预应力混凝土梁桥在移动荷载作用下的动力响应分析

建立预应力钢筋混凝土等直梁强迫振动的运动微分方程,分析了梁在预应力钢筋作用下的横向振动问题.将运动微分方程解耦,得到梁在预应力作用下自振频率的解析解以及梁振动时的动力响应.分析了梁的自振频率与预应力和偏心距的关系.通过实例计算,得到了关于不同速度移动荷载车辆作用下梁的动力挠度曲线,并给出了考虑预应力和不考虑预应力时梁的动力效应比较.结果表明:随着车辆荷载移动速度的增大,梁的动力挠度随之增大;考虑预应力时梁的动力效应略有降低.     

基于改进萤火虫算法的移动车辆参数识

提出了一种基于萤火虫优化算法的移动车辆参数直接识别方法.采用四自由度双轴十二参数车辆模型和欧拉梁有限元模型建立了车桥耦合系统的动力方程,并利用Newmark直接积分法求解了系统的动力响应.通过引入一种局部搜索策略和末位淘汰机制改进了萤火虫优化算法的收敛速率,并提高了识别结果的精度.本文方法仅利用车辆振动的竖向加速度响应测量就能进行移动车辆参数的识别.数值算例表明,改进的萤火虫优化算法可以准确地识别出车辆的质量、悬挂刚度和阻尼等参数,并且对测量噪声不敏感.     

基于改进萤火虫算法的移动车辆参数识别

提出了一种基于萤火虫优化算法的移动车辆参数直接识别方法。采用四自由度双轴十二参数车辆模型和欧拉梁有限元模型建立了车桥耦合系统的动力方程,并利用Newmark直接积分法求解了系统的动力响应。通过引入一种局部搜索策略和末位淘汰机制改进了萤火虫优化算法的收敛速率,并提高了识别结果的精度。本文方法仅利用车辆振动的竖向加速度响应测量就能进行移动车辆参数的识别。数值算例表明,改进的萤火虫优化算法可以准确地识别出车辆的质量、悬挂刚度和阻尼等参数,并且对测量噪声不敏感。     

高速铁路碎石道砟振动的离散元模拟

道砟振动对其磨损、破碎和道床累积变形有显著影响,为揭示高速车辆移动荷载作用下道砟动态响应特性,建立有砟道床离散元模型,开展车辆-轨道耦合动力学计算得到离散元模型输入荷载,模拟分析高速车辆以不同速度通过时有砟道床的振动响应,并与车辆-轨道耦合动力学计算结果进行对比分析。结果表明,轨枕、道砟和道床块振动位移波形相似,位移幅值沿道床深度方向减小,道床块振动位移与轨枕底面以下0.3m处道砟的振动位移相当;轨枕、道床块振动速度与加速度随行车速度提高而增大;受道砟颗粒间复杂相互作用的影响,道砟振动加速度会出现突变。道床离散元模型能合理反映道砟颗粒的振动响应特性,道床块模型体现了道床层在有砟轨道结构中的动力传递与减振特性,两种道床模型的计算结果具有一定的相似性。     

移动集中质量作用下Euler-Bernoulli梁的振动频率分析

研究了移动载荷作用下Euler-Bernoulli梁振动频率的变化规律。首先根据Euler-Bernoulli梁振动的控制方程,引入载荷和位移边界条件,建立梁单元的动力刚度矩阵和形状函数矩阵,然后采用傅里叶变换的思想,建立移动载荷惯性力引起的附加动力刚度矩阵,进而得到系统整体的动力刚度矩阵。通过Wittrick-Williams法进行求解得到移动载荷作用下Euler-Bernoulli梁的振动频率,与有限元法计算结果的比较,验证了此方法的正确性,体现了此方法在精度和计算规模上的优势。根据上述方法,揭示简支梁和悬臂梁振动频率随着移动质量速度与质量的变化规律。     

车-钢桥面铺装耦合振动系统动力效应分析

为研究行车车速、桥面的不平度和桥面损伤对车-桥面铺装耦合振动系统动力效应的影响规律,将汽车等效为两自由度五参数模型,将正交异性桥面铺装等效为梁-板结构.在车辆与桥面铺装接触点采用接触力和位移协调的条件,建立车辆和桥面铺装动力耦合系统模型和振动方程组.利用模态分析法以及时变力学系统的求解方法-状态空间法,借助大型有限元软件ANSYS和MATLAB编程技术,求解车-钢桥面铺装耦合振动系统的动力响应.分析由桥面铺装的不平度、车速以及桥面损伤等引起的行驶车辆的随机动荷载对桥面铺装冲击系数的影响,并考虑桥面的不平整将车辆荷载简化成沿铺装层表面的随机动荷载和车辆荷载简化成沿铺装层表面纵向移动的恒载两种加载方式的分析结果进行比较.研究结果表明,在进行铺装层结构设计计算以及复合梁疲劳试验时,可考虑冲击系数为1.5.     

