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.

A discussion about the limitations of the Eurocode’s high-speed load model for railway bridges

High-speed railway bridges are subjected to normative limitations concerning maximum permissible deck accelerations.For the design of these structures,the European norm EN 1991-2 introduces the high-speed load model(HSLM)—a set of point loads intended to include the effects of existing high-speed trains.Yet,the evolution of current trains and the recent development of new load models motivate a discussion regarding the limits of validity of the HSLM.For this study,a large number of randomly generated load models of articulated,conventional,and regular trains are tested and compared with the envelope of HSLM effects.For each type of train,two sets of 100,000 load models are considered:one abiding by the limits of the EN 1991-2 and another considering wider limits.This comparison is achieved using both a bridge-independent metric(train signatures)and dynamic analyses on a case study bridge(the Canelas bridge of the Portuguese Railway Network).For the latter,a methodology to decrease the computational cost of moving loads analysis is introduced.Results show that some theoretical load models constructed within the stipulated limits of the norm can lead to effects not covered by the HSLM.This is especially noted in conventional trains,where there is a relation with larger distances between centres of adjacent vehicle bogies.

Big Model Strategy for Bridge Structural Health Monitoring Based on Data-Driven, Adaptive Method and Convolutional Neural Network (CNN) Group

This study introduces an innovative“Big Model”strategy to enhance Bridge Structural Health Monitoring(SHM)using a Convolutional Neural Network(CNN),time-frequency analysis,and fine element analysis.Leveraging ensemble methods,collaborative learning,and distributed computing,the approach effectively manages the complexity and scale of large-scale bridge data.The CNN employs transfer learning,fine-tuning,and continuous monitoring to optimize models for adaptive and accurate structural health assessments,focusing on extracting meaningful features through time-frequency analysis.By integrating Finite Element Analysis,time-frequency analysis,and CNNs,the strategy provides a comprehensive understanding of bridge health.Utilizing diverse sensor data,sophisticated feature extraction,and advanced CNN architecture,the model is optimized through rigorous preprocessing and hyperparameter tuning.This approach significantly enhances the ability to make accurate predictions,monitor structural health,and support proactive maintenance practices,thereby ensuring the safety and longevity of critical infrastructure.

Finite element model updating and validating of Runyang Suspension Bridge based on SHMS

Based on the finite element （FE） program ANSYS, a three-dimensional model for the Runyang Suspension Bridge （RSB） is established. The structural natural frequency, vibration mode, stress and displacement response under various load cases are given. A new method of FE model updating is presented based on the physical meaning of sensitivity and the penalty function concept. In this method, the structural model is updated by modifying the parameters of design, and validated by structural natural vibration characteristics, stress response as well as displacement response. The design parameters used for updating are bounded according to measured static response and engineering judgment. The FE model of RSB is updated and validated by the measurements coming from the structural health monitoring system （SHMS）, and the FE baseline model reflecting the current state of RSB is achieved. Both the dynamic and static results show that the method is effective in updating the FE model of long span suspension bridges. The results obtained provide an important research basis for damage alarming and health monitoring of the RSB.

Finite Element Model Updating of Bridge Structures Based on Sensitivity Analysis and Optimization Algorithm

The dynamic characteristics of bridge structures, such as the natural frequencies, mode shapes and model damping ratio, are the basis of structural dynamic computation, seismic analysis, vibration control and structural health condition monitoring. In this paper, a three-dimensional finite-element model is established for a highway bridge over a railway on No.312 National Highway and the ambient test is carried out in site, the dynamic characteristics of the bridge are studied using the finite-element analysis and ambient vibration measurements. Comparison between the theoretical and experimental results shows that the frequency differences of the modes range between 0.44% and 8.77%. If the measurement is more reliable, the finite element model updating is necessary. Thus, a set of design variables is selected based on sensitivity analysis, then the finite element model of the bridge is updated based on optimization algorithm. The results of model updating show that the proposed updating method in this paper is more simple and effective, the updated finite element model can reflect the dynamic characteristics of the bridge better, the analytical results can provide the theoretical basis for damage identification and health condition monitoring of the bridge.

