Vibration of railway bridges under a moving train by using bridge-track-vehicle element

During the last two decades, much attention has been paid to various vibration problems associated with railways. They include the dynamic response of railway bridges and railway tracks at grade under the action of moving trains. However, studies on the role of track structures on the vibration of railway bridges are rather limited. In this paper, a new element called bridge-track-vehicle element is proposed for investigating the interactions among a moving train, and its supporting railway track structure and bridge structure. The moving train is modelled as a series of two-degree-of-freedom mass-spring-damper systems at the axle locations. A bridge-track-vehicle element consists of vehicles modelled as mass-spring-damper systems, an upper beam element to model the rails and a lower beam element to model the bridge deck. The two beam elements are interconnected by a series of springs and dampers to model the rail bed. The investigation shows that the effect of track structure on the dynamic response of bridge structure is insignificant. However, the effect of the bridge structure on the dynamic response of the track structure is considerable.     

Dynamics of wind-rail vehicle-bridge systems

An analytical model for dynamics of wind-vehicle-bridge (WVB) systems is presented in this paper in the time domain with wind, rail vehicles and bridge modeled as a coupled vibration system. The analytical model considers many special issues in a WVB system, which include fluid-solid interaction between wind and bridge, solid contact between vehicles and bridge, stochastic wind excitation on vehicles and bridge, time dependence of the system due to vehicle movement, and effect of bridge deck on vehicle wind load and vice versa. The models of wind, vehicles and bridge are presented with wind velocity fluctuations simulated using the simplified spectral representation method, with vehicles modeled as mass-spring-damper systems, and with bridge represented by a finite element model. The interactions between wind and bridge are similar to those considered in conventional buffeting analysis for long span bridges. In considering difficulties in measuring aerodynamic coefficients of moving vehicles on bridge deck, the cosine rule is adopted for the aerodynamic coefficients of moving vehicles to consider yaw angle effect, and expressions of wind forces on moving vehicles are then derived for engineering application. To include mutual effects of wind loads, aerodynamic parameters of vehicles and bridge deck are measured, respectively, using a composite section model test and a specially designed test device. The dynamic interaction between vehicle and bridge depends on both geometric and mechanical relationships between wheels of vehicles and rails on the bridge deck. The equations of motion of the coupled WVB system are derived and solved with a nonlinear iterative procedure. A cable-stayed bridge in China is finally selected as a numerical example to demonstrate dynamic interaction of the WVB system. The results show the validity of the present model as well as wind effects on the rail vehicles and the bridge.     

Identification of parameters of vehicles moving on bridges

This paper presents a method for identifying the parameters of vehicles moving on bridges. Two vehicle models, a single-degree-of-freedom model and a full-scale vehicle model, are used. The vehicle–bridge coupling equations are established by combining the equations of motion of both the bridge and the vehicle using the displacement relationship and the interaction force relationship at the contact point. Bridge responses including displacement, acceleration, and strain are used in the identification process. The parameters of vehicles moving on the bridge are then identified by optimizing an objective function, which is built up using the residual between the measured response time history and predicted response time history using the Genetic Algorithm. A series of case studies have been carried out and the identified results demonstrate that the proposed method is able to identify vehicle parameters very accurately. Field tests have also been performed on an existing bridge in Louisiana, and the parameters of a real truck are predicted. Since it is able to identify the parameters of moving vehicles, the methodology can be applied to improve the current weigh-in-motion techniques that usually require a smooth road surface and slow vehicle movement to minimize the dynamic effects. The methodology can also be implemented in routine traffic monitoring and control.     

移动荷载作用下四种车桥耦合模型研究

通过有限元软件ANSYS建立桥梁有限元模型，通过分析桥梁在移动荷载模型、移动质量模型、移动车轮加簧上质量模型以及四分之一车模型下挠度变化曲线，指出自重、惯性力、弹簧在桥梁挠度变形中起到的重要作用，比较四种方法的可靠性及其适用条件。     

Framework of vehicle–bridge–wind dynamic analysis

This paper presents a framework of dynamic analysis of coupled three-dimensional vehicle–bridge system under strong winds. A general formulation of this system is introduced to simulate a series of vehicles consisting of different numbers and different types of vehicles running on bridges under hurricane-induced strong winds. Each vehicle is modeled as a combination of several rigid bodies, axle mass blocks, springs, and dampers, considering wind and road roughness loads. With this vehicle–bridge model, coupled dynamic analysis of vehicles running on bridges is conducted with a numerical example. Effects of driving speeds on the dynamic performance of the vehicles as well as the bridge are discussed. It is found that the driving speeds mainly affect the vehicle's vertical relative response while they have insignificant effect on the rolling response of vehicles. Vehicle's absolute response is dominated by the bridge response when wind speed is high, while it is dominated by road roughness when the wind speed is low. Detailed accident analysis of vehicles on bridges under strong winds will be reported in an accompanying paper.     