基于虚拟变形法的车-桥耦合系统移动质量识别

利用双自由度质量-弹簧阻尼模型模拟移动车辆, 并基于虚拟变形(VDM)方法的结构快速重分 析思想, 提出一种车-桥耦合系统的移动质量快速识别的有效方法. 该方法以双自由度车体模 型的质量为变量, 通过最小化桥体结构实测响应和计算响应的平方距离来识别移动质量 (载荷), 避免了识别载荷时常遇到的病态问题, 对噪声鲁棒性强, 且需要传感器信息少. 每步优化 中, 利用在VDM方法基础上提出的移动动态影响矩阵概念, 无需时时重构车-桥耦合系统的时 变系统参数矩阵, 显著提高了计算效率. 利用数值框架梁模型, 通过比较不同车辆简化模型 对移动体质量及等效移动载荷的识别效果, 验证了该方法的可行性和有效性, 即使在5% 的噪声影响下, 利用一个传感器可以准确地识别多个移动体的质量.     

任意移动质量弹簧列作用下梁桥动力响应分析

将简支梁简化为 Euler 梁,基于振动理论推导建立了用于桥梁动力响应分析的任意移动质量弹簧列模型,并通过适当的参数选取将其退化成任意移动荷载列模型,使得两类经典模型合二为一。通过计算表明：在共振车速下,质量弹簧列模型条件下的桥梁响应较荷载列模型小;而在非共振车速下,两类模型条件下的桥梁响应差别不大。此外,对高铁简支梁应用分析可知：一定条件下在32m梁上行驶的车辆长度控制在19~23m范围内较合适;且该梁的共振车速约为156m/s、52m/s、39m/s,消振车速约为134m/s、78m/s、57m/s。这在实际应用时应予以注意。     

城市高架桥车-桥-墩系统竖向振动分析

假设城市高架桥为两端简支的欧拉-伯努利梁模型以及桥墩为底部固结的柱,考虑两自由度车辆移动系统与桥面结构表面接触处不平整产生的随机激励以,建立了多个移动车辆系统-桥-墩的耦合力学模型,并且给出了耦合振动方程详细的求解步骤.数值分析采用Wilson-θ法求解.通过仿真分析,讨论了在不同路面等级、不同车辆移动速度下桥梁跨中位移响应和桥墩轴力的变化规律.最后根据车-桥-墩耦合力学模型和车-桥耦合力学模型,比较了两种分析模型对桥墩底部轴力和桥梁跨中截面位移的影响.分析结果表明桥墩对桥梁跨中截面位移的影响可以忽略不计,但是对桥墩本身所受轴力的影响则非常显著.     

无单元法求解欧拉梁及梁系的自由振动问题

双变量无单元法以广义移动最小二乘法为理论基础,同时考虑挠度和转角双变量.采用双变量无单元法建立了欧拉粱的质量矩阵和刚度矩阵,并进行自由振动的计算.不同边界条件欧拉梁动力特性的算例表明:双变量无单元法比与只考虑挠度的单变量无单元法具有更高的插值精度,并能在高阶振型计算中获得明显优于有限元的计算精度.通过试算法对影响半径中的scale乘子进行了讨论,认为在动力计算中Scale取3.5较合理.最后在欧拉粱的基础上,将无单元法应用于梁系模型的自由振动计算,显示了该法在复杂模型中的精确性.     

Vibration suppression for high-speed railway bridges using tuned mass dampers

This paper deals with the applicability of passive tuned mass dampers (PTMDs) to suppress train-induced vibration on bridges. A railway bridge is modeled as an Euler–Bernouli beam and a train is simulated as series of moving forces, moving masses or moving suspension masses to investigate the influence of various vehicle models on the bridge features with or without PTMD. According to the train load frequency analysis, the resonant effects will occur as the modal frequencies of the bridges are close to the multiple of the impact frequency of the train load to the bridge. A single PTMD system is then designed to alter the bridge dynamic characteristics to avoid excessive vibrations. Numerical results from simply supported bridges of Taiwan High-Speed Railway (THSR) under German I.C.E., Japanese S.K.S. and French T.G.V. trains show that the proposed PTMD is a useful vibration control device in reducing bridge vertical displacements, absolute accelerations, end rotations and train accelerations during resonant speeds, as the train axle arrangement is regular. It is also found that the inner space of bridge box girder of THSR is wide and deep enough for the installation and movement of PTMD.     

