• Structural Engineering and Mechanics
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• v.61 no.3
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• pp.335-345
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• 2017

Free vibration analysis for continuous bridge under any number of vehicles is conducted in this paper. Calculation strategy for natural frequency and mode shape is proposed based on Euler-Bernoulli beam theory and numerical assembly method. Firstly, a half-car planar model is adopted; equations of motion and displacement functions for bridge and vehicle are established, respectively. Secondly, the undermined coefficient matrices for wheels, vehicles, intermediate support, left-end support and right-end support are derived. Then, the numerical assembly technique for conventional finite element method is adopted to construct the overall matrix of coefficients for whole system. Finally, natural frequencies and corresponding mode shapes are determined based on iterative method and overall matrix solution. Numerical simulation is presented to verify the effectiveness of the proposed method. The results reveal that the solutions of present method are exact ones. Natural frequencies and associate modal shapes of continuous bridge under different conditions of vehicles are investigated. The influences of vehicle parameters on natural frequencies are also demonstrated.

• Journal of the Korean Society for Railway
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• v.12 no.6
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• pp.974-982
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• 2009

To improve the effectiveness and economics the bridge design methodology considering the bridge/rail longitudinal analysis and bridge/vehicle dynamic effect suggested in this study. The reliability-based Life-Cycle Costs(LCC) effective optimum design is applied to a 2-main steel girder bridge, 5$\times$(1@50m) for comparison with conventional design, initial cost optimization and equivalent LCC optimization. As a result of the optimum design based on reliability, it may be stated that the design of High-Speed railway bridges considering the bridge/rail longitudinal analysis and bridge/vehicle dynamic effect are more efficient than typical existing bridges and LCC optimization without respect to bridge/rail longitudinal analysis and bridge/vehicle dynamic effect. The result of optimization design considering the interaction, design methodology suggested in this study, is higher than result of initial cost optimization design in initial cost, but that has the advantage than result of initial cost optimization design in expected LCC.

• Journal of the Korean Society of Hazard Mitigation
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• v.10 no.3
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• pp.31-38
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• 2010

In this study, it is suggested that it has to reliability-based design methodology with respect to bridge structure-rail longitudinal interaction and bridge structure-vehicle interaction. For the structural analysis, commercial package, ABAQUS, are used for a three-dimensional finite element analysis. The optimization process utilizes a well-known optimizer, ADS(Automated Design Synthesis). Optimization technique is utilized the ALM-BFGS method for global area search and Golden Section Method for 1-D search. In general, ALM-BFGS method don't need the 1-D search, and that algorithm converge a 0.1~0.2 of Push-Off factor. But in this study, value of Push-Off factor is used 90, therefore 1-D search should be needed for effective convergency. That algorithm contains the "heuristic decision method". As a result of optimum design of 2-main steel girder birdge with 5${\times}$(1@50m), design methodology suggested in this study was demonstrated more economic and efficient than existing design and LCC optimization not considering bridge-rail longitudinal interaction and bridge-vehicle interaction.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2003.10a
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• pp.444-451
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• 2003

In this study, a new three-dimensional finite element analysis model of high-speed railway bridges considering train-bridge interaction, in which various improved finite elements are used for modeling structural members, is proposed. The box-type bridge deck of a railway bridge is modeled by the NFS(Nonconforming Flat Shell) elements with 6 degrees of freedom. Track structures are idealized using the beam finite elements with the offset of beam nodes and those on Winkler foundation with two parameters. And, the vehicle model devised for a high-speed train is employed, which has an articulated bogie system. By Lagrange's equations of motion, the equations of motion of a bridge-train system can be formulated. Finally, by deriving the equations of the forces acting on a bridge considering bridge-train interaction the complete system matrices of total bridge-train system can be constructed. As numerical examples of this study, 2-span PC box-girder bridge is analyzed and results are compared with experimental results.

• Interaction and multiscale mechanics
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• v.3 no.4
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• pp.333-342
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• 2010

The Pseudo-Excitation Method (PEM) is applied to study the stochastic space vibration responses of train-bridge coupling system. Each vehicle is modeled as a four-wheel mass-spring-damper system with two layers of suspension system possessing 15 degrees-of- freedom. The bridge is modeled as a spatial beam element, and the track irregularity is assumed to be a uniform random process. The motion equations of the vehicle system are established based on the d'Alembertian principle, and the motion equations of the bridge system are established based on the Hamilton variational principle. Separate iteration is applied in the solution of equations. Comparisons with the Monte Carlo simulations show the effectiveness and satisfactory accuracy of the proposed method. The PSD of the 3-span simply-supported girder bridge responses, vehicle responses and wheel/rail forces are obtained. Based on the $3{\sigma}$ rule for Gaussian stochastic processes, the maximum responses of the coupling system are suggested.

• Wind and Structures
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• v.29 no.5
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• pp.299-312
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• 2019

Due to the rugged terrain, metro lines in mountain city across numerous wide rivers and deep valleys, resulting in instability of high-pier bridge and insecurity of metro train under crosswind. Compared with the conditions of no-wind, crosswind triggers severer vibration of the dynamic system; compared with the short-pier viaduct, the high-pier viaduct has worse stability under crosswind. For these reasons, the running safety of the metro vehicle traveling on a high-pier viaduct under crosswind is analyzed to ensure the safe operation in metro lines in mountain cities. In this paper, a dynamic model of the metro vehicle-track-bridge system under crosswind is established, in which crosswind loads model considering the condition of wind zone are built. After that, the evaluation indices and the calculation parameters have been selected, moreover, the basic characteristics of the dynamic system with high-pier under crosswind are analyzed. On this basis, the response varies with vehicle speed and wind speed are calculated, then the corresponding safety zone is determined. The results indicate that, crosswind triggers drastic vibration to the metro vehicle and high-pier viaduct, which in turn causes running instability of the vehicle. The corresponding safety zone for metro vehicle traveling on the high-pier is proposed, and the metro traffic on the high-pier bridge under crosswind should not exceed the corresponding limited vehicle speed to ensure the running safety.

