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.

Auto-parametric resonance of a continuous-beam-bridge model under two-point periodic excitation:an experimental investigation and stability analysis

The auto-parametric resonance of a continuous-beam bridge model subjected to a two-point periodic excitation is experimentally and numerically investigated in this study.An auto-parametric resonance experiment of the test model is conducted to observe and measure the auto-parametric resonance of a continuous beam under a two-point excitation on columns.The parametric vibration equation is established for the test model using the finite-element method.The auto-parametric resonance stability of the structure is analyzed by using Newmark's method and the energy-growth exponent method.The effects of the phase difference of the two-point excitation on the stability boundaries of auto-parametric resonance are studied for the test model.Compared with the experiment,the numerical instability predictions of auto-parametric resonance are consistent with the test phenomena,and the numerical stability boundaries of auto-parametric resonance agree with the experimental ones.For a continuous beam bridge,when the ratio of multipoint excitation frequency(applied to the columns)to natural frequency of the continuous girder is approximately equal to 2,the continuous beam may undergo a strong auto-parametric resonance.Combined with the present experiment and analysis,a hypothesis of Volgograd Bridge's serpentine vibration is discussed.

Vibration analysis of maglev three-span rigid frame bridge considering magnetic force

The dynamic interaction between the maglev vehicle and the three-span rigid frame bridge is discussed. With the consideration of magnetic force, the interaction model is developed. Numerical simulations are performed to study the dynamic characteristics of the bridge during vehicle movement along the bridge. The results show that a reasonable value of the linear stiffness ratio of columns to beams is between 2. 0 and 3.0. The dynamic responses of the bridge are aggravated with the decrease in bending rigidity and the increase in vehicle speed and the span ratio of the bridge. It is suggested that a definite way is to control impact coefficients and acceleration in the dynamic design of the bridge. It is unsuitable to adopt the moving load model and the moving mass model in the design. The proposed results can serve in the design of high-speed maglev three-span rigid frame bridges.

Application and optimization design of non-obstructive particle damping-phononic crystal vibration isolator in viaduct structure-borne noise reduction

The problems associated with vibrations of viaducts and low-frequency structural noise radiation caused by train excitation continue to increase in importance.A new floating-slab track vibration isolator-non-obstructive particle damping-phononic crystal vibration isolator is proposed herein,which uses the particle damping vibration absorption technology and bandgap vibration control theory.The vibration reduction performance of the NOPD-PCVI was analyzed from the perspective of vibration control.The paper explores the structure-borne noise reduction performance of the NOPD-PCVIs installed on different bridge structures under varying service conditions encountered in practical engineering applications.The load transferred to the bridge is obtained from a coupled train-FST-bridge analytical model considering the different structural parameters of bridges.The vibration responses are obtained using the finite element method,while the structural noise radiation is simulated using the frequency-domain boundary element method.Using the particle swarm optimization algorithm,the parameters of the NOPD-PCVI are optimized so that its frequency bandgap matches the dominant bridge structural noise frequency range.The noise reduction performance of the NOPD-PCVIs is compared to the steel-spring isolation under different service conditions.

Effect of vehicle weight on natural frequencies of bridges measured from traffic-induced vibration

Recently,ambient vibration test(AVT)is widely used tu estimate dynamic characteristics of large civil struc- tures.Dynamic characteristics ean be affected by various envirnnmental factors such as humidity,intensity of wind,and temperature.Besides these environmental conditions,tire mass of vehicles may change the measured valnes when traffic-in- duced vibration is used as a source of AVT tor bridges.The effect of vehicle mass on dynamic characteristics is investigated through traffic-induced vibration tests on three bridges;(1)three-span suspension bridge(128m+404m+128m),(2) five-span continuous steel box girder bridge(59m+3@ 95m+59m),(3)simply supported plate girder bridge(46m). Acceleration histories of each measurement location under normal traffic are recorded for 30 minutes at field.These recor- ded histories are divided into individual vibrations and are combined into two groups aceording to the level of vibration;one by heavy vehicles such as trucks and buses and the other by light vehicles such as passenger cars.Separate processing of the two groups of signals shows that,for the middle and long-span bridges,the difference can be hardly detected,but,for the short span bridges whose mass is relatively small,the measured natural frequencies can change up to 5.4%.

