Bridge Interaction System Research Articles

Random Vibration Analysis of a Vehicle–Bridge Interaction System Subjected to Traveling Seismic Ground Motions Using Pseudo-excitation Method

Random Vibration Analysis of a Vehicle–Bridge Interaction System Subjected to Traveling Seismic Ground Motions Using Pseudo-excitation Method

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.

A Novel Moving Load Integration Method for Real-Time Hybrid Shaking Table Test of High-Speed Maglev Vehicle–Bridge Interaction System

Real-time hybrid shaking table test for high-speed maglev vehicle–bridge interaction (VBI) system is an important method to study dynamic response of the system. Numerical experiments are usually conducted in advance to guarantee the test performed smoothly. This paper presents a novel moving load integration method combined with a truncated bridge model for fast calculation of bridge responses, and presents a framework for performing numerical experiment of a real-time hybrid test of VBI system. A realistic numerical experiment is conducted on a real-time simulator, i.e. xPC Target, integrating three commercial software, i.e. SIMPACK, ANSYS, and MATLAB-Simulink[Formula: see text], to model a real TR08 single-carriage maglev train, a 5-spans bridge and 28 shaking tables, respectively. The driving speed is 400–600[Formula: see text]km/h and the time step size in the test is 1/256[Formula: see text]s. The accuracy of moving load integration method with truncated bridge model is verified, the effects of speed on the dynamic responses of VBI systems are studied, the time delay of shaking tables and compensation algorithm is investigated, and the effects of local nonlinearity of the bridge on system responses are studied. This paper provides a practical method and valuable reference for the real-time hybrid shaking table test of vehicle–bridge coupled systems.

Enhanced drive‐by bridge modal identification via dual Kalman filter and singular spectrum analysis

The drive-by bridge health monitoring is to assess the bridge condition using the acceleration responses measured on the body or axle of instrumented vehicles. The vehicle responses are greatly affected by the road surface roughness that makes the bridge dynamic information blurred. Instead of direct using vehicle responses for the bridge monitoring, the dynamic response of contact point (CP) between the vehicle and bridge is further explored to enhance the drive-by bridge modal identification. A novel three-step framework is proposed to extract the components related to the bridge vibration from vehicle responses. The first step is to identify the input forces of two successive vehicles by solving the combined state-input estimation problem using dual Kalman filter. The CP responses of two contact points are calculated using the input forces and vehicle parameters. In the second step, the subtraction technique is applied to the identified CP responses of the two instrumented vehicles and the effect of the road surface roughness can be significantly reduced. Finally, an automatic singular spectrum analysis technique (auto SSA) is incorporated to decompose the response residual. Then the mono-component modes related to the bridge response are extracted from the response residual for drive-by bridge modal identification and/or the nonstationary characteristic identification of vehicle–bridge interaction (VBI) system. Results of numerical and experimental study demonstrate that the method can significantly suppress the vehicle response component and reduce the effect of road surface roughness to enhance the bridge modal identification.

Bridge Damping Extraction Method from Vehicle–Bridge Interaction System Using Double-Beam Model

When vehicles interact with a bridge, a vehicle–bridge interaction (VBI) system is created. The frequency and modal shape of VBI systems have been widely studied, but the damping of VBI systems has not been adequately investigated. In recent years, several incidents of abnormal bridge vibration due to changes in bridge damping have occurred and aroused widespread concern in society. Damping is an important evaluation index of structural dynamic performance. Knowing the damping ratio of a VBI system is useful for analyzing the damping changes while a bridge is in service. This paper presents a method to extract bridge damping values from a VBI system, which can serve as a guide for bridge damping evaluation. First, a double-beam theoretical model was used to simplify the VBI system for cases involving uniform traffic flow. The damping ratio equation for the simplified VBI system was obtained using the extended dynamic stiffness method (EDSM). A double-beam finite element model and a VBI finite element model were established. The damping ratios of the two models were separately calculated and then compared with the simplified VBI model results. The results verified the accuracy of the simplified method. This paper then explains that bridge damping values can be extracted by estimating the equivalent traffic flow parameters and using the damping formula for the simplified VBI system. The bridge damping ratios extracted using this method in an engineering case ranged from 0.75% to 0.78%, which is smaller than the range that was directly identified using monitoring data (0.83–1.19%). The results show that the method can effectively extract bridge damping ratios and improve damping ratio identification.

