Dominant frequencies of train-induced vibrations

This paper investigates the dynamic characteristics of ground vibrations induced by moving vehicles including the mass rapid transit system, high-speed train railway, and general railway on bridges, embankments, and in tunnels using field experiments and theoretical solutions. The results indicate that train-induced ground vibrations at the trainload dominant frequencies are significantly large for both subsonic and supersonic train speeds, and the vibrations from carriage natural frequencies and engine frequencies are minor. For trains moving on bridges, the resonant vibrations are serious when the natural frequencies of the bridge are close to the trainload dominant frequencies, but resonance does not occur when the carriage natural frequencies and trainload dominant frequencies match. The trainload dominant frequency and its influence factor can be computed using the two simple equations deducted in this paper.     

Finite element modelling for fatigue stress analysis of large suspension bridges

Fatigue is an important failure mode for large suspension bridges under traffic loadings. However, large suspension bridges have so many attributes that it is difficult to analyze their fatigue damage using experimental measurement methods. Numerical simulation is a feasible method of studying such fatigue damage. In British standards, the finite element method is recommended as a rigorous method for steel bridge fatigue analysis. This paper aims at developing a finite element (FE) model of a large suspension steel bridge for fatigue stress analysis. As a case study, a FE model of the Tsing Ma Bridge is presented. The verification of the model is carried out with the help of the measured bridge modal characteristics and the online data measured by the structural health monitoring system installed on the bridge. The results show that the constructed FE model is efficient for bridge dynamic analysis. Global structural analyses using the developed FE model are presented to determine the components of the nominal stress generated by railway loadings and some typical highway loadings. The critical locations in the bridge main span are also identified with the numerical results of the global FE stress analysis. Local stress analysis of a typical weld connection is carried out to obtain the hot-spot stresses in the region. These results provide a basis for evaluating fatigue damage and predicting the remaining life of the bridge.     

Damage identification in plates using finite element model updating in time domain

A response sensitivity-based approach is presented for identifying the local damages in isotropic plate structures from the measured structural dynamic responses. The local damage is simulated by a reduction in the elemental Young's modulus of the plate. In the forward analysis, the forced vibration responses of the plate under external force are obtained from Newmark direct integration. In the inverse analysis, a response sensitivity-based finite element model updating approach is used to identify local damages of the plate in time domain. The damage identification results are obtained iteratively with the penalty function method with Tikhonov regularization using the measured structural dynamic responses. Two numerical examples are investigated to illustrate the correctness and efficiency of the proposed method. Both single damage and multiple damages cases are studied. The effects of measurement noise and measurement point on the identification results are investigated. Studies in this paper indicate that the proposed method is efficient and robust for both single and multiple damages for plate structures. Good identified results can be obtained from the short time histories of a few number of measurement points.     

Eigenproperties of suspension bridges with damage

The vertical vibration of suspension bridges with a damage in the main cables is studied using a continuum formulation. Starting from a model for damaged suspended cables recently proposed in the literature, an improved expression for the dynamic increment of cable tension is derived. The nonlinear equation of motion of the damaged bridge is obtained by extending this model to include the stiffening girder. The linear undamped modal eigenproperties are then extracted, in closed-form, from the linearized equation of motion, thus generalizing to the presence of an arbitrary damage the expressions known from the literature for undamaged suspension bridges. The linear dynamics of the damaged bridge reveals to be completely described by means of the same two non-dimensional parameters that govern the linear dynamics of undamaged bridges and which account for the mechanical characteristics of both the main cable and the girder, with the addition of three non-dimensional parameters characterizing damage intensity, position and extent. After presenting the mathematical formulation, a parametric analysis is conducted with the purpose of investigating the sensitivity of natural frequencies and mode shapes to damage, which, in fact, is a crucial point concerning damage detection applications using inverse methods. All through the paper, systematic comparisons with finite element simulations are presented for the purpose of model validation.     

Experimental analysis of a high-speed railway bridge under Thalys trains

In this paper dynamic experiments on the Antoing Bridge located on the high-speed railway line between Paris and Brussels are reported. The experiments were co-operatively carried out by the Northern Jiaotong University from China, the Catholic University of Leuven, the Free University of Brussels and the Belgium Railway Company NMBS-SNCB from Belgium. The bridge is composed of multi-span simply supported PC girders with spans of 50 m and U-shaped sections. The loads are the high-speed Thalys trains with articulated vehicles. The speeds of the Thalys trains were between 265 and 310 km/h. In the experiments, the dynamic responses of the bridge such as the deflections, the accelerations and the strains that were measured by a laser velocity displacement transducer accelerometers and strain gauges, respectively. Many useful results have been obtained from the analysis of the recorded data. The tests and the measured results can be a reference for the study and the design of high-speed railway bridges.     