Dynamic finite element model updating of prestressed concrete continuous box-girder bridge

The dynamic finite element model （FEM） of a prestressed concrete continuous box-girder bridge, called the Tongyang Canal Bridge, is built and updated based on the results of ambient vibration testing （AVT） using a real-coded accelerating genetic algorithm （RAGA）. The objective functions are defined based on natural frequency and modal assurance criterion （MAC） metrics to evaluate the updated FEM. Two objective functions are defined to fully account for the relative errors and standard deviations of the natural frequencies and MAC between the AVT results and the updated FEM predictions. The dynamically updated FEM of the bridge can better represent its structural dynamics and serve as a baseline in long-term health monitoring, condition assessment and damage identification over the service life of the bridge .

Mechanics model of additional longitudinal force transmission between bridges and continuously welded rails with small resistance fasteners

A new mechanics model, which reveals additional longitudinal force transmission between the continuously welded rails and the bridges, is established on the fact that the influence of the mutual relative displacement (among) the rail, the sleeper and the beam is taken into account. An example is presented and numerical results are compared. The results show that the additional longitudinal forces calculated with the new model are less than those of the previous, especially in the case of the flexible pier bridges. The new model is also suitable for the analysis of the additional longitudinal force transmission between rails and bridges of ballastless track with small resistance fasteners without taking the sleeper displacement into account, and compared with the ballast bridges, the ballastless bridges have a much stronger additional longitudinal force transmission between the continuously welded rails and the bridges.

Settlement characteristics of bridge approach embankment based on scale model test

In order to analyze the effects of backfill materials, geometries and slab setting on the settlement of bridge approach embankment, scale model was built based on the structural characteristics of bridge approach embankment, and scale model tests were carried out under different conditions. The results show that when graded gravels were selected as the backfill materials, the effect of setting approach slab to reduce the differential settlement is more prominent. When lime soils were selected as the backfill material, approach slab can moderate the longitudinal settlement slope. When using different backfill materials, the ultimate settlement of the positive trapezoidal backfill geometries is less than that of the inverted trapezoid, and the backfill geometries have little effect on the settlement slope.

Modeling and Current Programmed Control of a Bidirectional Full Bridge DC-DC Converter

Modelling of bidirectional full bridge DC-DC converter as one of the most applicable converters has received significant attention. Mathematical modelling reduces the simulation time in comparison with detailed circuit response;moreover it is convenient for controller design purpose. Due to simple and effective methodology, average state space is the most common method among the modelling methods. In this paper a bidirectional full bridge converter is modelled by average state space and for each mode of operations a controller is designed. Attained mathematical model results are in a close agreement with detailed circuit simulation.

Finite element model updating of existing steel bridge based on structural health monitoring

Based on the physical meaning of sensitivity,a new finite element(FE) model updating method was proposed. In this method,a three-dimensional FE model of the Nanjing Yangtze River Bridge(NYRB) with ANSYS program was established and updated by modifying some design parameters. To further validate the updated FE model,the analytical stress-time histories responses of main members induced by a moving train were compared with the measured ones. The results show that the relative error of maximum stress is 2.49% and the minimum relative coefficient of analytical stress-time histories responses is 0.793. The updated model has a good agreement between the calculated data and the tested data,and provides a current baseline FE model for long-term health monitoring and condition assessment of the NYRB. At the same time,the model is validated by stress-time histories responses to be feasible and practical for railway steel bridge model updating.

Influence of pier height on the safety of trains running on high-speed railway bridges during earthquakes

Sudden earthquakes pose a threat to the running safety of trains on high-speed railway bridges,and the stiffness of piers is one of the factors affecting the dynamic response of train-track-bridge system.In this paper,a experiment of a train running on a high-speed railway bridge is performed based on a dynamic experiment system,and the corresponding numerical model is established.The reliability of the numerical model is verified by experiments.Then,the experiment and numerical data are analyzed to reveal the pier height effects on the running safety of trains on bridges.The results show that when the pier height changes,the frequency of the bridge below the 30 m pier height changes greater;the increase of pier height causes the transverse fundamental frequency of the bridge close to that of the train,and the shaking angle and lateral displacement of the train are the largest for bridge with 50 m pier,which increases the risk of derailment;with the pier height increases from 8 m to 50 m,the derailment coefficient obtained by numerical simulations increases by 75% on average,and the spectral intensity obtained by experiments increases by 120% on average,two indicators exhibit logarithmic variation.