Wind-induced vibration control of bridges using liquid column damper

The potential application of tuned liquid column damper (TLCD) for suppressing wind-induced vibration of long span bridges is explored in this paper.By installing the TLCD in the bridge deck,a mathematical model for the bridge-TLCD system is established.The governing equations of the system are developed by considering all three displacement components of the deck in vertical,lateral,and torsional vibrations,in which the interactions between the bridge deck,the TLCD,the aeroelastic forces,and the aerodynamic forces are fully reflected.Both buffeting and flutter analyses are carried out.The buffeting analysis is performed through random vibration approach,and a critical flutter condition is identified from flutter analysis.A numerical example is presented to demonstrate the control effectiveness of the damper and it is shown that the TLCD can be an effective device for suppressing wind-induced vibration of long span bridges,either for reducing the buffeting response or increasing the critical flutter wind velocity of the bridge.

Effects of fundamental factors on coupled vibration of wind-rail vehicle-bridge system for long-span cable-stayed bridge

In a wind-vehicle-bridge(WVB) system,there are various interactions among wind,vehicle and bridge.The mechanism for coupling vibration of wind-vehicle-bridge systems is explored to demonstrate the effects of fundamental factors,such as mean wind,fluctuating wind,buffeting,rail irregularities,light rail vehicle vibration and bridge stiffness.A long cable-stayed bridge which carries light rail traffic is regarded as a numerical example.Firstly,a finite element model is built for the long cable-stayed bridge.The deck can generally be idealized as three-dimensional spine beam while cables are modeled as truss elements.Vehicles are modeled as mass-spring-damper systems.Rail irregularities and wind fluctuation are simulated in time domain by spectrum representation method.Then,aerodynamic loads on vehicle and bridge deck are measured by section model wind tunnel tests.Eight vertical and torsional flutter derivatives of bridge deck are identified by weighting ensemble least-square method.Finally,dynamic responses of the WVB system are analyzed in a series of cases.The results show that the accelerations of the vehicle are excited by the fluctuating wind and the track irregularity to a great extent.The transverse forces of wheel axles mainly depend on the track irregularity.The displacements of the bridge are predominantly determined by the mean wind and restricted by its stiffness.And the accelerations of the bridge are enlarged after adding the fluctuating wind.

Damping Identification of Bridges Under Nonstationary Ambient Vibration

This research focuses on identifying the damping ratio of bridges using nonstationary ambient vibration data. The damping ratios of bridges in service have generally been identified using operational modal analysis （OMA） based on a stationary white noise assumption for input signals. However, most bridges are generally subjected to nonstationary excitations while in service, and this violation of the basic assumption can lead to uncertainties in damping identification. To deal with nonstationarity, an amplitude-modulating function was calculated from measured responses to eliminate global trends caused by nonstationary input. A natural excitation technique （NExT）-eigensystem realization algorithm （ERA） was applied to estimate the damping ratio for a stationarized process. To improve the accuracy of OMA-based damping estimates, a comparative analysis was performed between an extracted stationary process and nonstationary data to assess the effect of eliminating nonstationarity. The mean value and standard deviation of the damping ratio for the first vertical mode decreased after signal stationarization.

Relation of the infrasound characteristics and the continuous steel bridge vibration modes generated by the vibration of moving heavy trucks

As heavy trucks pass over highway bridges, bridge vibration occurs and generates infrasound. General trucks in Japan with rear leaf suspension have whole body vibration （suspension spring vibration） frequencies of about 3 Hz. Also, the frequencies of the wheel vibration （tire spring vibration） are about 10-20 Hz. The continuous steel highway bridges with middle span length have vibration modes with the same phase in each span at the frequencies of about 3 Hz and also have those with the secondary mode shape at the frequencies of about 10-20 Hz. Truck vibrations and bridge vibrations are closely related. In this work, vibration tests are conducted using a heavy test truck for two cases of infrasound complaints in order to investigate the relation between the continuous steel bridge vibration modes generated by the vibration of moving heavy trucks and its infrasound characteristics. As a result of the examination, two types of bridge vibration modes are caused by the vibrations of a moving heavy truck. Moreover, the bending vi- bration modes with the same phase in each span have the most powerful infrasound pressure, since each span vibrates with the same phase. Two countermeasures, including viscoelastic damper at the end of the girders and extended deck method, are proposed to reduce the amplitude of bridge vibration and its infrasound.

