Vehicle Track Bridge Research Articles

Control Mechanism and Noise Reduction Effect of CVDM on Rail Transit Steel Bridge: Experimental and Numerical Study

Steel bridge, as one of the main structural types in bridge design, has been widely used in rail transit. However, the train-induced vibro-acoustic problem of the bridge has become increasingly prominent. The vibration and noise characteristics must be more significant and complex than steel truss bridge because of too many components. Viscoelastic damping materials (VDMs) have the characteristics of both viscous liquid and elastic solid, and have better damping performance than other damping materials. Therefore, VDM plays an important role in vibration and noise reduction technology. In applications, VDM is usually combined with constraining materials to form composite viscoelastic damping materials (CVDM). In this paper, based on the dynamic receptance method and superposition principle, the coupling model of vehicle–track–bridge in the frequency domain is first established, and then the vibration and noise prediction model of a steel truss bridge with CVDM is established based on RUK theory and statistical energy analysis (SEA) method. Based on the prediction model, the natural dynamic characteristics of typical components of steel truss bridges with CVDM were investigated, and the control mechanism and influence rule of CVDM on train-induced vibration and noise of steel bridges were revealed.

An improved model for the nonlinear simulation of the high‐speed vehicle‐track‐bridge coupling system under seismic shaking

AbstractWith the continuous development of high‐speed railway (HSR) construction technology, many HSR bridges are close to near‐fault earthquake zones. Due to the short warning time for earthquakes occurring in these areas, the scene of trains running on the HSR bridges under earthquakes will become more and more common. In order to effectively evaluate the train running safety performance on the HSR bridge under earthquakes, an improved model for the nonlinear simulation of the high‐speed vehicle‐track‐bridge (VTB) coupling system under seismic shaking is proposed. The commercial finite element software was utilized for the general modeling of track‐bridge structure, and nonlinear hysteric behaviors of key components were realized by using the local nonlinearity correction method. By adopting the unconditional stable explicit dynamic integration algorithm and an efficient wheel–rail contact model, an explicit dynamic solution framework is established. It can efficiently solve the nonlinear coupled vibration of the VTB system under earthquakes. Finally, based on the improved model developed in this paper, the influence of hysteretic behaviors of bridge bearings on the nonlinear coupling vibration of the VTB system under near‐fault earthquakes is discussed.

Noise reduction mechanism of high-speed railway box-girder bridges installed with MTMDs on top plate

The issue of low-frequency structural noise radiated from high-speed railway (HSR) box-girder bridges (BGBs) is a significant challenge worldwide. Although it is known that vibrations in BGBs caused by moving trains can be reduced by installing multiple tuned mass dampers (MTMDs) on the top plate, there is limited research on the noise reduction achieved by this method. This study aims to investigate the noise reduction mechanism of BGBs installed with MTMDs on the top plate. A sound radiation prediction model for the BGB installed with MTMDs is developed, based on the vehicle–track–bridge coupled dynamics and acoustics boundary element method. After being verified by field tested results, the prediction model is employed to study the reduction of vibration and noise of BGBs caused by the MTMDs. It is found that installing MTMDs on top plate can significantly affect the vibration distribution and sound radiation law of BGBs. However, its impact on the sound radiation caused by vibrations dominated by the global modes of BGBs is minimal. The noise reduction achieved by MTMDs is mainly through changing the acoustic radiation contributions of each plate of the bridge. In the lower frequency range, the noise reduction of BGB caused by MTMDs can be more effective if the installation of MTMDs can modify the vibration frequency and distribution of the BGB to avoid the influence of small vibrations and disperse the sound radiation from each plate.

Track vertical irregularity estimation for railway bridges using a novel and lightweight deep-learning architecture

A comprehensive methodology is presented for the estimation of track vertical irregularities of railway bridges from vehicle responses, based on a novel and lightweight multi-layer-perceptron (MLP) deep learning architecture. Firstly, a vehicle–track–bridge interaction (VTBI) model is established for the generation of the datasets of deep learning networks. Secondly, the lightweight deep learning architecture is meticulously designed to identify the track's vertical irregularities. Then, the effectiveness of the proposed technique is validated through examples of a single-span simple bridge and a three-span bridge. Further, the sensitivity of the present method against various factors is investigated, including different combinations of vehicle responses, measurement noise, vehicle speed and different classes of track irregularity. It is confirmed that the identified track irregularities of the railway bridges, regardless of irregularity class and noise level, are in excellent agreement with the ground-truth ones. The increase in vehicle speed to some extent reduces the estimation accuracy of the irregularity. The proposed method has higher identification accuracy and efficiency for longer irregularity sequences of multi-span railway bridges.

