Dynamic Response Impact of Vehicle Braking on Simply Supported Beam Bridges with Corrugated Steel Webs Based on Vehicle-Bridge Coupled Vibration Analysis

A novel approach for analyzing coupled vibrations between vehicles and bridges is presented,taking into account spatiotemporal effects and mechanical phenomena resulting fromvehicle braking.Efficient modeling and solution of bridge vibrations induced by vehicle deceleration are realized using this method.The method’s validity and reliability are substantiated through numerical examples.A simply supported beam bridge with a corrugated steel web is taken as an example and the effects of parameters such as the initial vehicle speed,braking acceleration,braking location,and road surface roughness on the mid-span displacement and impact factor of the bridge are analyzed.The results show that vehicle braking significantly amplifies mid-span displacement and impact factor responses in comparison to uniform vehicular motion across the bridge.Notably,the influence of wheelto-bridge friction forces is of particular significance and cannot be overlooked.When the vehicle initiates braking near the middle of the span,both the mid-span displacement and impact factor of the bridge exhibit substantial increases,further escalating with higher braking acceleration.Under favorable road surface conditions,the midspan displacement and the impact factor during vehicle braking may exceed the design values stipulated by codes.It is important to note that road surface roughness exerts a more pronounced effect on the impact factor of the bridge in comparison to the effects of vehicle braking.

Vehicle-Bridge Interaction Simulation and Damage Identification of a Bridge Using Responses Measured in a Passing Vehicle by Empirical Mode Decomposition Method

To prevent early bridge failures, effective Structural Health Monitoring (SHM) is vital. Vibration-based damage assessment is a powerful tool in this regard, as it relies on changes in a structure’s dynamic characteristics as it degrades. By measuring the vibration response of a bridge due to passing vehicles, this approach can identify potential structural damage. This dissertation introduces a novel technique grounded in Vehicle-Bridge Interaction (VBI) to evaluate bridge health. It aims to detect damage by analyzing the response of passing vehicles, taking into account VBI. The theoretical foundation of this method begins with representing the bridge’s superstructure using a Finite Element Model and employing a half-car dynamic model to simulate the vehicle with suspension. Two sets of motion equations, one for the bridge and one for the vehicle are generated using the Finite Element Method, mode superposition, and D’Alembert’s principle. The combined dynamics are solved using the Newmark-beta method, accounting for road surface roughness. A new approach for damage identification based on the response of passing vehicles is proposed. The response is theoretically composed of vehicle frequency, bridge natural frequency, and a pseudo-frequency component related to vehicle speed. The Empirical Mode Decomposition (EMD) method is applied to decompose the signal into its constituent parts, and damage detection relies on the Intrinsic Mode Functions (IMFs) corresponding to the vehicle speed component. This technique effectively identifies various damage scenarios considered in the study.

Seismic response analysis of road vehicle-bridge system for continuous rigid frame bridges with high piers

The objective of this study is to investigate the effects of earthquakes on road vehicle-bridge coupling vibration systems. A two-axle highway freight vehicle is treated as a 13 degree-of-freedom system composed of several rigid bodies, which are connected by a series of springs and dampers. The framework of the earthquake-vehicle-bridge dynamic analysis system is then established using an earthquake as the extemal excitation. The equivalent lateral contact force serves as the judgment criteria for sideslip accidents according to reliability theory. The entire process of the vehicle crossing the bridge is considered for a very high pier continuous rigid frame bridge. The response characteristics of the vehicle and the bridge are discussed in terms of various parameters such as earthquake ground motion, PGA value of the earthquake, incident angle, pier height, vehicle speed and mass. It is found that seismic excitation is the most influential factor in the responses of the vehicle-bridge system and that the safety of vehicles crossing the bridge is seriously impacted by the dual excitations of earthquake and bridge vibration.

Alterable-element Method for Vehicle-bridge Interaction Considering the Transient Jump of Wheel

The so called "alterable-element method" (AEM) was introduced to deal with the coupling interac-tion of vehicle and sub-structure considering the actual transient jump of wheel, while the classical "contact all along" assumption based on which wheels and lower structure are always contact was abandoned. The alterable element used in this method is a conceptional element, which is used to calculate the coupling interaction of upper and lower structures and has some typical characteristics: firstly it flows along with the moving of contact point; secondly whether it is used for calculation depends on the contact state; thirdly its sizes could change according to specific problems and so on. VISUAL FORTRAN program was coded, and different moving vehicle models were presented taking into consideration the effects of random corrugation in the numerical study. The numerical solutions are favored comparing with the results obtained by alternative methods when there is no jump phenomenon existed. With abrupt irregularity, the transient jump of wheel was studied using the present method.