Simplified Method and Influence Factors of Vibration Characteristics of Isolated Curved Girder Bridge

The isolated curved girder bridge's vibration characteristics play a major part in the seismic responses of structures and anti-seismic properties.A clear analytic relationship between design parameters and the system's vibration characteristics could be established by its simplified dynamic analysis model,making it convenient for providing a reference to the optimization of design and safety analysis.A double-mass six-degree-of-freedom model for curved girder bridges with isolation bearings installed at the top of the bridge piers is built and a simplified analysis method for the vibration characteristics of the system is provided.Combined with the Matlab programming,the influences of radius of curvature,central angle,bridge deck width and damping ratio of the isolation layer and circular frequency of the isolation layer of isolated curved girder bridges on the pseudo-undamped natural circular frequency(called pseudo-frequency for short)and system damping ratio are systematically analyzed,and the sensitivity of vibration characteristics of isolated curved girder bridges is studied.The results show that the vibration characteristics of isolated curved girder bridges can be reflected well with this simplified model and calculation method.The pseudo-frequency of curved girder and system damping ratios increases with the increase of the isolation layer.The third-order vibration characteristic is more sensitive to the parameters of a curved girder,and the first-order vibration characteristic is sensitive to both central angle and radius of curvature to some extent while insensitive to the width of the bridge deck.Furthermore,the second-order vibration characteristic is not sensitive to the parameters of a curved girder.

Vibration Measurement of Pedestrian Bridge Using Double Magnetic Suspension Vibrator Based on Wavelet Analysis

Aiming at the problem of pedestrian bridge vibration measurement,a vibration measurement system of pedestrian bridge with dual magnetic suspension vibrator structure was designed according to absolute vibration measurement principle. The relationship between the magnetic repulsion force of vibrator and its displacement was obtained by the experimental method and the least square fitting method. The vibration equations of two magnetic suspension vibrators were deduced respectively,and the measurement sensitivity of the system was deduced. The amplitude-frequency characteristic of the system was studied. A simulation model of vibrator measurement system with double magnetic suspension vibrator was established. The analysis shows that the sensitivity of the vibration measurement system with double magnetic suspension vibrator is higher than that with single magnetic suspension vibrator. The four vibration waveforms were measured,that is,no one passes through a pedestrian bridge,there are cars running under the pedestrian bridge,single pedestrian passes through the pedestrian bridge and multiple pedestrians pass through the pedestrian bridge. The multi-scale one-dimensional wavelet decomposition function was used to analyze the vibration signals. The vibration characteristics were obtained using one dimension wavelet decomposition function under four different conditions. Finally,the vibration waveforms of four cases were reconstructed. The measured results show that the vibration measurement system of pedestrian bridge with double magnetic suspension vibrator structure has high measurement sensitivity. The design has a certain value to monitor a pedestrian bridge.

Modeling of cable vibration effects of cable-stayed bridges

The analysis of dynamic responses of cable-stayed bridges subjected to wind and earthquake loads generally considers only the motions of the bridge deck and pylons.The influence of the stay cable vibration on the responses of the bridge is either ignored or considered by approximate procedures.The transverse vibration of the stay cables,which can be significant in some cases,are usually neglected in previous research.In the present study,a new three-node cable element has been developed to model the transverse motions of the cables.The interactions between the cable behavior and the other parts of the bridge superstructure are considered by the concept of dynamic stiffness.The nonlinear effect of the cable caused by its self-weight is included in the formulation.Numerical examples are presented to demonstrate the accuracy and efficiency of the proposed model. The impact of cable vibration behavior on the dynamic characteristics of cable-stayed bridges is discussed.