Dynamic Response Study of Overhead Contact System Portal Structure Based on Vehicle–Track–Bridge Coupled Vibration

In light of the rapid development of electrified railways, the safety and stability of train operations, as well as the catenary’s interaction with current quality, have garnered widespread attention. Electrified train operation with additional track irregularities serves as a principal excitation source within the vehicle–bridge–catenary system, significantly influencing the vibration characteristics of the system. Addressing the aforementioned issues, we first established the vehicle–track dynamics model and the bridge–catenary finite element model based on the principles of coupled dynamics of the vehicle–track system. These models are interconnected using dynamic forces between the wheel and rail. Subsequently, within the vehicle–track coupled system, track random irregularities are introduced as input excitations for the coupled model, and the dynamic response of the system is simulated and solved. Then, the obtained wheel–rail forces are applied to the bridge–catenary coupled system finite element model in the form of time-varying moving load forces. Finally, the dynamic response characteristics of the catenary portal structure under different conditions are determined. Meanwhile, a study on the vibration characteristics of the truss-type pillar portal structure was conducted, and the results were compared with those of existing models. The results indicate that the vertical and lateral forces between the vehicle and track are positively correlated with the speed and irregularity amplitude. Response values such as the derailment coefficient and wheel load reduction rate are within the specified range of relevant standards. The low-order natural resonant frequency of the truss-type pillar structure has, on average, increased by 0.86 compared to the existing pillar structure, which signifies improved stability. Furthermore, under various conditions, the average reductions in maximum displacement and stress response of this pillar structure are 13.2% and 14.19%, respectively, in comparison to the existing pillar structure, rendering it more suitable for practical engineering applications.

Comparison of time-domain and frequency-domain models for vibration prediction of a rail transit viaduct paved with floating slab track

Noise from rail transit viaducts often has a negative effect on surrounding buildings and nearby residents. To reduce the bridge vibration and radiated noise, floating slab tracks have been widely adopted in rail transit viaducts. To calculate the vibration of coupled track-bridge systems, both time-domain and frequency-domain methods can be applied although their relative performance is not very clear. This study aims to compare the two approaches and then provide some guidelines in choosing the appropriate method for predicting the vibration. The principle and methodology of the two calculation methods are firstly introduced, and the models for the train, floating slab track and bridge are developed using similar parameters. To further improve the efficiency and accuracy of the frequency-domain method, a half period method and a weighted average method are proposed to calculate the average responses of a certain point on the rail, floating slab and bridge to approximate the response during the pass-by. An indirect method is used to estimate the wheel–rail combined roughness from the measured rail acceleration when the train is running on the bridge, and compared with the direct measurement rail roughness. For the vibration of the bridge and floating slab, comparisons are made between results obtained from the time-domain and frequency-domain methods with different train speeds, and between results from experiment and simulation with different roughness. It is found that the wheel–rail contact forces and other structural responses from the two approaches show good consistency in the frequency region above 20 Hz. It is shown that a good approximation of the response during the pass-by can be obtained using the frequency-domain method by adopting the half period average or a simplified weighted average of two wheel position cases. When using the measured roughness and estimated roughness, the simulated vibration of the floating slab and bridge match well with the experimental results, and the indirect method can be used to modify direct measurement roughness in lower frequency regions. In the vibration prediction, the rail vibration or roughness, and other parameters in the vehicle–track–bridge system, should be measured accurately to ensure high reliability.

