Science and Technology(18ZDXK05; 15ZDXK01)
长沙理工大学土木工程重点学科基金资助项目(18ZDXK05; 15ZDXK01)
作者信息
    1.长沙理工大学　土木工程学院，长沙　410114
    2.长沙理工大学　桥梁工程安全控制教育部重点实验室，长沙　410114

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