Formulation of equations of motion of finite element form for vehicle–track–bridge interaction system with two types of vehicle model

Vehicle, track and bridge are considered as an entire system in this paper. Two types of vertical vehicle model are described. One is a one foot mass–spring–damper system having two‐degree‐of‐freedom, and the other is four‐wheelset mass–spring–damper system with two‐layer suspension systems possessing 10‐degree‐of‐freedom. For the latter vehicle model, the eccentric load of car body is taken into account. The rails and the bridge deck are modelled as an elastic Bernoulli–Euler upper beam with finite length and a simply supported Bernoulli–Euler lower beam, respectively, while the elasticity and damping properties of the rail bed are represented by continuous springs and dampers. The dynamic contact forces between the moving vehicle and rails are considered as internal forces, so it is not necessary to calculate the internal forces for setting up the equations of motion of the vehicle–track–bridge interaction system. The two types of equations of motion of finite element form for the entire system are derived by means of the principle of a stationary value of total potential energy of dynamic system. The proposed method can set up directly the equations of motion for sophisticated system, and these equations can be solved by step‐by‐step integration method, to obtain simultaneously the dynamic responses of vehicle, of track and of bridge. Illustration examples are given. Copyright 2004 © John Wiley & Sons, Ltd.     

An element for analysing vehicle–bridge systems considering vehicle's pitching effect

Vehicle–bridge interaction (VBI) elements that were derived by treating a vehicle as discrete sprung masses lack the capability to simulate the pitching effect of the car body on the vehicle and bridge responses. To overcome this drawback, a vehicle is modelled instead as a rigid beam supported by two spring‐dashpot units in this paper. The equations of motion written for the vehicle and the bridge (beam) elements are coupled due to the existence of the interacting forces at contact points. To resolve this problem, the vehicle equations are first reduced to equivalent stiffness equations using Newmark's discretization scheme. Then, the vehicle degrees of freedom (DOFs) are condensed to those of the beam elements in contact. The rigid vehicle–bridge interaction elements derived can be effectively used in computation of not only the bridge response, but also the vehicle response, as required in design of high‐speed railroad bridges. Copyright © 1999 John Wiley & Sons, Ltd.     

多个移动车辆作用下简支梁的动力响应分析

将简支梁桥简化为欧拉-伯努利梁模型,考虑四自由度车辆移动系统与结构表面接触处不平顺产生的随机激励,建立了多个移动车辆振动系统与梁的耦合动力效应模型。在数值算例中,计算了不同模态截断阶数情况下由动力效应产生的挠曲线;讨论了移动速度变化时,在梁上作用不同荷载组合情况下冲击系数的变化规律;并讨论了跨径变化时冲击系数的变化规律;最后比较了在不同等级平整度情况下梁的动弯矩、动剪力的结果。     

时速400 km/h铁路常用跨度预应力混凝土简支梁竖向基频限值研究

建立有限元模型,计算常用跨度预应力混凝土简支箱梁的竖向基频,以设计荷载对桥梁的动力效应不小于运营列车对桥梁的动力效应为准则,确定梁体容许动力系数;基于移动荷载模型,得到常用跨度简支箱梁在列车作用下的动力系数;在综合分析桥梁动力响应与列车类型、运营速度、桥梁竖向基频关系的基础上,提出了时速400 km/h常用跨度预应力混凝土简支箱梁的竖向基频限值。研究表明:通过调整车长与桥梁跨度之比可避开基阶振型的共振,有利于行车安全;在车长25 m左右的列车作用下,跨度24 m、32 m和40 m的预应力混凝土简支箱梁竖向自振基频限值取125/L、155/L和90/L时,可以有效地降低梁体动力响应。     

铁路简支梁桥竖向共振影响因素的分析

采用车-桥系统模型,对影响铁路简支梁桥竖向共振的各种因素进行了分析。分析结果表明:列车静轴重荷载是引起简支梁桥竖向共振现象的主要原因,而其它因素(如桥梁本身的跨度、刚度及阻尼,车辆的长度、轮对的质量、悬挂弹簧的刚度和阻尼等)对桥梁竖向共振的发生和发展也有着重要的影响。     