Bridge-Borne Noise Induced by High-Speed Freight Electric Multiple Units: Characteristics, Mechanisms and Control Measures

The high-speed freight electric multiple unit (EMU) is one of the important development directions for railway freight transportation. To investigate the bridge radiation noise induced by the freight EMU, a noise prediction model consisting of the containers–vehicle–track–bridge dynamic model, finite element model, and boundary element model are established and validated. Through simulation, the bridge radiation noise under different train loading conditions is compared, and the noise radiation mechanism is revealed. Moreover, the noise reduction effect of the noise wall is studied, and the influences of noise wall heights and sound absorption materials are investigated. Results indicate that the bridge sound power and the sound pressure levels (SPLs) of near-field points increase slightly with train loads in the frequency range below 20 Hz and above 125 Hz, with a maximum increase of about 6.8 dB. The structure resonance, intense local vibration, and high acoustic radiation efficiency cause strong bridge radiation noise. The noise wall can realize a good overall noise reduction effect in the sound shadow zone; nevertheless, SPLs increased in areas between the bridge and the noise wall. The ground reflection affects the superposition of transmitted, reflected, and diffracted sound waves, which causes nonlinear relationships of noise reduction effects with the noise wall height. From the perspective of human hearing sensitivity, the loudness levels of typical field points increase with the frequency in the range of 20~80 Hz, and SPLs below 25 Hz are less than the threshold of hearing. Setting the noise wall can effectively reduce the loudness levels, and the reduction effect increases with the noise wall height.

Research on inversion of wheel-rail force based on neural network framework

Wheel-rail force is a critical parameter for vehicle-track-bridge (VTB) structure system, playing a pivotal role in ensuring the safe operation of trains and service performance of track and bridge structures. This paper proposes a methodological framework for efficient and accurate prediction of wheel-rail force, that bidirectional gated recurrent unit (Bi-GRU) neural network is developed and the hyperparameters of networks are optimized through grey wolf optimization (GWO). Based on the developed VTB system model, numerical experiments are carried out to produce datasets which are verified through field test. In order to make the data more universal and comprehensive, Latin hypercube sampling (LHS) is introduced to randomize the parameters of VTB model. The datasets generated from VTB system, with rail seat force as input and wheel-rail force as output, serve as the training data for framework. Additionally, the inversion effects under various working conditions are examined and discussed. The results indicate that the model can precisely inverse continuous wheel-rail forces from the moment the wheels enter the first test rail seat until leave the last test point of rail seat. When the neural network learns from the features of at least three or more rail seats on each track slab (with intervals not exceeding 2 rail seats), it can accurately inverse the time history curve of wheel-rail forces. The framework presents a viable alternative for the wheel-rail force analysis, and promising potential for the realization of online monitoring of wheel-rail force.

Temperature effects on noise radiated by concrete railway structures

In recent years, concerns have arisen regarding the periodic deformation of high-speed railway tracks owing to the temperature effects caused by the solar radiation. This phenomenon has prompted investigations into temperature-induced changes in the dynamic responses of vehicle–track–bridge systems. Previous studies have commonly taken the additional track irregularity caused by thermal deformation as the sole factor affecting dynamic responses while neglected changes in the structural frequency response characteristics. Structural radiation noise is also a prominent issue that affects the lives of people and the environment. However, studies on track–bridge-borne noise rarely consider the influence of temperature. To address the impact of temperature on structure-borne noise radiated by tracks and bridges, this study employed a sequentially coupled multi-physics analysis method. This approach allowed a comprehensive exploration of the temperature effects on track irregularities, structural frequency responses, and sound radiation efficiency. A full-scale temperature deformation field test of a CRTS III slab was also conducted to determine the necessary initial thermodynamic boundary conditions. The analysis results revealed that the thermally induced deterioration of track irregularity and changes in structural frequency response characteristics were the primary factors affecting structure-borne noise radiated by track–bridges under local climate conditions.