Resonance characteristics of high-speed trains passing simply supported bridges

This paper investigates the resonant characteristics of three-dimensional bridges when high-speed trains pass them. Multi-span bridges with high piers and simply supported beams were used in the dynamic finite element analysis. The dominated train frequencies proposed in this study can be clearly seen from the finite element result. To avoid resonance, the dominated train frequencies and the bridge natural frequencies should be as different as possible, especially for the first dominated train frequency and the first bridge natural frequency in each direction. If the two first frequencies are similar, the bridge resonance can be serious. This study also indicates that a suitable axial stiffness between two simple beams can reduce vibrations at a near-resonance condition. The axial stiffness of the continuous railway and the friction of the bearing plate should be enough to obtain this axial stiffness.     

Optimal design of passive viscous dampers for controlling the resonant response of orthotropic plates under high-speed moving loads

In this article, the resonant response of plates traversed by moving loads is addressed being its main application the dynamic performance of railway bridges under high-speed traffic. An innovative alternative to reduce the deck inadmissible oscillations that may appear in short simply supported structures in resonant conditions is proposed, based on artificially increasing the superstructure damping by retrofitting the deck with fluid viscous dampers. A particular auxiliary structure transforming the deck vertical deflection into relative movement within the devices is envisaged, being the main objectives of the study to optimise the retrofitting system parameters and to prove its efficiency under the action of railway vehicles. For these purposes, the retrofitted deck behaviour is first investigated using an orthotropic plate model under harmonic excitation. On the basis of an analytical approach, a dimensionless version of the equations of motion is presented, the governing parameters are extracted and an intensive sensitivity analysis of the plate response is performed. Finally, analytical closed-form expressions for the optimal dampers constants are derived and their adequacy is numerically evaluated. To this end, an existing bridge belonging to the Spanish Railway network is analysed using a three-dimensional finite element code specifically programmed by the authors for this application. In the end the controlling effect of the retrofitting system and the applicability of the optimal parameters analytical expressions are proven for a wide range of circulating velocities.     

A damage identification technique based on embedded sensitivity analysis and optimization processes

A vibration based structural damage identification method, using embedded sensitivity functions and optimization algorithms, is discussed in this work. The embedded sensitivity technique requires only measured or calculated frequency response functions to obtain the sensitivity of system responses to each component parameter. Therefore, this sensitivity analysis technique can be effectively used for the damage identification process. Optimization techniques are used to minimize the difference between the measured frequency response functions of the damaged structure and those calculated from the baseline system using embedded sensitivity functions. The amount of damage can be quantified directly in engineering units as changes in stiffness, damping, or mass. Various factors in the optimization process and structural dynamics are studied to enhance the performance and robustness of the damage identification process. This study shows that the proposed technique can improve the accuracy of damage identification with less than 2 percent error of estimation.     

Mechanism of resonance and cancellation for train-induced vibrations on bridges with elastic bearings

In this paper, the mechanism involved in the phenomena of resonance and cancellation in the train-induced vibrations of railway bridges with elastic bearings is explained using an analytical approach. The train is modelled as a sequence of moving loads of constant intervals. The vibration shape of the elastically supported beam is approximated by the combination of a flexural sine mode and a rigid body mode. The present results indicate that under certain conditions, resonances of much higher peaks can be excited on elastically supported beams by moving trains at much lower speeds than those on simply supported beams. The cancellation is a phenomenon more decisive than that of resonance, in that it can suppress the latter even when the condition of resonance is met. Moreover, the speed for cancellation to occur is generally independent of the support stiffness. To verify the analytical results presented herein, a field test was conducted on two adjacent elastically supported bridges in existing railway lines. In the design of railway bridges, it is important that the phenomenon of resonance not be overlooked, as it is harmful not only to the riding comfort of passengers, but to the maintenance of railway tracks.     

A sensitivity-based structural damage identification method with unknown input excitation using transmissibility concept

Unknown input excitation and local damages universally coexist in a practical situation. Therefore, in this paper a structural damage identification method based on the transmissibility concept in state space domain is proposed without the need for input measurements. On the basis of the transformation matrix which is computed using the system Markov parameters in state space, the relationship between two different sets of acceleration response measurements can be formulated under the same input excitation. A sensitivity-based model updating approach is applied to identify the local damages by minimizing the difference between the measured response and the reconstructed response. The sensitivity of the dynamic acceleration response with respect to the elemental stiffness factors is derived analytically in the state space domain, which accelerates the process of damage identification. A numerical cantilever beam is employed to validate that the variation of structural parameters induced by the local damages can be accurately and effectively identified without the input excitation information by the proposed method even with measurement noise considered. A laboratory test is further carried out to verify the proposed structural damage identification method based on the response reconstruction technique.     