Performances of dynamic vibration absorbers for beams subjected to moving loads

The goal of this work is a general assessment regarding the performances of linear and nonlinear dynamic vibration absorbers (DVAs) applied to the specific problem of moving loads or vehicles. The problem consists of a simply supported linear Euler–Bernoulli beam excited with a moving load/vehicle; a DVA is connected to the beam in order to reduce the vibrations. The moving vehicle is modeled by a single degree of freedom mass spring system. The partial differential equations governing the beam dynamics is reduced to a set of ordinary differential equations by means of the Bubnov–Galerkin method. A parametric analysis is carried out to find the optimal parameters of the DVA that minimize the maximum vibration amplitude of the beam. For the case of a moving vehicle, the energy absorbed by the DVA is evaluated. Comparisons among the performances of different types of linear and DVAs are carried out. The goal is to clarify if the use of nonlinearities in the DVAs can effectively improve their performances. The study shows that the most effective type of DVA for the test cases considered is the piecewise linear elastic restoring force.     

车辆-桥梁耦合作用分析

文章通过拉氏方程，在时变动力学的基础上，建立车-桥耦合振动的系统方程。重点探讨了车的质量、车速、刚度、阻尼比、桥跨、桥的阻尼比，桥面粗糙程度等参数在车．桥耦合振动中的作用。其中车速、车的刚度、桥的形式、桥的阻尼起着重要作用。文中还比较了把车辆分别模拟为移动力、移动刚体、移动的弹性体时车．桥互相作用力的差别，得出有必要将车辆模拟为移动的弹性体，以减小分析高速车辆所引起的互相作用力的误差。并考虑了车-桥耦合振动中行驶车辆的转动效应，虽然它的影响是很小的；还尝试性的讨论了桥上行车舒适度的问题，车的阻尼起着很重要的作用。     

不确定性移动载荷激励下弹性简支梁的动态响应边界分析及应用

不确定性移动载荷激励下的弹性梁振动是土木、机械和航空航天等工程领域普遍存在的一类重要问题。在许多实际工程中,不确定移动载荷的样本测试数据有限或测试成本较高,本文引入区间过程模型对此类动态不确定性参数进行描述,提出了一种求解不确定移动载荷激励下弹性梁振动响应边界的非随机振动分析方法。首先,介绍了确定性移动载荷激励下弹性梁的振动微分方程及其解析求解方法;其次,引入区间过程模型,以上下边界函数的形式对不确定性移动载荷进行度量,进而基于模态叠加法发展出弹性梁振动响应边界求解的非随机振动分析方法;最后,将上述非随机振动分析方法应用于车桥耦合振动问题。     

基于车桥耦合理论的梁式桥阻尼比识别研究

提出一种基于车桥耦合动力学理论的梁式桥阻尼比识别方法. 首先按照动力学理论将测试车设计为单自由度体系, 然后利用安装在测试车上的传感器采集信号, 从测试车与桥梁接触点响应信号中得到梁式桥响应的信号, 基于车桥耦合动力学原理滤波处理得到包含梁式桥第一阶频率的信号, 最后假定梁式桥阻尼比值, 通过假定的梁式桥阻尼比值获取假定的梁式桥第一阶振型, 不断循环直至假定的阻尼比值下计算的第一阶振型最大值点居中, 即为识别的梁式桥真实阻尼比. 本文首先从车桥耦合动力学理论推导上说明了该方法的可行性, 然后考虑在不同车速与非恒定车速、路面粗糙度、环境噪音等影响因素下进行车桥耦合动力学模型分析, 最后通过实桥试验进行了初步验证. 研究结果表明: 该方法能一定程度上克服外界不利因素的影响, 达到识别梁式桥阻尼比的目的, 为识别梁式桥阻尼比提供一种更优方法, 其具有参数设置较少、操作简单方便以及更高测试精度等优点, 同时有助于推动基于车桥耦合的车桥耦合动力学理论技术在梁式桥模态参数识别工作中的实际工程应用.      