Static and dynamic response characteristics of a ballastless track structure of a high-speed railway bridge with interlayer debonding under temperature loads

The ballastless track structure of a high-speed railway (HSR) undergoes interlayer debonding during its service due to train loads, environmental loads, and construction. A CRTS Ⅱ ballastless track slab structure is a longitudinally-continuous reinforced concrete structure, and the temperature load is a major factor in the occurrence of interlayer debonding. However, the effect of temperature loads on the static and dynamic response of the CRTS Ⅱ ballastless track structure of an HSR bridge following interlayer debonding is unknown. This study established a finite element simulation model of a ballastless track structure over a bridge and a vertically-coupled dynamic vehicle–track–bridge simulation model. The deformation generated by the track structure at temperature loads was inputted as track irregularity to the dynamic simulation model, and the change laws of the deformation and dynamic response of the track structure under different temperature loads was studied. The results showed that under different temperature loads, the ballastless track slab first undergoes longitudinal deformation, followed by transverse deformation. On this basis, the dynamic response of the HSR ballastless track structure over a bridge with interlayer debonding was found to increase with increasing temperature loads, while the frequency band changed from single to complex. This study not only provides insights into the effects of temperature loads on track structure damage, but also lays a theoretical foundation for the development of maintenance and repair plans for railroad departments.

Performance Analysis of Short-Span Simply Supported Bridges for Heavy-Haul Railways with A Novel Prefabricated Strengthening Structure

A novel prefabricated strengthening structure (NPSS) is proposed to improve the vertical stiffness and load-bearing capacity of existing short-span bridges for heavier axle-load trains passing through. The strengthening principle of the NPSS is revealed through theoretical derivation. A refined calculation model is prepared to investigate the effects of two important parameters on the structural behavior of the bridge, including the support stiffness and the installation location of the NPSS. The calculation model is also verified with four-point bending test of a bridge removed from a heavy-haul railway. With the calculation model and the response surface methodology (RSM), the functional relationships among the crucial mechanical indexes of the bridge and the two parameters of the NPSS are methodically established. Thus, the optimal values of the parameters are determined via a multi-objective optimization model and the analysis hierarchy process-fuzzy comprehensive evaluation method. Furthermore, the feasibility of the optimal parameters is appropriately verified based on simulations of the vehicle–track–bridge dynamics. The existence of the NPSS with optimal parameters could enhance the vertical stiffness of the bridge by 21.0% and bearing capacity by 19.5%. In addition, it could reduce the midspan dynamic deflection amplitude by 23.4% and vertical vibration acceleration amplitude of the bridge by 25.2%. The results of the study are expected to contribute to the capacity development and rehabilitation of existing heavy-haul railways with low cost and convenient construction without railway outage.

A Code-Type Method to Assess the Running Safety of Railway Vehicles on Bridges Shaken by Earthquakes Including Girder’s Torsional Motion

The safety of railway vehicles running on bridges needs to be evaluated in the seismic design of bridges. This study examined the spectral intensity calculated from the lateral vibration of the bridge deck during earthquakes, a Japanese code-based index to measure bridge vibration’s strength. In addition, the effect of the torsion of the bridge deck on vehicle derailment is investigated using a nonlinear vehicle–track–bridge model. The bridge deck torsion increases the derailment risk, especially for bridges with a low natural frequency. The reason lies in that the lateral and torsional deck motions are highly correlated for bridges with lower frequency. Based on this observation, a code-type formula was proposed to evaluate the vehicle running safety including both lateral and torsional motions of the bridge deck. The accuracy of the proposed formula was demonstrated by comparison with vehicle–track–bridge simulation excited by ground motion records. The new procedure overcomes the non-conservative assessment of derailment caused by ignoring bridge torsion.

Dynamic Response of Spatial Train-Track-Bridge Interaction System Due to Unsupported Track Using Virtual Work Principle

An improved spatial vehicle–track–bridge interaction system considering the unsupported track is proposed using the virtual work principle. When the track fails to be supported due to the defects under the track, the corresponding bridge–rail connection coupled matrix should be removed. Using the proposed dynamic model, a novel numerical analysis of the unilateral and bilateral unsupported sleepers in the bridge and the subgrade is carried out. The results indicate that the wheel–rail contact force changes dramatically when the vehicles pass through the unsupported track. The unsupported track has a little effect on the displacement of the bridge, but it increases the acceleration of the bridge. The displacement and acceleration of the track increase significantly with the expansion of the supported defects under the track and the increase of driving speed. For unilateral unsupported sleepers, the dynamic response on the unsupported side is slightly smaller than that of the bilateral unsupported sleeper, while the unsupported side has a limited effect on the other side of the normal support.