Time-Varying Transmissibility Analysis of Vehicle–Bridge Interaction Systems with Application to Bridge-Friendly Vehicles

It is well known that the natural frequencies of a coupled vehicle–bridge interaction system are time-varying. While this knowledge is useful for applications in bridge health monitoring, it does not provide an understanding of the relations between the excitation and coupled system responses, nor leads to developments of effective control strategies to mitigate vibration. In this paper, a novel theoretical framework for the time-varying displacement transmissibility is developed using a time-frozen technique. The time–frequency characteristics of the transmissibility functions are investigated to gain fundamental understanding and insights of the coupling dynamics in relation to the matching of bridge and vehicle natural frequencies. An important aspect of the transmissibility formulation is that it leads to the development of physics-based vibration control strategies in the frequency domain. By applying the principle of fixed points from vibration absorber designs to the transmissibility functions, an optimally tuned vehicle suspension to mitigate bridge vibration is obtained. The tuning strategy depends only on a priori known structural parameters. Thus, the tuning strategy provides useful guidelines in practice and is shown to be effective in reducing the vibrations of both the moving vehicle and the bridge. This work paves a foundation for further research in the design of bridge-friendly vehicles via parameter tuning.

Extracting the time‐dependent resonances of a vehicle–bridge interacting system by wavelet synchrosqueezed transform

The dynamic response of a vehicle–bridge interaction (VBI) system is a noisy, nonstationary, and multicomponent response with closely spaced spectral components. Considering the ultimate goal as utilizing the VBI system instantaneous frequencies (IFs) for bridge condition monitoring, this paper carries out a systematic study to investigate the performance of four advanced time-frequency analysis techniques on a series of VBI responses: Hilbert–Huang transformation (HHT), continuous wavelet transform (CWT), robust local mean decomposition (robust-LMD), and wavelet synchrosqueezed transform (WSST). The novel contribution of this study is the application of the two latter techniques. The synthesized tests demonstrate that the WSST is the best method to precisely separate and localize in time the closely spaced resonances. Therefore, the WSST is applied to field measurements obtained from the Boyne viaduct in Ireland, as well. The results verify the capacity of this method to deal with time-varying vibrations adequately.

Analytical Analysis of Interaction Between a Heavy Vehicle and a Simply Supported Light Bridge Based on Frequency Modulation

This paper analyzes the interaction between a heavy vehicle and a simply supported light bridge based on frequency modulation technique, in which variations of instantaneous frequencies of both bridge and heavy vehicle are considered. The bridge is modeled as a simply supported Euler beam and the heavy vehicle is simplified as a spring-mass system. The variation of instantaneous frequencies of both bridge and vehicle induced by the moving vehicle is usually neglected in classical analysis to decouple the pair of governing equations. However, the coupled vehicle–bridge interaction (VBI) system becomes time-varying and the pair of governing equations cannot be decoupled when the vehicle/bridge mass ratio cannot be neglected. The instantaneous frequencies of both bridge and heavy vehicle including their higher vibration modes are investigated herein. An analytical solution describing the dynamic response of the time-varying VBI system is developed by using the frequency modulation technique. Both Finite Element (FE) method and published experimental data are used for comparison purpose. The predictions of the proposed method match better with those obtained from the FE simulations and experimental measurements than the classical method. Five numerical examples have been adopted to compare the performance of the proposed model and the classical method: the former performs generally well, especially when the vehicle is heavy, or the vehicle frequency is near to the bridge frequency. The classical method is only a special case of the proposed model if either the mass or the stiffness of the vehicle is relatively small compared to the corresponding terms of the bridge. The performance of the proposed method has also been examined in four typical scenarios, where vehicle damping, multi-degree-of-freedom (MDOF) vehicle, road surface roughness, and two-span continuous bridge are involved.