Random dynamic analysis of vertical train–bridge systems under small probability by surrogate model and subset simulation with splitting

The response of the train–bridge system has an obvious random behavior.A high traffic density and a long maintenance period of a track will result in a substantial increase in the number of trains running on a bridge,and there is small likelihood that the maximum responses of the train and bridge happen in the total maintenance period of the track.Firstly,the coupling model of train–bridge systems is reviewed.Then,an ensemble method is presented,which can estimate the small probabilities of a dynamic system with stochastic excitations.The main idea of the ensemble method is to use the NARX(nonlinear autoregressive with exogenous input)model to replace the physical model and apply subset simulation with splitting to obtain the extreme distribution.Finally,the efficiency of the suggested method is compared with the direct Monte Carlo simulation method,and the probability exceedance of train responses under the vertical track irregularity is discussed.The results show that when the small probability of train responses under vertical track irregularity is estimated,the ensemble method can reduce both the calculation time of a single sample and the required number of samples.

Wavelet-Based Nonstationary Wind Speed Model in Dongting Lake Cable-Stayed Bridge

The wind-rain induced vibration phenomena in the Dongting Lake Bridge (DLB) can be observed every year, and the field measurements of wind speed data of the bridge are usually nonstationary. Nonstationary wind speed can be decomposed into a deterministic time-varying mean wind speed and a zero-mean stationary fluctuating wind speed component. By using wavelet transform (WT), the time-varying mean wind speed is extracted and a nonstationary wind speed model is proposed in this paper. The wind characteristics of turbulence intensity, integral scale and probability distribution of the bridge are calculated from the typical wind samples recorded by the two anemometers installed on the DLB using the proposed nonstationary wind speed model based on WT. The calculated results are compared with those calculated by the empirical mode decomposition (EMD) and traditional approaches. The compared results indicate that the wavelet-based nonstationary wind speed model is more reasonable and appropriate than the EMD-based nonstationary and traditional stationary models for characterizing wind speed in analysis of wind-rain-induced vibration of cables.

Time-dependent behavior comparison of long-span concrete arch bridge between prototype and model

Beipanjiang Bridge is a long-span concrete arch bridges with stiffened skeleton(CABSS)in China.It has a fixed end arch with the span of 445 m and the rise of 100 m.To evaluate the rationality of the construction sequence and the time-dependent behavior of CABSS,an experimental study of a model bridge was explored.But the measured displacement and stress ratios of arch rib between prototype and model bridge did not subject to linear similarity relation when the time-dependent behavior was considered.So,the three-dimensional finite element models were established,and verified by the measured data.Then,the displacements and stresses of the prototype and model were compared with each other,when the elastic analysis or coupling of temperature and shrinkage,creep effect was considered.Furthermore,a parametric study was studied.The results showed that when the temperature,shrinkage and creep effect of concrete are considered,the finite element analysis results of prototype and model agree well with the measured results.The displacement and stress ratios of prototype and model bridge in construction and bridge completed stage do not present the geometric similarity ratio 7.5 and 1.0,respectively.They are also much influenced by concrete predicting model and variation of temperature.

An Improved Time Domain Approach for Analysis of Floating Bridges Based on Dynamic Finite Element Method and State-Space Model

The floating bridge bears the dead weight and live load with buoyancy,and has wide application prospect in deep-water transportation infrastructure.The structural analysis of floating bridge is challenging due to the complicated fluid-solid coupling effects of wind and wave.In this research,a novel time domain approach combining dynamic finite element method and state-space model(SSM)is established for the refined analysis of floating bridges.The dynamic coupled effects induced by wave excitation load,radiation load and buffeting load are carefully simulated.High-precision fitted SSMs for pontoons are established to enhance the calculation efficiency of hydrodynamic radiation forces in time domain.The dispersion relation is also introduced in the analysis model to appropriately consider the phase differences of wave loads on pontoons.The proposed approach is then employed to simulate the dynamic responses of a scaled floating bridge model which has been tested under real wind and wave loads in laboratory.The numerical results are found to agree well with the test data regarding the structural responses of floating bridge under the considered environmental conditions.The proposed time domain approach is considered to be accurate and effective in simulating the structural behaviors of floating bridge under typical environmental conditions.