Self-excited vibration problems of maglev vehicle-bridge interaction system

The self-excited vibration problems of maglev vehicle-bridge interaction system were addressed, which greatly degrades the stability of the levitation control, decreases the ride comfort, and restricts the cost of the whole system. Firstly, the coupled model containing the quintessential parts was built, and the mechanism of self-excited vibration was explained in terms of energy transmission from levitation system to bridge. Then, the influences of the parameters of the widely used integral-type proportion and derivation(PD) controller and the delay of signals on the stability of the interaction system were analyzed. The result shows that the integral-type PD control is a nonoptimal approach to solve the self-excited vibration completely. Furthermore, the differential-type PD controller can guarantee the passivity of levitation system at full band. However, the differentiation of levitation gap should be filtered by a low-pass filter due to noise of gap differentiation. The analysis indicates that a well tuned low-pass filter can still keep the coupled system stable.

Aerodynamic coefficient of vehicle-bridge system by wind tunnel test

The changes of three components of aerodynamic force were discussed with the attack angle conversion for three kinds of section models. Based on the project of Shanghai Yangtze River Bridge, the wind tunnel test was conducted to obtain its three components of aerodynamic force including 75 conditions of the construction stage, the bridge without vehicles and the bridge with vehicles from - 12 degrees to ＋ 12 degrees. For the bridge with vehicles, the drag force coefficient and the absolute value of both lift coefficient and moment coefficient were decreased by the vehicles. The test resuh shows that the bridge railing and vehicles have much influence on the three components of aerodynamic force of the vehicle-bridge system for Shanghai Yangtze River Bridge.

Dynamic Impact Factor Induced by Idling Vehicle-Bridge Coupling Vibration

To analyze the impact effect induced by vehicle-bridge coupling vibration during traffic congesting, hundreds and thousands of congestion scenarios consisting of various vehicle platoons were collected and used to develop vehicle models as well as traffic congestion load models. Furthermore, the idling vehicle-bridge coupling model was established by the finite element method and the congestion models were applied to calculate dynamic impact factors. Compared with the value specified in Chinese codes, the calculated values were 1.15-2.67 times as large as the latter, which indicates the impact factors caused by idling vehicle-bridge coupling under congestion situations were much larger than those in normal traffic conditions. As a result, a calibration factor of 1.7 was recommended for bridge design or evaluation when considering vehicle-bridge coupling vibration under heavy traffic congestion. The proposed analytical model, analysis method, and results could also be beneficial references to further investigation in this field.

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.

Reinforcement Effect Evaluation on Dynamic Characteristics of an Arch Bridge Based on Vehicle-Bridge Coupled Vibration Analysis

To numerically evaluate the reinforcement effect on dynamic characteristics of a concrete-filled steel tube arch bridge with vibration problems,a 12-degree-of-freedom sprung-mass dynamic vehicle model and a 3D finite element bridge model were established.Then,the coupled equations of vehicle-bridge interaction were derived and a computer program was developed using the FORTRAN language.This program can accurately simulate vehicle-bridge coupled vibration considering the bumping effect and road surface irregularity during motion of the vehicle.The simulated results were compared with those of relevant literatures to verify the correctness of the self-developed program.Then,three reinforcement schemes for the bridge(Addition of longitudinal beams,Reinforcement of bridge decks,and Replacement of suspenders)were proposed and numerically simulated,and the vibration reduction effects of the three schemes were evaluated based on the numerical results to find effective ones.It is confirmed that the reinforcement scheme of Addition of longitudinal beams shows the most significant vibration reduction effect.It is recommended in the engineering practice that the combination of the reinforcement schemes of Addition of longitudinal beams and Replacement of bridge deck can be used to solve the excessive vibration problem.