A numerical model to predict three-dimensional interaction dynamic of low-medium-speed maglev vehicle–guideway bridge system

This paper established a numerical model to investigate the dynamic behavior of LMS (low-medium-speed) maglev vehicle-guideway bridge coupling system. In this model, the vehicle was simulated as a 3D (3-dimensional) multi-rigid body with 45 DOFs (degree of freedoms), and the guideway bridge was built through finite element method. Two-dimensional magnet-guideway relationship was introduced, and the control strategies of active suspension control based on PID controller and passive guidance control were employed to reflect the vehicle-guideway interaction. A solution program was then developed to solve the vehicle-guideway interaction problem. Through case study, the vibration responses achieved from 3D interaction model were compared to those from corresponding 2D (2-dimensional) model. Besides, the effects of pier and guideway irregularity on dynamic responses of vehicle-guideway bridge coupling system were investigated, and the frequency responses of vehicle and guideway were also analyzed. The result shows that ignoring the pier modeling or guideway irregularity would significantly undervalue the vibration responses of maglev vehicle-guideway bridge interaction system. The frequency responses indicate that the vibrations of vehicle-guideway bridge system are significantly related to the geometric dimensions of maglev vehicle, especially the distance between two magnet units. Finally, parametric study was carried out to determine the effects of key parameters (i.e., vehicle speed and natural frequency of guideway) on guideway responses.

Time‐varying frequency‐based scaled flexibility identification of a posttensioned concrete bridge through vehicle–bridge interaction analysis

Dynamic testing methods have been widely used in engineering practice for investigating dynamic properties of bridges; however, only basic dynamic parameters (i.e., natural frequencies, damping ratios, and unscaled modal shapes) can be identified, which are insufficient for condition assessment and health monitoring. To address this limitation, this article takes a three-span posttensioned concrete bridge as testbed; more useful structural parameters including mass-normalized mode shapes and scaled flexibility matrix are intended to be identified from moving vehicle-induced responses. For identifying scaled flexibility matrix, structural scaling factor between arbitrarily scaled mode shapes and mass-normalized mode shapes needs to be calculated firstly. In this article, time-varying frequencies of vehicle–bridge interaction (VBI) system were adopted for structural scaling factor identification, and the sensitivity of parameters identification error on calculated scaling factor was also investigated. The effectiveness of the proposed method was verified by in situ measurements of the studied three-span concrete bridge. In field testing, static load test and classical impact vibration testing were performed on this bridge for verifying the correctness of the proposed method. The good agreement between predicted deflections by using the scaled flexibility and reference values illustrates the reliability of the proposed method.

Extracting multiple bridge frequencies from test vehicle – a theoretical study

The coupled differential equation group for the vehicle bridge interaction system is reestablished to include both the vehicle and bridge damping effects. The equation group can be uncoupled and closed-form solutions for both the bridge and vehicle can be obtained under the assumption that the vehicle acceleration magnitude is much lower than the gravitational acceleration constant. Then based on a simply supported boundary condition scenario, several critical parameters including bridge damping, vehicle frequency, vehicle speed, vehicle mass, and vehicle damping are studied to investigate their effects on extracting multiple bridge frequencies from the vehicle. The results show that the bridge damping plays a significant role in the vibration behaviour of both the vehicle and the bridge compared to the vehicle damping. The vehicle is preferred to be designed with a high frequency beyond the interested bridge frequencies to be extracted since low vehicle frequency tends to attenuate bridge frequencies that are higher than the vehicle frequency. A camel hump phenomenon can be observed on the extracted bridge frequencies from the vehicle, especially for scenarios that involve high bridge vibration mode and high vehicle speed. Vehicle speed is preferred to be maintained low to meet the theoretical assumption and to reduce the camel hump phenomenon. Although vehicle mass is not necessarily limited in this study, there is a magnitude balance among vehicle mass, vehicle speed, and damping to meet the theoretical assumption. This theoretical work may give some indications for designing a special field test vehicle to monitor bridge in a more comprehensive way.