汽车对桥梁冲击作用分析

为了分析汽车桥梁系统参数变化对动力放大系数的影响规律，将桥梁等效为等长的欧拉梁单元，将汽车等效为两自由度五参数模型，在状态空间求解车桥耦合振动方程得到系统的动力响应，定义了由垂向挠度和弯矩表示的动力放大系数。在数值模拟中研究了桥上路面不平顺、桥梁损伤、汽车参数和汽车速度对冲击系数的影响。     

高速车辆过桥时的舒适性分析

车辆过桥引发的振动问题已有很多研究，目前大部分工作集中在桥梁结构的安全性方面，本文从舒适性角度出发，讨论了桥梁结构的振动对车辆垂向加速度的影响，基于移动荷载简支梁模型，给出了车辆垂向加速度与车速及梁桥固有频率之间的数学关系，并分析了路桥过渡段及临界速度情况下车辆的最大加速度。     

Precise identification of moving vehicular parameters based on improved glowworm swarm optimization algorithm

This paper proposes an indirect method for the identification of moving vehicular parameters using the dynamic responses of the vehicle. The moving vehicle is modelled as 2-DOF system with 5 parameters and 4-DOF system with 12 parameters, respectively. Finite element method is used to establish the equation of the coupled bridge–vehicle system. The dynamic responses of the system are calculated by Newmark direct integration method. The parameter identification problem is transformed into an optimization problem by minimizing errors between the calculated dynamic responses of the moving vehicle and those of the simulated measured responses. Glowworm swarm optimization algorithm (GSO) is used to solve the objective function of the optimization problem. A local search method is introduced into the movement phase of GSO to enhance the accuracy and convergence rate of the algorithm. Several test cases are carried out to verify the efficiency of the proposed method and the results show that the vehicular parameters can be identified precisely with the present method and it is not sensitive to artificial measurement noise.     

京沪高速铁路南京长江大桥列车走行性分析

运用桥梁结构动力学与车辆动力学的研究方法,将车桥作为联合动力体系,建立了高速列车与大跨度斜拉桥的车桥耦合动力分析模型。以京沪高速铁路南京长江大桥3塔斜拉桥方案为例,分析了大跨度斜拉桥在ICE高速列车作用下的车桥动力响应特点;同时,基于合理的列车走行性评价指标,对高速列车通过大跨度斜拉桥时的走行安全性与舒适性进行了详细分析,初步探讨了大跨度斜拉桥用于高速铁路的可行性。     

重载列车过桥时桥梁的垂向动力分析

本文建立了具有6个自由度重载列车的车辆振动分析模型和重载铁路桥梁的梁段单元模型,通过轮轨接触处的位移协调条件与轮轨相互作用力的平衡关系建立了重载车辆-桥梁系统耦合运动方程,采用迭代求解,编制了重载铁路车-桥耦合振动分析程序。对影响重载铁路简支梁桥的跨中挠度的各种因素进行了分析,分析结果表明：列车的轴重、速度、加速度、减速度及轨道不平顺对重载铁路桥梁的跨中挠度和竖向加速度有着重要影响。     

移动载荷作用下斜拉桥结构的动态响应计算分析

运用斜拉桥的近似分析方法,将漂浮体系的斜拉桥结构简化成两端简支且中间离散弹性支撑梁、变地基系数梁和均匀地基系数地基梁三种模型。建立了移动载荷作用下斜拉桥结构的动力学方程,用四阶龙格库塔法对动力学方程进行了计算,对三种模型的固有频率和三种模型在相同移动载荷作用下的动态响应进行了比较,并对移动载荷移动速度、垂直振动的刚度和阻尼对桥梁动态响应的影响进行分析。结果表明,当拉索等效弹性系数较小时,三种模型的固有频率和挠度曲线差别较小,当拉索等效弹性系数较大时,三种模型的固有频率和挠度曲线差别明显;桥梁动态响应的频谱由桥梁的固有频率和移动载荷的自振频率组成;移动载荷垂直振动的刚度越大,阻尼越小,桥梁振动的响应越大。     