• Wind and Structures
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• v.19 no.2
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• pp.145-167
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• 2014

Wind-vehicle-bridge (WVB) interaction can be regarded as a coupled vibration system. Aerodynamic forces and moment on vehicles and bridge decks play an important role in the vibration analysis of the coupled WVB system. High-speed vehicle motion has certain effects on the aerodynamic characteristics of a vehicle-bridge system under crosswinds, but it is not taken into account in most previous studies. In this study, a new testing system with a moving vehicle model was developed to directly measure the aerodynamic forces and moment on the vehicle and bridge deck when the vehicle model moved on the bridge deck under crosswinds in a large wind tunnel. The testing system, with a total length of 18.0 m, consisted of three main parts: vehicle-bridge model system, motion system and signal measuring system. The wind speed, vehicle speed, test objects and relative position of the vehicle to the bridge deck could be easily altered for different test cases. The aerodynamic forces and moment on the moving vehicle and bridge deck were measured utilizing the new testing system. The effects of the vehicle speed, wind yaw angle, rail track position and vehicle type on the aerodynamic characteristics of the vehicle and bridge deck were investigated. In addition, a data processing method was proposed according to the characteristics of the dynamic testing signals to determine the variations of aerodynamic forces and moment on the moving vehicle and bridge deck. Three-car and single-car models were employed as the moving rail vehicle model and road vehicle model, respectively. The results indicate that the drag and lift coefficients of the vehicle tend to increase with the increase of the vehicle speed and the decrease of the resultant wind yaw angle and that the vehicle speed has more significant effect on the aerodynamic coefficients of the single-car model than on those of the three-car model. This study also reveals that the aerodynamic coefficients of the vehicle and bridge deck are strongly influenced by the rail track positions, while the aerodynamic coefficients of the bridge deck are insensitive to the vehicle speed or resultant wind yaw angle.

• Wind and Structures
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• v.17 no.2
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• pp.203-225
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• 2013

An analysis framework for vehicle-bridge dynamic interaction system under turbulent wind is proposed based on the relevant theory of wind engineering and dynamics. Considering the fluctuating properties of wind field, the stochastic wind velocity time history is simulated by the Auto-Regressive method in terms of power spectral density function of wind field. The bridge is represented by three-dimensional finite element model and the vehicle by a multi-rigid-body system connected by springs and dashpots. The detailed calculation formulas of unsteady aerodynamic forces on bridge and vehicle are derived. In addition, the form selection of wind barriers, which are applied as the windbreak measures of newly-built railways in northwest China, is studied based on the suggested evaluation index, and the suitable values about height and porosity rate of wind barriers are studied. By taking a multi-span simply-supported box-girder bridge as a case study, the dynamic response of the bridge and the running safety indices of the train traveling on the bridge with and without wind barriers are calculated. The limit values of train speed with respect to different wind velocities are proposed according to the allowance values in the design code.

• Journal of Korean Society of Steel Construction
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• v.25 no.4
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• pp.335-346
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• 2013

AASHTO LRFD and Korean Bridge Design Code (Limit State Design) specify to consider Truck and Lane load simultaneously determined from reliability-based live load model, and impact shall be applied to the truck load while it shall not be applied to the lane load. In this paper, vehicle-bridge interaction analysis under moving truck and lane loads were performed to estimate impact factor of the cables and girders for the selected multi-cable-stayed composite bridges with 230m, 400m and 540m main span. A 6-d.o.f. vehicle was used for truck load and a series of single-axle vehicles was applied to simulate equivalent lane load. The effect of damping ratio on the impact factor was estimated and then the essential parameters to impact factor, i.e., road surface roughness and vehicle speed were considered. The road surface roughness was randomly generated based on ISO 8608 and it was applied to the truck load only in the vehicle-bridge interaction analysis. The impact factors evaluated from dynamic interaction analysis were also compared with those by the influence line method that is currently used in design practice to estimate impact factor in cable-stayed bridge.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.26 no.6A
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• pp.989-999
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• 2006

In this paper, numerical analysis method to perform linear dynamic analysis of bridge considering the road surface roughness and bridge-vehicle interaction when vehicle is moving on bridge is presented. The vehicle and bridge are modeled as three-dimension where contact length of tire and pitching of tandem spring are considered and single truck with 2-axles and 3- axles, and tractor-trailer with 5-axles are modeled as 7-D.O.F., 8-D.O.F., and 14-D.O.F., respectively. Dynamic equations of vehicle are derived from the Lagrange's equation and solution of the equation is obtained by Newmark-${\beta}$ method. The surface roughness of bridge deck for this analysis is generated from power spectral density (PSD) function. Beam element for the main girder, shell element for concrete deck and rigid link between main girder and concrete deck are used. The equations of the motion of bridges are solved by mode-superposition procedures. The proposed procedure is validated by comparing the results with the experimental data by Whittemore and Fenves.