Vehicle-bridge coupled vibrations in different types of cable stayed bridges

Numerical analyses of the coupled vibrations of vehicle-bridge system and the effects of different types of cable stayed bridges on the coupled vibration responses have been presented in this paper using ANSYS. The bridge model and vehicle model were independently built which have no internal relationship in the ANSYS. The vehicle-bridge coupled vibration relationship was obtained by using the APDL program which subsequently imposed on the vehicle and bridge models during the numerical analysis. The proposed model was validated through a field measurements and literature data. The judging method, possibility, and criterion of the vehicle-bridge resonance （coupled vibrations） of cable stayed bridges （both the floating system and half floating system） under traffic flows were presented. The results indicated that the interval time between vehicles is the main influence factor on the resonance excitation frequency under the condition of equally spaced traffic flows. Compared to other types of cable stayed bridges, the floating bridge system has relatively high possibility to cause vehicle-bridge resonance.

Numerical analysis of vehicle-bridge coupling vibration concerning nonlinear stress-dependent damping

Damping is known to have a considerable influence on the dynamic behavior of bridges.The fixed damping ratios recommended in design codes do not necessarily represent the complicated damping characteristics of bridge structures.This study investigated the application of stress-dependent damping associated with vehicle-bridge coupling vibration and based on that investigation proposed the stress-dependent damping ratio.The results of the investigation show that the stress-dependent damping ratio is significantly different from the constant damping ratio(5%)defined in the standard specification.When vehicles travel at speeds of 30,60,and 90,the damping ratios of the bridge model are 3.656%,3.658%,and 3.671%,respectively.The peak accelerations using the regular damping ratio are 18.9%,21.3%,and 14.5%of the stress-dependent damping ratio,respectively.When the vehicle load on the bridge is doubled,the peak acceleration of the mid-span node increases by 5.4 times,and the stress-related damping ratio increases by 2.1%.A corrugated steel-web bridge is being used as a case study,and the vibration response of the bridge is compared with the measured results.The acceleration response of the bridge which was calculated using the stress-dependent damping ratio is significantly closer to the measured acceleration response than that using the regular damping ratio.

Sectional model test study on vortex-excited resonance of vehicle-bridge system of Shanghai Bridge over Yangtse River

It is necessary to study how vehicles influence the vortex-excited resonance of vehicle-bridge systems,because lock-in wind speed is low and vortex-excited resonance is sensitive to any change in the main girder sections.Based on the Shanghai Bridge over the Yangtse River,the vortex-excited resonance of a 1∶60 scale sectional model was tested in a TJ-1wind tunnel,with or without vehicles at the attack angle of 0°,+3 and–3°,respectively.The conversion relationships between the resonant amplitudes of the sectional model and that of the prototype bridge were also established by mode shape correction.The result indicates that:1)for the bridge with vehicles,the vertical vortex-excited resonance is accompanied by torsion vibration with the same frequency,and vice versa,2)the amplitude of vortex-excited resonance of the bridge with vehicles is much larger than that of the bridge without vehicles,and 3)the lock-in wind speed of the vortex-excited resonance becomes smaller due to the disturbance of vehicles.It is obvious that vehicles bring about changes in the aerodynamic shape of the main girder.Therefore,the influence of vehicles on vortex-excited resonance performance of vehicle-bridge systems,in terms of both amplitude and mode,should not be ignored.

An Analysis of the Dynamic Behavior of Damaged Reinforced Concrete Bridges under Moving Vehicle Loads by Using the Moving Mesh Technique

This work proposes a numerical investigation on the effects of damage on the structural response of Reinforced Concrete(RC)bridge structures commonly adopted in highway and railway networks.An effective three-dimensional FE-based numerical model is developed to analyze the bridge’s structural response under several damage scenarios,including the effects of moving vehicle loads.In particular,the longitudinal and transversal beams are modeled through solid finite elements,while horizontal slabs are made of shell elements.Damage phenomena are also incorporated in the numerical model according to a smeared approach consistent with Continuum Damage Mechanics(CDM).In such a context,the proposed method utilizes an advanced and efficient computational strategy for reproducing Vehicle-Bridge Interaction(VBI)effects based on a moving mesh technique consistent with the Arbitrary Lagrangian-Eulerian(ALE)formulation.The proposed model adopts a moving mesh interface for tracing the positions of the contact points between the vehicle’s wheels and the bridge slabs.Such modeling strategy avoids using extremely refined discretization for structural members,thus drastically reducing computational efforts.Vibrational analyses in terms of damage scenarios are presented to verify how the presence of damage affects the natural frequencies of the structural system.In addition,a comprehensive investigation regarding the response of the bridge under moving vehicles is developed,also providing results in terms of Dynamic Amplification Factor(DAFs)for typical design bridge variables.