Estimation of gross weight,suspension stiffness and damping of a loaded truck from bridge measurements

Particle filter method (PFM) based on Bayesian inference gives a reliable estimate of hidden parameters from the noisy measured signal. A new method of vehicle parameter identification based on measured bridge response has been proposed using PFM. An uncoupled iterative technique is utilised for solving bridge vehicle interaction problem which has been used as a forward solution of the PFM. A field test under moving truck has been conducted on an existing pre-stressed concrete bridge to collect response data at different locations. Based on the extracted bridge natural frequencies and measured peak acceleration responses at five sensor locations, finite element model of the tested bridge has been updated using response surface-based model updating technique. In addition to estimation of test truck parameters using measured bridge response, dynamic wheel load induced in the bridge has been determined. Excellent agreement has been found between the measured and reconstructed bridge response using estimated parameters.     

Characteristic dynamic traffic load effects in bridges

When formulating an approach to assess bridge traffic loading with allowance for Vehicle-Bridge Interaction (VBI), a trade-off is necessary between the limited accuracy and computational demands of numerical models and the limited time periods for which experimental data is available. Numerical modelling can simulate sufficient numbers of loading scenarios to determine characteristic total load effects, including an allowance for VBI. However, simulating VBI for years of traffic is computationally expensive, often excessively so. Furthermore, there are a great many uncertainties associated with numerical models such as the road surface profile and the model parameter values (e.g., spring stiffnesses) for the heavy vehicle fleet. On site measurement of total load effect, including the influence of VBI, overcomes many of these uncertainties as measurements are the result of actual loading scenarios as they occur on the bridge. However, it is often impractical to monitor bridges for extended periods of time which raises questions about the accuracy of calculated characteristic load effects.Soft Load Testing, as opposed to Proof Load or Diagnostic Load Testing, is the direct measurement of load effects on bridges subject to random traffic. This paper considers the influence of measurement periods on the accuracy of soft load testing predictions of characteristic load effects, including VBI, for bridges with two lanes of opposing traffic. It concludes that, even for relatively short time periods, the estimates are reasonably accurate and tend to be conservative. Provided the data is representative, Soft Load Testing is shown to be a useful tool for calculating characteristic total load effect.     

铰接车辆模型识别粗糙桥梁频率和振型的数值分析

根据车桥耦合振动理论和桥梁间接测量法基本原理,对实际工程某连续梁桥建立桥梁模型,采用2辆单轴1/4车辆模型模拟测量车辆,1辆双轴半车模型模拟牵引车辆提供额外桥梁激励,三车前后铰接建立车辆模型。基于分离法原理与车辆动力学理论,利用约束方程实现任意时刻车轮与桥面接触点的位移协调关系,采用APDL编程实现铰接车辆过桥的耦合动力时程响应分析。提取前后测试车辆匀速通过不同等级粗糙桥面时车辆振动加速度时程响应,对通过桥梁同一位置处的前后测试车辆加速度数值进行相减处理并应用快速傅里叶变换识别桥梁频率。采用带通滤波技术与汉宁窗相结合的处理方法提取分离出与桥梁固有频率相关的桥频分量响应,利用桥频分量响应及其希尔伯特变换构造出与每阶固有频率相对应的振型。结果表明:在A、B、C级桥面不平整度条件下,采用铰接车辆模型识别出的桥梁前3阶频率相对误差均在1%以内; 对加速度时程响应数据加窗处理后识别出的桥梁前3阶振型MAC值均在0.95以上,满足工程精度需求; 研究结果可以为移动传感间接测量方法在桥梁检测工程中的应用提供理论参考。     