Long-Term Monitoring of Local Track Irregularity and Its Influence for Simply Supported Girder Bridge of HSR

By analyzing dynamic track geometric irregularity data of high-speed railway (HSR) with ballast track in China, there is a peak of [5, 11] m wavelength for the longitudinal level at the beam joint of simply supported girder bridges. The difference between the absolute value of track longitudinal level at the beam joint and that at the midspan is one to three mm. Under annual temperature cycle, the ballast at the beam joint loosens because of the bridge–track interaction, which results in the longitudinal level at the beam joint gets larger in winter and smaller in summer, that means the longitudinal level is negatively correlated with temperature, and at the same time, the development of the track longitudinal level and Track Quality Index (TQI) with the temperature are given. In addition, the vertical acceleration of axle box and bogie, and wheel–rail vertical force are larger when the train passes the beam joint than when it passes the midspan, which threatens running safety significantly. This article established a three-dimensional vehicle–track–bridge finite element model (FEM), thus the thresholds of track longitudinal level at the beam joint for simply supported girder bridge with ballast track in 250 km/h HSR were proposed, i.e., the maximum of dynamic track longitudinal level is 14 mm, and the maximum of static value is 11 mm. Once one of the two thresholds exceeds the corresponding limit, the train speed should be reduced to 160 km/h or below.

The Influence of an Integration Time Step on Dynamic Calculation of a Vehicle-Track-Bridge under High-Speed Railway

In order to study the influence of an integration time step on dynamic calculation of a vehicle-track-bridge under high-speed railway, a vehicle-track-bridge (VTB) coupled model is established. The influence of the integration time step on calculation accuracy and calculation stability under different speeds or different track regularity states is studied. The influence of the track irregularity on the integration time step is further analyzed by using the spectral characteristic of sensitive wavelength. According to the results, the disparity among the effect of the integration time step on the calculation accuracy of the VTB coupled model at different speeds is very small. Higher speed requires a smaller integration time step to keep the calculation results stable. The effect of the integration time step on the calculation stability of the maximum vertical acceleration of each component at different speeds is somewhat different, and the mechanism of the effect of the integration time step on the calculation stability of the vehicle-track-bridge coupled system is that corresponding displacement at the integration time step is different. The calculation deviation of the maximum vertical acceleration of the car body, wheel-sets and bridge under the track short wave irregularity state are greatly increased compared with that without track irregularity. The maximum vertical acceleration of wheel-sets, rails, track slabs and the bridge under the track short wave irregularity state all show a significant declining trend. The larger the vibration frequency is, the smaller the range of integration time step is for dynamic calculation.

A Modified Numerical Substructure Method for Dynamic Analysis of Vehicle–Track–Bridge Systems

This paper presents a modified numerical substructure method for simulating the dynamic response of vehicle–track–bridge (VTB) systems. The method can be used to analyze large-scale VTB systems accurately and efficiently. Based on the principle of virtual work, the equations of motion are derived for two separate subsystems, i.e. a small-scale of finely modeled VTB substructure and a coarsely meshed large main bridge subsystem using different level of refinement. Different from the conventional dynamic substructuring approaches, the bridge spans close to the vehicle are modeled in both the main and substructure models, and the contradiction of repeatedly modeling is solved using a “nonlinear force corrector”. A special wheel–rail interaction (WRI) element is used to simulate the fast-moving interaction force between the vehicle and rail. In this way, the two models remain unchanged while the vehicle moves forward, and the computational accuracy is the same as the large-scale purely refined model, while the efficiency is significantly improved, particularly, for the large-scale long VTB systems. Two examples of realistic VTB systems with either smooth or un-smooth rails are used to verify the proposed method. The results demonstrate that the presented method has remarkable advantages of computational efficiency and accuracy, providing a practically useful tool for analysis of large-scale VTB systems.