简支梁桥与多跨连续梁桥上移动荷载的识别与参数分析

移动车辆荷载反复作用会导致桥梁疲劳损伤甚至破坏,移动荷载识别是桥梁健康监测的重要措施之一。采用样条函数逼近法对简支梁桥与多跨连续梁桥上的移动荷载进行识别和参数分析。基于模态叠加法和梁固有振动的精确解,建立了移动荷载作用下简支梁和连续梁的运动方程;利用样条最小二乘法逼近桥梁应变响应,由样条数值微分求得响应导数;再通过Tikhonov正则化方法结合奇异值分解技术得到了荷载识别的正则解。对一简支梁和一三跨连续梁进行了数值仿真,并对一些影响因素进行了参数分析。利用已有的试验数据验证了方法的可靠性。结果表明,样条函数逼近法能有效地识别简支梁与连续梁桥上的移动荷载,具有很强的实用性和抗噪性能;而且简支梁桥上的荷载识别精度和抗噪性能高于连续梁桥;利用Tikhonov正则化方法可得到荷载识别的稳定解,并有利于提高识别精度,降低对噪声的敏感性。     

Dynamic analysis of a functionally graded simply supported Euler–Bernoulli beam subjected to a moving oscillator

The dynamic behavior of a functionally graded (FG) simply supported Euler–Bernoulli beam subjected to a moving oscillator has been investigated in this paper. The Young’s modulus and the mass density of the FG beam vary continuously in the thickness direction according to the power-law model. The system of equations of motion is derived by using Hamilton’s principle. By employing Petrov–Galerkin method, the system of fourth-order partial differential equations of motion has been reduced to a system of second-order ordinary differential equations. The resulting equations are solved using Runge–Kutta numerical scheme. In this study, the effect of the various parameters such as power-law exponent index and velocity of the moving oscillator on the dynamic responses of the FG beam is discussed in detail. To validate the present formulation, the mid-point displacement of the beam is compared with that of the existing literature, and also a comparison study is performed for free vibration of an FG beam. Good agreement is observed. The results indicated that the above-mentioned parameters have a significant role in the analysis.     

高速铁路铰接式列车车桥系统动力响应分析

根据铰接式车辆结构和悬挂形式的特点,建立了铰接车辆单元模型,以现有通用软件为基础直接生成桥梁模型的质量、刚度矩阵,并以实测轨道不平顺为系统激励,求解车桥耦合动力相互作用问题;以欧洲布鲁塞尔-巴黎高速铁路线上的Thalys铰接式列车通过Antoing桥为例,分析了桥梁的动挠度、竖向和横向加速度等动力响应及运行车辆的振动加速度响应,并对铰接式列车的振动特性进行了初步的探讨;最后通过现场试验对分析模型和计算结果进行了验证。     

大跨度提篮拱桥车桥耦合振动分析

目前国内外规范对桥梁设计关于桥梁刚度限值的规定只适用于单跨和多跨简支梁等小跨度常规桥梁,特殊结构桥梁都超出了目前我国各种规范和暂规所能涵盖的范围.提出了列车、大跨度提篮拱桥空间振动的有限单元分析模型,采用计算机模拟方法,计算了列车以不同车速通过该大跨度提篮拱桥的空间振动响应,检算该桥是否具有足够的横向、竖向刚度及良好的运营平稳性,所得结果可供设计参考.     