Accident assessment of vehicles on long-span bridges in windy environments

Currently, there are very few systematic analyses of vehicle performance on bridges in windy environments. There are thus no scientific data to support bridge management in this regard, such as when to close traffic on bridges. This paper presents a framework of vehicle accident analysis model on long-span bridges in windy environments. In the accompanying paper, a three-dimensional analysis of the coupled bridge-vehicle-wind system is developed. Each vehicle is modeled as a combination of several rigid bodies, axle mass blocks, springs, and dampers. Dynamic interaction analysis is then conducted on the vehicle-bridge system to predict the “global” bridge and vehicle dynamic responses without considering accident occurrences. The results of the global bridge-vehicle vibrations serve as the basis for the present accident analysis of the “local” vehicle vibrations. With the global vibrations as inputs of the accident model, the lateral response, yaw response of the vehicle, and the reaction forces of each individual wheel are obtained and the stability condition of the vehicles are analyzed. The vehicle accidents on long-span bridges are then identified with given accident criteria. The developed framework can be used in not only analyzing the vehicle performance on highways and on bridges, but also in predicting useful information for emergency preparedness agencies in developing evacuation plans.     

超重车途经河源市胜利大桥安全评估

随着交通运输业的发展,超重车过桥的情况日益增多。以河源市胜利大桥为例,以有限元分析手段建立桥梁分析模型,根据超重车参数抽象出车辆荷载模型,对超重车过桥的过程进行模拟计算。在对承载力分析的基础上研究了全桥的安全程度,给出了超重车过桥的决策建议及相关保障措施。研究成果可为类似情况提供参考和帮助。     

公路连续梁桥冲击系数的探讨

通过建立四座三跨连续梁桥在移动车辆荷载作用下的有限元模型,给模型赋不同的参数,研究了连续梁桥自振频率和车辆自振频率对车辆冲击效应的影响,分析表明,对于连续梁桥的冲击系数,除了基频对其有影响外,桥梁第二阶、第三阶频率以及车辆自身的动力特性对其也有影响。     

Development of a Bridge Bumper to Protect Bridge Girders from Overheight Vehicle Impacts

Abstract:   Bridges with low clearance are vulnerable to collision with overheight vehicles. Collisions of overheight vehicles can cause fatalities and injuries to the drivers and passengers of the overheight vehicles, and damage to bridge girders. The repair of the damaged bridges can be costly and time consuming. This article investigates the feasibility of developing a bridge bumper that minimizes the physical injuries and the likelihood of fatalities and protects the structural elements of bridges by absorbing the impact energy. The article presents the results of small-scale impact experiments using the proposed bridge bumper with several options of energy-absorbing materials to protect a reinforced concrete beam. Finite element analyses are carried out to simulate the small-scale impact experiments. Optimization of the finite element model is conducted for the response quantities of interest with respect to the geometrical parameters and the material properties of the proposed bridge bumper. Such analysis can guide the design of an optimal bridge bumper that maximizes the energy dissipation and minimizes the damage to the bridge girder and the likelihood of fatalities and injuries. A possible full-scale implementation of the proposed bridge bumper is also described.     

改进动态影响因子评估既有多肋混凝土梁桥性能

在很多设计规范中,桥面上移动车辆的动态影响一般被处理为动力系数(动态影响系数)。由于既有桥梁路面的退化,根据现场测量所计算的影响系数比设计规范中规定的值高。建立3维车辆-桥耦合模型,用以模拟桥和车辆之间的相互作用以及研究多肋混凝土梁桥的影响因子。对桥的跨度、车速、路面条件对影响因子的影响进行了检测。对影响因子进行了卡方试验。试验显示:在相同路面条件下获得的影响因子遵循极值-I分布。最后,提出适用于新桥和既有桥计算影响因子的简化表达式。对5个桥影响因子的相应置信水平研究显示:破旧路面的短跨桥、旧桥,采用AASHTO标准时,将低估了影响因子。所提表达式能够用于AASHTO标准的修正。     

Bridge–Vehicle Interaction in Curved Box Girder Bridges

Dynamic interaction between a moving vehicle and a bridge is a problem of considerable complexity, and its solution is governed by the dynamic characteristics of both the vehicle and bridge. The finite–element method, which is versatile and powerful, can be used to model the bridge–vehicle interaction and to obtain accurate results. Curved bridges are normally regular in geometry, and it is possible to simplify the conventional finite–element method to obtain fast results. In this paper, the spline finite–strip method of analysis is used along with a horizontally curved folded–plate model of the bridge. The vehicle is modeled as a three–axle tractor trailer combination with seven degrees of freedom.     