Relationship between track stiffness and dynamic performance of vehicle–track–bridge system

Track stiffness irregularity is superficially invisible on rail surface, while causes dynamical impact and track deformation when trains running through. Aiming at this issue, this work presents an investigation on the influence of track stiffness on dynamic behaviours of the high-speed vehicle–track–bridge dynamic system. Primarily, a determination method of track stiffness irregularity is analytically deduced, in which a novel solution of deformation of free beam is proposed. Then a high-speed vehicle–track–bridge dynamic interaction model is established based on the vehicle–track–bridge dynamic interaction theory. On this basis, the influence of track stiffness on the dynamic behaviours of the coupled system is investigated both in time domain and in frequency domain. Results show that the distribution of track stiffness in longitudinal direction indeed affects the vibrations of the system. More vibration details of system in full frequency bands can be revealed by considering track elasticity. The most sensitive indicator to different track types is the pitch acceleration of bogie. The wave amplitude caused by length of slab is very small, however its influence on vehicle vibrations is great, indicating that tiny track stiffness change caused by length of slab cannot be ignored in dynamic investigations.

Vertical track irregularity analysis of high-speed railways on simply-supported beam bridges based on the virtual track inspection method

Understanding the relationship between the static and dynamic track geometry irregularities is crucial for the proper maintenance of rail infrastructures and the reduction of on-site workload. This paper focuses on the analysis of the dynamic and static track irregularities on simply-supported beam bridges for high-speed railways. Based on the simulation of three-dimensional vehicle–track–bridge dynamics, a virtual track inspection method is proposed according to the measurement principle with the inertial reference. With the static irregularity provided as the initial input to the simulation model, the virtual track inspection of dynamic track irregularities is carried out considering different supporting structures, i.e. subgrade and bridges. Furthermore, the characteristics and advantages of the proposed model are investigated in the “rigid track structure”. Then, using the virtual track inspection method, this paper analyzes the relationship between the dynamic and static track irregularities (in the vertical direction) on the simply-supported beam bridge in both the time and frequency domains with respect to different train speeds, and the simulation results are validated by real-world measurements. Numerical results show that the stiffness irregularity in the vertical direction is periodical, with the cycle length equal to the span of the bridge. Furthermore, there is an obvious linear relationship between the dynamic and static irregularities. Also, the regression coefficient increases with increasing vehicle speed.

Analysis of the Vibration Characteristics of Ballastless Track on Bridges Using an Energy Method

Although the high-speed railway (HSR) system has been widely agreed to be a sustainable and convenient means of transportation, the vibration induced has already been deemed an urgent environmental problem. For the sake of investigating the vibration characteristics of the ballastless track on bridges in the HSR system from the point of view of energy, a numerical model of the vehicle–track–bridge coupled system is developed herein and the energy method based on power flow theory is employed. In addition, a corresponding evaluation method of the power flow theory is developed to evaluate the vibration characteristics of the track–bridge system. The conclusions indicate that (1) the vibration energy gradually attenuates from top to bottom of the track–bridge system in its transfer process. Moreover, the attenuation effects are mainly the result of the elasticity and damping effects of the fasteners and the slab mat layer. (2) With increasing slab mat layer stiffness, the vibration energy of the rail slightly decreases; on the contrary, that of the slab track and the bridge obviously increases. (3) With increasing fastener stiffness, the vibration energy of the entire track–bridge system increases. (4) With increasing running speed, the vibration energy of the entire track–bridge system rises obviously. The results reveal that the reasonable stiffness levels of the fasteners and the slab mat layer are 40 to 60 kN/mm and 40 to 60 MPa/m, respectively, under the investigated condition in this work. This work also presents a novel way to study the vibration characteristics of the ballastless track on bridges of HSRs in terms of energy.

Effect of random structural damage on vehicle–track–bridge coupled response

With the rapid development of high-speed railway construction around the world, the structural damage problem of tracks and bridges has attracted more and more attention. In this paper, considering the random structural damages of tracks and bridges, an efficient computational procedure is developed based on the probability density evolution method to systematically investigate the random characteristics of the dynamic responses varying with the damages in vehicle–track–bridge time-dependent systems. Firstly, a vehicle–track–bridge dynamic model with random structural damage parameters is established, and the random motion equations are derived based on the generalized energy principle. Then, the probability density evolution equation for each random response is established and the random feature is investigated by the proposed computational procedure. Finally, the representative numerical examples are applied and some conclusions for the effects of the random structural damages on the dynamic responses of the vehicle–track–bridge systems are presented.