Dynamic response of a monorail steel bridge under a moving train

This study proposes a dynamic response analysis procedure for traffic-induced vibration of a monorail bridge and train. Each car in the monorail train is idealized as a dynamic system of 15-degrees-of-freedom. The governing equations of motion for a three-dimensional monorail bridge-train interaction system are derived using Lagrange's formulation for monorail trains, and a finite-element method for modal analysis of monorail bridges. Analytical results on dynamic response of the monorail train and bridge are compared with field-test data in order to verify the validity of the proposed analysis procedure, and a positive correlation is found. An interesting feature of the monorail bridge response is that sway motion is caused by torsional behavior resulting from eccentricity between the shear center of the bridge section and the train load.     

Dynamic analysis of a coupled high-speed train and bridge system subjected to collision load

A dynamic analysis model is established for a coupled high-speed train and bridge system subjected to collision-load. A 7×32 m simply-supported high-speed railway bridge with box girders is considered as an illustrating case study. A high-speed China-Star train is traveling on the bridge. The time history curve of a drifting-floe collision force is obtained from a field experiment and introduced as the excitation load on the bridge piers. Then, the dynamic response of the coupled train–bridge system subjected to the measured drifting-floe collision is calculated. Afterwards, the running safety indices such as derailment factor, offload factor and lateral wheel-rail force of train vehicles are investigated. The results show that the dynamic response of the bridge subjected to a collision load is much greater than the one without a collision, resulting in a big influence on the running safety of high-speed trains. For the case study, a critical train speed curve is proposed to evaluate the running safety of train vehicles on the bridge under drifting-floe collision with various intensities.     

Concrete bridge-borne low-frequency noise simulation based on train–track–bridge dynamic interaction

Both the vibration of a railway bridge under a moving train and the associated bridge-borne noise are time-varying in nature. The former is commonly predicted in the time domain to take its time-varying and nonlinear properties into account, whereas acoustic computation is generally conducted in the frequency domain to obtain steady responses. This paper presents a general procedure for obtaining various characteristics of concrete bridge-borne low-frequency noise by bridging the gap between time-domain bridge vibration computation and frequency-domain bridge-borne noise simulation. The finite element method (FEM) is first used to solve the transient train–track–bridge dynamic interaction problem, with an emphasis on the local vibration of the bridge. The boundary element method (BEM) is then applied to find the frequency-dependent modal acoustic transfer vectors (MATVs). The time-domain sound pressure is finally obtained with the help of time–frequency transforms. The proposed procedure is applied to a real urban rail transit U-shaped concrete bridge to compute the bridge acceleration and bridge-borne noise, and these results are compared with the field measurement results. Both sets of results show the proposed procedure to be feasible and accurate and the dominant frequencies of concrete bridge-borne noise to range from 32 Hz to 100 Hz.     

光纤光栅多参数桥梁结构监测系统的研究

从土木工程应用的实际情况出发,利用光纤光栅传感器具有波长绝对编码和易于复用的特点,提出工程化同时测量温度、应变和压力的全光栅型低成本分布式传感方案。设计了基于连续波调频技术的光纤光栅多参量桥梁结构监测系统,将光频域反射复用与波分复用技术相结合,实现分布式光栅传感网络的寻址,提高了系统复用容量。实验表明：所设计的传感系统能够准确监测结构重要部位的内部应变及车流量等参数,为桥梁结构的静、动载测试提供了准确的数据,同时也为桥梁的工作状态评估和健康诊断提供了依据。     

DYNAMIC ANALYSIS OF LARGE-DIAMETER SAGGED CABLES TAKING INTO ACCOUNT FLEXURAL RIGIDITY

For the purpose of developing a vibration-based tension force evaluation procedure for bridge cables using measured multimode frequencies, an investigation on accurate finite element modelling of large-diameter sagged cables taking into account flexural rigidity and sag extensibility is carried out in this paper. A three-node curved isoparametric finite element is formulated for dynamic analysis of bridge stay cables by regarding the cable as a combination of an “ideal cable element” and a fictitious curved beam element in the variational sense. With the developed finite element formulation, parametric studies are conducted to evaluate the relationship between the modal properties and cable parameters lying in a wide range covering most of the cables in existing cable-supported bridges, and the effect of cable bending stiffness and sag on the natural frequencies. A case study is eventually provided to compare the measured natural frequencies of main cables of the Tsing Ma Bridge and the computed frequencies with and without considering cable bending stiffness. The results show that ignoring bending stiffness gives rise to unacceptable errors in predicting higher order natural frequencies of the cables, and the proposed finite element formulation provides an accurate baseline model for cable tension identification from measured multimode frequencies.     