风-车-桥系统空间耦合振动研究

风-车-桥耦合振动系统中将自然风作为空间相关的平稳随机过程,车辆采用质点-弹簧-阻尼器模型,桥梁采用有限元模型。在分析风桥间的流固耦合作用、车桥间的接触耦合作用及风对车辆的空间脉动作用的基础上,将风、车、桥三者作为一个交互作用、协调工作的耦合动力系统,提出了一种较为完善的风-车-桥系统空间耦合振动分析模型。基于轮轨接触点处的几何协调条件和力学平衡关系,建立了系统运动方程的分离迭代求解算法。最后以京沪高速铁路南京大桥为工程背景,采用自行研发的桥梁结构分析软件BANSYS对比分析了风-车-桥系统振动特点。     

移动车辆载荷作用下桥梁动态响应(Ⅰ)

在车辆不同速度作用下桥梁的变形有其复杂性,对其研究为工程界所广泛关注。本文利用AN-SYS软件建立了桥梁的有限元模型,通过数值模拟计算分析了车辆以不同速度通过桥梁时,桥体发生的动态响应特征,从而为移动荷载作用下桥梁振动控制措施的改进提供依据。     

Dynamic analysis of three-dimensional bridge–high-speed train interactions using a wheel–rail contact model

A formulation of three-dimensional dynamic interactions between a bridge and a high-speed train using wheel–rail interfaces has been developed. In the interface, contact loss is allowed, the vertical contact is represented by finite tensionless stiffness and the lateral contact is idealized by finite contact stiffness and creepage damping. Such stiffness and damping are nonlinearly dependent on normal contact force. The relative rotations of a wheelset to the rails about its vertical and longitudinal axes are included. Bridge eccentricities and deck displacement due to torsion are accounted for in bridge deck modeling. A numerical algorithm using separate integrations for bridges and trains, and iterations for interface compatibilities is established. A case study of a ten-car train passing over a two-span continuous bridge at various speeds and rail irregularity wavelength ranges is analyzed. The responses of the bridge, car-bodies and wheelsets are investigated for their behavior, acceptability and relations with the wavelengths. Analytical and numerical evaluations of resonant speeds are in good agreement, and the exit span vibration is more amplified than the entrance one at those speeds. The computed relative displacements of all wheelsets to the rail facilitate an explicit assessment for derailment risk.     

Improvement effects of bottom lateral bracings on dynamic performance of curved steel twin I-girder bridges under running vehicles

The torsional stiffness of curved twin I-girder bridges is very low, which may lead to a vulnerability to eccentric dynamic loads. This study is intended to investigate the improvement effect of bottom lateral bracings on dynamic performance of curved twin I-girder bridges under running vehicles, using a developed numerical approach. In this approach, to conduct the running vehicle-bridge interaction analysis, finite element method is used to create the detailed models of both the curved bridge and the running vehicle. Parametric studies are carried out using these numerical models to investigate the effect of bottom lateral bracings on the dynamic performance of the curved bridge under running vehicles. The numerical results indicate that the proposed bottom lateral bracing systems can increase the torsional stiffness of the bridge, whose increasing rate depends on the type of bracing configuration. The bottom lateral bracings can also distribute dynamic loads smoothly between the two main girders, which leads to a more stable structure.     

单拱面预应力混凝土系杆拱梁桥极限承载力分析的截面内力塑性系数法

基于UpdatedLagrangian (更新拉格朗日 )列式单元增量平衡方程 ,提出了一种建立钢筋混凝土空间梁单元弹塑性刚度矩阵的新方法———单元节点截面内力塑性系数法 ,并编制了单拱面预应力混凝土系杆拱梁桥空间稳定极限承载力计算程序。理论分析结果与两个模型试验结果十分接近 ,验证了分析方法的正确性及可靠性。该方法可以用于大型桥梁的空间稳定极限承载力分析     

Fuzzy logic modeling of deflection behavior against dynamic loading in flexible pavements

Flexible pavements are especially affected by moving vehicles. As a result of the moving vehicles, the pavement starts to deteriorate. For the determination of the structural capacity of the pavement, non-destructive testing equipments are used. These are mainly Benkelman beam, Dynaflect and falling weight deflectometer (FWD). In such a process, the most important thing is to analyze the collected data. In general, linear elastic theory and finite element method are used for this purpose. Since linear elastic theory and finite element method are time consuming, a fuzzy logic approach is used for the elimination of this drawback during the course of this study. Results indicate that the fuzzy logic approach can be used for the modeling of the deflection behavior against dynamic vehicle loading for flexible pavements. The fuzzy model is able to predict the deflection behavior against dynamical loading. The new approach can capture the non-linearity of surface deflection behavior.