Longitudinal Seismic Response of Train–Bridge Interaction System With Slip in Moderate Earthquakes

Abstract This study assesses the seismic responses of viaduct structures in the Japanese high-speed rail system under moderate earthquake forces considering the slip between tracks and wheels. Equations of motion for the train–bridge interaction system were derived, where the track–wheel interaction was described by the Coulomb friction law. A full train–bridge finite element model incorporating nonslip and stick–slip interaction models was built using commercial finite element analysis software: abaqus. Simulation results indicate that the slip phenomenon might occur under a moderate earthquake and that a conventional nonslip model with an infinitely large friction coefficient is inappropriate. A parametric study revealed that the braking-train-induced slip friction little influenced the bridge response to moderate earthquake forces. The bridge's dynamic motions were dominated by ground motion irrespective of the values assigned as the train's initial speed and track–wheel friction coefficient. A computationally efficient method was proposed for calculating the longitudinal seismic responses of a bridge interacting with a braking train, following the linear superposition principle. As illustrated, this method could be helpful in reliability or uncertainty analysis when a great number of computationally expensive seismic analyses are required for train–bridge interaction systems.

Stochastic Analysis of Train–Bridge System Using the Karhunen–Loéve Expansion and the Point Estimate Method

This paper presents a new method for analyzing the dynamic behavior of train–bridge systems with random rail irregularity aimed at its simplicity, efficiency and accuracy. A vertical train–bridge system is considered, in which the bridge is regarded as a series of simply supported beams, and the train is regarded as a multibody system with suspensions. The Karhunen–Loéve expansion (KLE) is used to simulate the stochastic vertical rail irregularities, and the mean and standard deviation of the system response are calculated by the point estimate method (PEM), based on the Gaussian integration and the dimension reduction method. The proposed KLE–PEM method, which combines the key features of the KLE and PEM, is validated by comparing the results obtained with existing ones. The Monte Carlo simulation (MCS) is used to verify the rationality of the results obtained by the KLE–PEM approach. The results show that the KLE–PEM approach can accurately calculate the response of the vertical train–bridge interaction system with random irregularity. This paper further discusses the responses of the train and bridge system with different speeds for the train.

A Simple Approach for Simulating the Road Surface Roughness Involved in Vehicle-Bridge Interaction Systems

This paper presents an idea for modeling the road surface roughness in a vehicle–bridge interaction (VBI) system, by simulating it equivalently as two external forces each acting on the two subsystems of vehicle and bridge. Such an idea can be easily included in general-purpose commercial finite element (FE) software like ABAQUS and ANSYS. Compared with frequently used coupled and uncoupled FE models, the present approach is more convenient, since it does not require any self-developed FE codes. The other advantage is that it does not require very small elements in the FE modeling, as is the case with conventional approaches for simulating the irregularity in the profile of road surface roughness, which may be computationally inefficient.

Uncertainty Analysis on Vehicle-Bridge System with Correlative Interval Variables Based on Multidimensional Parallelepiped Model

For vehicle-bridge system, structural uncertainties, especially the interval variables with correlation, have a great influence on dynamic response. Therefore, this paper proposes an effective uncertainty analysis method for vehicle-bridge system based on multidimensional parallelepiped (MP) model, which can reasonably deal with the correlation of interval variables. First, the vehicle-bridge system is simplified as a four degrees-of-freedom mass-spring vehicle model running on a simply supported beam. MP model is adopted to describe the uncertainties of all the interval variables. Second, via affine coordinate system transform, the interval variables with correlation are transformed as the independent variables, which is very convenient for uncertainty analysis. Finally, the uncertain dynamic response is approximated through the first-order Taylor interval expansion, and the upper and lower bounds can be calculated using the dynamic response at midpoints and the partial difference multiplied by interval radius. Because the correlation is sufficiently considered, the uncertainty analysis results on vehicle–bridge interaction system will be much more accurate than the traditional interval analysis method (IAM). Numerical example demonstrates the correctness and effectiveness of the proposed method.

Concrete Curved Box Girders Interacted with Vehicles in Braking or Acceleration

In this study, an experimentally validated spatial analysis method for the vehicle–bridge interaction system was modified to include the features of vehicle braking and accelerating. The effect of braking or accelerating was considered as external force acting on the vehicular center of gravity and was quasi-statically distributed to every tandem, for which the formulae of load redistribution were derived. The effect of centrifugal force was also incorporated in the model. Based on the modified spatial analysis method, the dynamic responses of a three-span continuous concrete box girder bridge due to vehicle braking and accelerating were studied. Impact factors, including deflection, bending moment, torsional moment and shear force, were examined. The results show that vehicle braking has considerable effect on dynamic responses and the impact factors are related to braking rise time and braking position, but cases of vehicle braking do not always cause larger effects. While the increase in initial speed can produce higher maximum dynamic responses and corresponding impact factors, the dynamic responses in the first span of a multi-span bridge are smaller than those in other spans due to vehicle accelerating.