Safety evaluation of a vehicle–bridge interaction system using the pseudo-excitation method

A method for analysing the vehicle-bridge interaction system with enhanced objectivity is proposed in the paper, which considers the time-variant and random characteristics and allows finding the power spectral densities(PSDs) of the system responses directly from the PSD of track irregularity. The pseudo-excitation method is adopted in the proposed framework, where the vehicle is modelled as a rigid body and the bridge is modelled using the finite element method. The vertical and lateral wheel-rail pseudo-excitations are established assuming the wheel and rail have the same displacement and using the simplified Kalker creep theory, respectively. The power spectrum function of vehicle and bridge responses is calculated by history integral. Based on the dynamic responses from the deterministic and random analyses of the interaction system, and the probability density functions for three safety factors(derailment coefficient, wheel unloading rate, and lateral wheel axle force) are obtained, and the probabilities of the safety factors exceeding the given limits are calculated. The proposed method is validated by Monte Carlo simulations using a case study of a high-speed train running over a bridge with five simply supported spans and four piers.

Numerical analysis of dynamic response of vehicle–bridge coupled system on long-span continuous girder bridge

To systematically study the vehicle-bridge coupled dynamic response and its change rule with different parameters, a vehicle model with seven degrees of freedom was built and the total potential energy of vehicle space vibration system was deduced. Considering the stimulation of road roughness, the dynamic response equation of vehicle-bridge coupled system was established in accordance with the elastic system principle of total potential energy with stationary value and the ＂set-in-right-position＂ rule. On the basis of the self-compiled Fortran program and bridge engineering, the dynamic response of long- span continuous girder bridge under vehicle load was studied. This study also included the calculation of vehicle impact coefficient, evaluation of vibration comfort, and analysis of dynamic response parameters. Results show the impact coefficient changes with lane number and is larger than the value calculated by the ＂general code for design of highway bridges and culverts （China）＂. The Dieckmann index of bridge vibration is also related to lane number, and the vibration comfort evaluation is good in normal conditions. The relevant conclusions from parametric analyses have practical significance to dynamic design and daily operation of long-span continuous girder bridges in expressways. Safety and comfort are expected to improve significantly with further control of the vibration of vehicle-bridge system.

Maglev self-excited vibration suppression with a virtual sky-hooked damper

This work addresses the problem of self-excited vibration,which degrades the stability of the levitation control,decreases the ride comfort,and restricts the construction cost of maglev system.Firstly,a minimum model containing a flexible bridge and a single levitation unit is presented.Based on the simplified model,the principle underlying the self-excited vibration is explored.After investigations about the energy transmission between the levitation system and bridge,it is concluded that the increment of modal damping can dissipate the accumulated energy by the bridge and the self-excited vibration may be avoided.To enlarge the equivalent modal damping of bridge,the sky-hooked damper is adopted.Furthermore,to avoid the hardware addition of real sky-hooked damper,considering the fact that the electromagnet itself is an excellent actuator that is capable of providing sufficiently fast and large force acting on the bridge to emulate the influence of the real sky-hooked damper,the technique of the virtual sky-hooked damper is proposed.The principle underlying the virtual sky-hooked damper by electromagnet is explored and the vertical velocity of bridge is estimated.Finally,numerical and experimental results illustrating the stability improvement of the vehicle-bridge interaction system are provided.

Dynamic Performance of Straddle Monorail Curved Girder Bridge

In this work,a monorail vehicle-bridge coupling(VBC)model capable of accurately considering curve alignment and superelevation is established based on curvilinear moving coordinate system,to study the VBC vibration of straddlemonorail curved girder bridge and the relevant factors influencing VBC.While taking Chongqing Jiao Xin line as an example,the VBC program is compiled using Fortran,where the reliability of algorithm and program is verified by the results of Chongqing monorail test.Moreover,the effects of curve radius,vehicle speed,and track irregularity on the corresponding vehicle and bridge vibrations are compared and analyzed.It is observed that the test results of lateral vibration acceleration(LVA)and vertical vibration acceleration(VVA)of track beam,and LVA of vehicle,are consistent with the simulation results.Owing to the track irregularity,vibration of track beam and vehicle increases significantly.Besides,an increase in vehicle speed gradually increases the vibration of track beam and vehicle.For the curve radius(R)≤200 m,lateral and vertical vibrations of the track beam and vehicle decrease significantly with an increasing curve radius.Alternatively,when 200 m<R<600 m,the lateral vibration of the track beamand vehicle decreases slowly with an increasing curve radius,while the relevant vertical vibration remains stable.Similarly,when R≥600 m,the lateral and vertical vibrations of the track beam and vehicle tend to be stable.Accordingly,the results presented here can provide a strong reference for the design,construction,and safety assessment of existing bridges.