基于智能驾驶电动汽车的多车?桥梁耦合系统动力学特性研究

迫于能源和环保问题的压力, 电动汽车及智能驾驶受到了各国高度重视. 轮毂电机驱动电动汽车车轮振动剧烈, 与桥梁路面动力学相互作用更加突出, 现有研究主要针对传统汽车, 关于电动车轮与公路桥梁接触动力学相互作用及智能驾驶车队的多车?桥梁耦合作用研究尚不多见. 本文以轮毂电机驱动电动汽车为研究对象, 考虑车轮和桥面多点接触关系, 研究了两个智能驾驶汽车过桥时的车桥耦合动力学特性. 分析了电机质量、电机激励、轮胎悬架刚度非线性、车距、车速对系统振动特性的影响, 以及桥面不平顺激励、三重耦合激励对电动汽车平顺性的影响. 研究表明: 车距和车速是影响车?桥系统振动特性的重要因素, 在车?桥耦合动态设计中, 车距和车速的影响应重点关注; 桥面越平坦, 电机激励及桥面二次激励对车辆平顺性和道路友好性影响越加显著, 当汽车行驶在平坦桥面时两种激励对轮毂电机驱动电动汽车的影响不容忽视. 所建模型有望为智能驾驶电动汽车与桥梁的耦合作用研究提供理论参考.      

车-桥-线竖平面振动及其能量转化机制精细建模

建立了考虑车-桥(线)纵向振动及其能量相互转化机制的竖平面内精细耦合运动方程.将车-桥(线)视为一个整体系统,车辆各剐体的纵向运动均作为独立的自由度,考虑到车-桥(线)纵向振动及其能量相互转化机制,车辆驱动或制动作用采用轮轨间的纵向相互作用力和轮对作用力矩模拟,桥梁、线路结构采用梁单元离散,线路与桥梁之间的钢轨基础采用竖向和纵向的均布弹簧阻尼连接,建立了竖平面内精细耦合运动方程,它可合理模拟车桥(线)间能量相互转化的过程.简支梁桥算例表明:车辆在桥上无驱动或制动运行过程中,不考虑轨道结构时车速先增加后减小,而考虑轨道结构时车速只有减小的趋势,轮对还发生了高频的纵向振动,且车体和轮对的纵向振动对轨道竖向不平顺较为敏感;此外,考虑轮轨滚动碾压作用和能量转化机制时,钢轨加速度响应略偏大.本文研究可为实际车辆动态变速运行的模拟和更精细空间耦合模型的建立提供研究基础.     

Transverse vibrations of prestressed continuous beams on rigid supports under the action of moving bodies

The main objective of the paper is to investigate the dynamic response of the prestressed beams on rigid supports to moving concentrated loads. The governing equation of the transverse vibration of a prestressed continuous beam under the ununiformly distributed load is analytically formulated, taking into account the effect of the prestressing. The forced transverse vibration of the beam under the action of a large number of moving bodies has been investigated by using the method of substructures. In addition, the reaction forces at every rigid supports can be determined from the obtained differential equations. A comparison between the numerical results for the prestressed and the non-prestressed beam is presented to show the influence of the prestressing and the moving velocity of the bodies on the dynamic response of the beam. The calculating results are also examined and validated by experimental measurements at a large ferroconcrete bridge in Vietnam.     

Coupling vibration of vehicle-bridge system

By applying the sinusoidal wave mode to simulate the rugged surface of bridge deck, accounting for vehicle-bridge interaction and using Euler-Bernoulli beam theory, a coupling vibration model of vehicle-bridge system was developed. The model was solved by mode analyzing method and Runge-Kutta method, and the dynamic response and the resonance curve of the bridge were obtained. It is found that there are two resonance regions, one represents the main resonance while the other the minor resonance, in the resonance curve. The influence due to the rugged surface, the vibration mode of bridge, and the interaction between vehicle and bridge on vibration of the system were discussed. Numerical results show that the influence due to these parameters is so significant that the effect of roughness of the bridge deck and the mode shape of the bridge can‘ t be ignored and the vehicle velocity should be kept away from the critical speed of the vehicle_     

Absolute versus relative formulations of the moving oscillator problem

In the general framework of the bridge-vehicle dynamic interaction, the so-called “moving oscillator” problem is revisited in order to provide a deeper insight into some analytical and physical aspects not specifically analyzed in previous investigations. Without lack of generality, the case of a stream of moving oscillators crossing a simply supported beam with arbitrary time law is considered. The formulations in terms of both absolute and relative displacements of the moving oscillators are critically reviewed and compared, and alternative sets of differential equations with time-dependent coefficients are derived. The study enlightens, both theoretically and numerically, that impulsive contributions to the dynamic response appear in the relative displacement formulation at the time instants in which each vehicle enters or exits the bridge. It is demonstrated that such contributions, somehow “hidden” in the absolute displacement formulation, may have a significant influence on the vibration of the moving oscillators, and thus cannot be a priori neglected in the analysis. It is also shown that the analytical and computational difficulties associated with these additional impulses make preferable the use of the absolute displacement formulation. Far from being restricted to the case of simply supported beams, these findings are valid for any type of bridge structure which induces a discontinuity in the slope of the road profile experienced by the vehicles.