Damping Effect of a Passing Vehicle for Indirectly Measuring Bridge Frequencies by EMD Technique

The indirect approach for measuring bridge frequencies from a passing vehicle has become an attractive method recently because it provides mobility, reliability, and safety for setting up sensors in comparison with the traditional method for measurement. In the vehicle–bridge interaction system, it is realized that the bridge frequencies can be identified from the spectral analysis of the passing vehicle. However, there exist many factors affecting the identified results of bridge frequencies, and one key factor is the vehicle damping. This study investigates the effect of vehicle damping on the identification of the first bridge frequency for three different levels of road surface roughness by the empirical mode decomposition (EMD) technique. The numerical experimentation shows the following properties that can be utilized in a field measurement: (1) higher vehicle damping tends to suppress the vehicle frequency, and (2) the use of vehicle damping helps to suppress the effect of rough surface roughness and make the first bridge frequency visible.

Wave Number-Based Technique for Detecting Slope Discontinuity in Simple Beams Using Moving Test Vehicle

The wavelength characteristic is a useful clue for locating and assessing the severity of slope discontinuity in beams. In this study, the slope discontinuity of a beam is represented by an internal hinge restrained by elastic springs, and the wavelength of the beam is calculated indirectly from the vertical response of a test vehicle during its travel over the beam. The key parameters of the problem at hand are first unveiled using an approximate, closed-form solution for the response of the vehicle moving at low speeds over the bridge. Then a two-beam element model with slope discontinuity is formulated for the vehicle–bridge interaction (VBI) system for use in numerical simulation. In the examples, the wavenumber-based response of the test vehicle is used to identify the location and severity of the discontinuity in the beam. It is demonstrated that the wavelength-based technique presented herein by using the moving test vehicle as a moving sensor system offers a promising, alternative approach for damage detection in girder type bridges.

Nonlinear dynamic analysis of a parametrically excited vehicle–bridge interaction system

In this paper, a nonlinear supported Euler–Bernoulli beam under harmonic excitation coupled to a 2 degree of freedom vehicle model with cubic nonlinear stiffness and damping is investigated. The equations of motion are derived by Newton’s law and discretized into a set of coupled second-order nonlinear differential equations via Galerkin’s method with cubic nonlinear terms. Based on the created model, numerical simulations have been conducted using the Runge–Kutta integration method to perform a parametric study on influences of the nonlinear support stiffness coefficient, mass ratio, excitation amplitude and position relation for the vehicle–bridge interaction (VBI) system by using bifurcation diagram and 3-D frequency spectrum. The results indicate that depending on different parameters, a diverse range of periodic motion, quasi-periodic response, chaotic behavior and jump discontinuous phenomenon are observed. And the chaotic regions are scattered between a number of periodic/quasi-periodic motions. The study may contribute to a further understanding of the dynamic characteristics and present useful information to dynamic design and vibration control for the VBI system.

Predicting the Bounds of Vehicle-Induced Bridge Responses Using the Interval Analysis Method

AbstractA method for predicting the bounds of vehicle-induced bridge responses with uncertain bridge and vehicle parameters is presented. The uncertainties in the parameters of the bridge and vehicle are represented with interval variables instead of conventional random variables with known probability distributions. First, a three-dimensional vehicle–bridge interaction (VBI) system, which has no closed-form solution and can account for road roughness, is established. Then, by introducing the interval analysis method (IAM) based on the first-order Taylor series expansion, the expressions of the bridge responses, including displacement and bending moment at the midspan, can be explicitly given as functions of the interval parameters, and the lower and upper bounds of the bridge responses are determined by the particle swarm algorithm instead of direct interval arithmetic to avoid excessive overestimation of the responses. The subinterval technique can also be adopted to improve the accuracy of the IAM. A n...