Prediction of the Local Scour at the Bridge Square Pier Using a 3D Numerical Model

In this paper, the problem on local scour around a single square pier was studied by using both the numerical and physical models. The numerical model for the study is FSUM based on a finite-difference method to solve the Reynolds averaged Navier-Stokes equations (RANS) and the equations for suspended sediment concentration and bed morphology. The computed result was verified through data measured in the experimental flume with a sand bed. In general, the typical features of local scour around the pier were successfully simulated by FSUM, such as stream flow, bow flow, down flow, horseshoe vortex. The comparison between the computation and experiment data shows a quite good fitness. Both numerical model and experiment results show that the maximum scour depth occurs at two front edges of the pier. Although the computed result shows a little bigger scour depth in comparison with the measurement in the physical model, it still confirms the reliability of numerical model in some measure.

Research on parametric modeling and computing of multi-tower suspension bridge based on ANSYS

Based on FEM (finite element method) program ANSYS and the OpenGL graphics, this paper develops the parametric modeling module and the computing module of the multi-tower suspension bridge, the modules being embedded into the ANSYS system, and the parametric modeling module parameters can be entered by way of interface, which can fast establish a multi-tower suspension bridge model. Calculation module can establish load conditions for the features of road bridge and specifications, in which multiple conditions can be defined and solved automatically. Post-processing part of the solution also serves the results of the subtotals and selects the output, so that the results of the output and finishing work have become more convenient and easier, and also the results can be saved in word, excel and other different file types.

Positional Error Model of Line Segments with Modeling and Measuring Errors Using Brownian Bridge

Spatial linear features are often represented as a series of line segments joined by measured endpoints in surveying and geographic information science.There are not only the measuring errors of the endpoints but also the modeling errors between the line segments and the actual geographical features.This paper presents a Brownian bridge error model for line segments combining both the modeling and measuring errors.First,the Brownian bridge is used to establish the position distribution of the actual geographic feature represented by the line segment.Second,an error propagation model with the constraints of the measuring error distribution of the endpoints is proposed.Third,a comprehensive error band of the line segment is constructed,wherein both the modeling and measuring errors are contained.The proposed error model can be used to evaluate line segments’overall accuracy and trustability influenced by modeling and measuring errors,and provides a comprehensive quality indicator for the geospatial data.

Software development of modeling assistant for continuous suspension bridges with multi-pylon

Building a reasonable and accurate finite element model is the first and critical step for structural analysis of complicated bridge. In this article, modeling assistant for continuous suspension with multi-pylon is developed based on .Net platform, with VB.Net, C# language and OpenGL graphic technique. With parameterized modeling method, finite element model of this kind of bridge can be built quickly and accurately, and multi-type element modeling with uniform parameters is realized. With advanced graphic technique, three-dimensional model graph can be real-timely previewed for intuitive data check. With an example of practice project, the accuracy and feasibility of this modeling method and practicality of this software are verified.

Health monitoring and comparative analysis of time-dependent effect using different prediction models for self-anchored suspension bridge with extra-wide concrete girder

The structural health status of Hunan Road Bridge during its two-year service period from April 2015 to April 2017 was studied based on monitored data.The Hunan Road Bridge is the widest concrete self-anchored suspension bridge in China at present.Its structural changes and safety were evaluated using the health monitoring data,which included deformations,detailed stresses,and vibration characteristics.The influences of the single and dual effects comprising the ambient temperature changes and concrete shrinkage and creep(S&C)were analyzed based on the measured data.The ANSYS beam finite element model was established and validated by the measured bridge completion state.The comparative analyses of the prediction results of long-term concrete S&C effects were conducted using CEB-FIP 90 and B3 prediction models.The age-adjusted effective modulus method was adopted to simulate the aging behavior of concrete.Prestress relaxation was considered in the stepwise calculation.The results show that the transverse deviations of the towers are noteworthy.The spatial effect of the extra-wide girder is significant,as the compressive stress variations at the girder were uneven along the transverse direction.General increase and decrease in the girder compressive stresses were caused by seasonal ambient warming and cooling,respectively.The temperature gradient effects in the main girder were significant.Comparisons with the measured data showed that more accurate prediction results were obtained with the B3 prediction model,which can consider the concrete material parameters,than with the CEB-FIP 90 model.Significant deflection of the midspan girder in the middle region will be caused by the deviations of the cable anchoring positions at the girder ends and tower tops toward the midspan due to concrete S&C.The increase in the compressive stresses at the top plate and decrease in the stresses at the bottom plate at the middle midspan will be significant.The pre-deviations of the towers toward the sidespan and pre-lift of the midspan girder can reduce the adverse influences of concrete S&C on the structural health of the self-anchored suspension bridge with extra-wide concrete girder.