A general solution to the identification of moving vehicle forces on a bridge

Bridge weigh‐in‐motion systems measure bridge strain caused by the passing of a truck to estimate static axle weights. For this calculation, they commonly use a static algorithm that takes the bridge influence line as reference. Such a technique relies on adequate filtering to remove bridge dynamics and noise. However, filtering can lead to the loss of a significant component of the underlying signal in bridges where the vibration does not have time to complete sufficient number of cycles and in cases of closely spaced axles traveling at high vehicle speeds. In order to overcome these limitations and also to provide additional information on the dynamics of the applied forces, this paper presents an algorithm based on first‐order Tikhonov regularization and dynamic programming. First, strain measurements are simulated using an elaborate three‐dimensional vehicle and orthotropic bridge interaction system. Then, strain is contaminated with noise and input into the moving force identification algorithm. The procedure to implement the algorithm and to derive the applied forces from the simulated strain record is described. Vehicle axle forces are shown to be accurately predicted for smooth and rough road profiles and a range of speeds. Copyright © 2008 John Wiley & Sons, Ltd.     

Multi cracks detection in Euler-Bernoulli beam subjected to a moving mass based on acceleration responses

In this paper, a novel approach has been proposed to detect crack in beam structures under moving mass using extreme learning machine and the least square support vector machine. For this purpose, acceleration responses of beam under moving mass were used as input to train machines. This data are acquired by the analysis of cracked structure applying the finite element method. To demonstrate the potential of the proposed vibration analysis over existing ones, a validation study has been done. To evaluate the performance of the presented method, a simply supported beam and a three-span continuous beam with and without noise in acceleration responses were considered. Also, the effect of the discrepancy in stiffness between the finite element model and the actual tested dynamic system has been investigated. The obtained results indicated that this method can provide a reliable tool to accurately identify cracks in beam structures under moving mass.     

基于精细Runge-Kutta混合积分法的车桥耦合振动非迭代求解算法

针对结构非线性问题,采用4阶Runge-Kutta法展开精细积分法中响应状态方程的Duhamel项,构造了一种既可以避免迭代又具有较高精度的精细Runge-Kutta混合积分方法,在此基础上提出了适用于车桥耦合振动高效求解的分析框架。车桥耦合系统由车辆、桥梁子系统组成,均采用有限元建模,其中车辆子系统采用部件刚体假定,而桥梁子系统借助于振型叠加法缩减自由度数目;两个子系统内部非线性作用以及系统间的相互作用通过非线性的虚拟力表达。以一节4轴客车匀速通过32m简支梁为研究对象,分别采用分析框架法、Runge-Kutta法进行动力分析。数值结果对比表明：相对于Runge-Kutta法,精细Runge-Kutta混合法能够显著提高计算收敛的积分步长;分析框架可以应用到实际工程中。     

Dynamic analysis of bridge–vehicle system with uncertainties based on the finite element model

A new method of dynamic analysis on the bridge–vehicle interaction problem considering uncertainties is proposed in this paper. The bridge is modeled as a simply supported Euler–Bernoulli beam with Gaussian random elastic modulus and mass density of material with moving forces on top. These forces are time varying with a coefficient of variation at each time instance and they are considered as Gaussian random processes. The mathematical model of the bridge–vehicle system is established based on the finite element model in which the Gaussian random processes are represented by the Karhunen–Loéve expansion and the equations will be solved by the Newmark  -β$\beta$ method. The proposed method is compared with the Monte Carlo method in numerical simulations with good agreements for cases with different vehicle speed and level of uncertainties in the excitation and system parameters. The mean value and variance of the structural responses are found to be very accurate even with large uncertainties in the excitation forces. The proposed method is also found to have superior performance in the computational efficiency compared with the Monte Carlo method.     

桥上列车移动荷载参数自动识别系统试验

提出了一种用于列车移动荷载参数自动识别的系统,并制作了等截面简支钢梁和试验列车模型进行试验研究。利用基于图像处理技术的桥梁动态位移采集系统,获取模型桥梁测点位置的动态位移响应,同时利用自行设计的列车模型参数采集系统获取列车模型的移动速度、轮轴个数和轴间距,最后采用桥梁列车多轴移动荷载识别系统识别出列车轴重荷载值。通过对不同移动速度、不同测点个数下列车参数识别效果的分析,验证了本文所述列车移动荷载参数自动识别系统的可行性和准确性,为今后荷载识别系统的实际应用做好准备。