Influence of Girder Vibration on Cable Damper's Performance of A Cable-stayed Bridge

The model combined by cable,girder and damper is founded to study the influence of girder vibration on cable damper 's performance of a cable-stayed bridge. The complex mode method and nondimensionalization are used to analyze the relationship between the girder's parameters and the performance of cable-related damper. The results indicate that the performance of cable-related damper will decrease greatly when the girder frequencies are near the frequencies of cable. The smaller absolute displacement of damper's piston caused by the very small vibration phase shift of girder and cable is the physical cause of the negative impact mentioned above.

Numerical and Experimental Study of Free Vibration Characteristics of a Cable-Stayed Bridge

The main aim of this study is to understand the dynamic behavior of a cable-stayed bridge, using both numerical and experimental analysis. A three-dimensional finite element model for the bridge was developed for the free vibration analysis and the ambient vibration properties of the bridge were determined through field testing. The experimental and numerical results of natural frequencies and the associated mode shapes were compared, and the high accuracy between them shows that the 3D model is capable of approximately representing the dynamic behavior of the bridge and the use of ambient vibration survives in future testing of the bridge. These dynamic characteristics can be used as the basis for updating the finite element model and also for global damage detection.

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.

Coupled Vibration of Long-Span Railway Curved Girder Bridges and Vehicles

The structure of a long curved girder bridge is represented with a three-dimensional curved finite element model. Each 4-axle ~vehicle is modeled by a dynamic system of 35 degrees of freedom. The random irregularities of the track are generated from a power spectral density function under the given track condition. The dynamic interaction between the bridge and train is realized through the contact forces between the wheels and track. Then based on these models, the coupled equations of motion are solved by applying the time-integration and iteration techniques to the coupled system. The proposed formulation and the associated computer program are then applied to a real curved girder bridge. The dynamic responses of the bridge-vehicle system and the derailments and offload factors related to the riding and running safeties of vehicles are computed. The results show that the formulation presented in this paper can well predict dynamic behaviors of both bridge and train with reasonable computation efforts.

Coupled Vibration Analysis of Vehicle-Bridge System Based on Multi-Boby Dynamics

For establishing the refined numerical simulation model for coupled vibration between vehicle and bridge, the refined three-dimensional vehicle model is setup by multi-body system dynamics method, and finite element method of dynamic model is adopted to model the bridge. Taking Yujiang River Bridge on Nanning-Guangzhou railway line in China as study background, the?refined numerical simulation model of whole vehicle and whole bridge system for coupled vibration analysis is set up. The dynamic analysis model of the cable-stayed bridge is established by finite element method, and the natural vibration properties of the bridge are analyzed. The German ICE Electric Multiple Unit (EMU) train refined three-dimensional space vehicle model is set up by multi-system dynamics software SIMPACK, and the multiple non-linear properties are considered. The space vibration responses are calculated by co-simulation based on multi-body system dynamics and finite element method when the ICE EMU train passes the long span cable-stayed bridge at different speeds. In order to test if the bridge has the sufficient lateral or vertical rigidity and the operation stability is fine. The calculation results show: The operation safety can be guaranteed, and comfort?index is “excellent”. The bridge has sufficient rigidity, and vibration is in good condition.

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.

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.

Operational modal identification of suspension bridge based on structural health monitoring system

An output-only modal identification method by a combination use of the peak-picking method and the cross spectrum methods are presented. Meanwhile, a novel mode shape optimum method of the deck is proposed. The methods are applied to the operational modal identification system of the Runyang Suspension Bridge, which can be used to obtain the modal parameters of the bridge from out-only data sets collected by its structural health monitoring system （SHMS）. As an example, the vibration response data of the deck, cable and tower recorded during typhoon Matsa excitation are used to illustrate the program application. Some of the modal frequencies observed from deck vibration responses are also found in the vibration responses of the cable and the tower. The results show that some modal shapes of the deck are strongly coupled with the cable and the tower. By comparing the identification results from the operational modal system with those from field measurements, a good agreement between them is achieved, but some modal frequencies identified from the operational modal identification system （OMIS）, such as L1 and L2, obviously decrease compared with those from the field measurements.