Fragility analysis for vehicle derailment on railway bridges under earthquakes

With the rapid development of high-speed railways around the globe,the safety of vehicles running on bridges during earthquakes has been paid more attention to.In the design of railway bridges,in addition to ensuring the safety of the bridge structure in earthquake,the vehicle safety should also be ensured.Previous studies have focused on the detailed analysis of vehicle derailment on bridges,proposing complex numerical algorithms for wheel-rail contact analysis as well as for parametric analysis,but they are inconvenient for designers.Intensity measure(IM)used in performance-based earthquake engineering is introduced in this study.A method to evaluate the vehicle safety on bridges under earthquakes is proposed with respect to the optimal IM.Then,the vehicle derailment case of the Kumamoto earthquake in Japan verifies the decoupling method of vehicle-bridge interaction model.In the assessment of vehicle derailments,eight IMs are systematically compared:the IMs of bridge deck motion are generally better than those of ground motion;the variation coefficient of spectral intensity of the bridge deck is the smallest at different frequencies.Finally,the derailment fragility cloud map is presented to evaluate the vehicle safety on bridges during earthquakes.

The coupled vibration of train and bridge as high-speed trains meet in crosswind

Purpose–This paper aims to study the influence of aerodynamics force of trains passing each other on the dynamic response of vehicle bridge coupling system based on numerical simulation and multi-body dynamics and put forward the speed threshold for safe running of train under different crosswind speeds.Design/methodology/approach–The computational fluid dynamics method is adopted to simulate the aerodynamic force in the whole process of train passing each other by using dynamic grid technology.The dynamic model of vehicle-bridge coupling system is established considering the effects of aerodynamic force of train passing each other under crosswind,the dynamic response of train intersection on the bridge under crosswind is computed and the running safety of the train is evaluated.Findings–The aerodynamic force of trains’intersection has little effects on the derailment factor,lateral wheel-rail force and vertical acceleration of train,but it increases the offload factor of train and significantly increases the lateral acceleration of train.The crosswind has a significant effect on increasing the derailment factor,lateral wheel-rail force and offload factor of train.The offload factor of train is the key factor to control the threshold of train speed.The impact of the aerodynamic force of trains’intersection on running safety cannot be ignored.When the extreme values of crosswind wind speed are 15 m$s
1,20 m$s
1 and 25 m$s
1,respectively,the corresponding speed thresholds for safe running of train are 350 km$h
1,275 km$h
1 and 200 km$h
1,respectively.Originality/value–The research can provide a more precise numerical method to study the running safety of high-speed trains under the aerodynamic effect of trains passing each other on bridge in crosswind.

Dynamic Characteristics of Long -Span Steel -Concrete CompositeBeam Bridge Based on Vehicle -Bridge Coupling Effect

In order to investigate the effect of vehicle-bridge coupling on the dynamic characteristics of the bridge,a steel-concrete composite beam suspension bridge is taken as the research object,and a three-dimensional spatial model of the bridge and a biaxial vehicle model of the vehicle are established,and then a vehicle-bridge coupling vibration system is constructed on the basis of the Nemak-βmethod,and the impact coefficients of each part of the bridge are obtained under different bridge deck unevenness and vehicle speed.The simulation results show that the bridge deck unevenness has the greatest influence on the vibration response of the bridge,and the bridge impact coefficient increases along with the increase in the level of bridge deck unevenness,and the impact coefficient of the main longitudinal girder and the secondary longitudinal girder achieves the maximum value when the level 4 unevenness is 0.328 and 0.314,respectively;when the vehicle speed is increased,the vibration response of the bridge increases and then decreases,and the impact coefficient of the bridge in the middle of the bridge at a speed of 60 km/h achieves the maximum value of 0.192.