A time-domain approach for damage detection in beam structures using vibration data with a moving oscillator as an excitation source

The problem of detecting local/distributed change of stiffness in bridge structures using ambient vibration data is considered. The vibration induced by a vehicle moving on the bridge is taken to be the excitation source. A validated finite element model for the bridge structure in its undamaged state is assumed to be available. Alterations to be made to this initial model, to reflect the changes in bridge behaviour due to occurrence of damage, are determined using a time-domain approach. The study takes into account complicating features arising out of dynamic interactions between vehicle and the bridge, bridge deck unevenness, spatial incompleteness of measured data and presence of measurement noise. The inclusion of vehicle inertia, stiffness and damping characteristics into the analysis makes the system time variant, which, in turn, necessitates treatment of the damage detection problem in time domain. The efficacy of the procedures developed is demonstrated by considering detection of localized/distributed damages in a beam-moving oscillator model using synthetically generated vibration data.     

Singular spectrum analysis for enhancing the sensitivity in structural damage detection

Time domain structural condition assessment methods have been studied extensively in the last two decades due to their effectiveness in dealing with limited and short duration measurements from a structure under operational conditions. The sensitivity-based method is revisited in this paper with an enhancement in the sensitivity with respect to local damages via the singular spectrum analysis technique. The measured response of the structure is decomposed and the sensitivity vectors as well as the computed response vectors are projected into the corresponding decomposition subspace. The projected identification equations associate with components which contain the least measurement noise and the most damage information are then used to detect local damages in the structure. The enhanced sensitivity-based method is shown to be capable of yielding more accurate identified results with noisy measurement in a planar truss structure compared to conventional sensitivity-based method. A seven-storey steel frame test is performed in the laboratory, and the proposed method is checked to be able to identify the damage location and extend of this structure with an acceptable accuracy.     

桥梁拉索损伤声发射监测研究进展

大量索承体系桥梁即将达到20–30年的拉索寿命期,开展有效的拉索损伤监测方法研究有利于保障大桥结构安全。本文简要论述了现有桥梁拉索损伤检测及监测方法的适用性,重点综述了近40年来声发射技术应用于桥梁拉索监测的研究进展,以及在腐蚀、疲劳、断丝等损伤监测方面所取得的研究成果。结合实测数据在采集、数据处理过程中的难点及参数分析盲点,探讨了现有研究成果应用于特大桥梁拉索损伤监测仍需解决的问题,并针对性地提出了研究思路。     

Critical speed for the dynamics of truck events on bridges with a smooth road surface

Simple numerical models of point loads are used to represent single and multiple vehicle events on two-lane bridges with a good road profile. While such models are insufficiently complex to calculate dynamic amplification accurately, they are presented here to provide an understanding of the influence of speed and distance between vehicles on the bridge dynamic response. Critical combinations of speed as a function of main bridge natural frequency and meeting point of two vehicles travelling in opposite directions are identified. It is proposed that such simple models can be used to estimate the pattern of critical speeds versus dynamic amplification of the bridge response for trucks on a relatively smooth surface. The crossing of a three-dimensional spring-dashpot truck is simulated over a bridge plate model to test this hypothesis for a range of road roughness. Further validation is carried out using the site-specific mean pattern associated to field measurements of bridge strains when traversed by a truck population. The latter is found to be closely resembled by the theoretical pattern derived from simple point load models.     

基于新型长周期光纤光栅的动态横向负荷传感器

首次发现高频CO₂激光脉冲写入的长周期光纤光栅(LPFG)具有很好的动态横向负荷响应特性——谐振峰幅值随横向负荷线性变化,其变化频率与横向负荷的变化频率完全相同根据这种动态横向负荷响应特性,提出了一套动态横向负荷传感器设计方案,用窄带光源作为输入,基于LPFG的滤波原理,测量光电探测器的输出就可以获得动态横向负荷该方法仅需对LPFG的谐振峰幅值进行测量,方便简捷,实时性好.