Bridge Subsystem Research Articles

A Practical Control Strategy for the Maglev Self-Excited Resonance Suppression

This paper addresses the control strategy for the suppression of maglev vehicle-bridge interaction resonance, which worsens the ride comfort of vehicle and degrades the safety of the bridge. Firstly, a minimum model containing a flexible bridge and ten levitation units is presented. Based on the minimum model, we pointed out that magnetic flux feedback instead of the traditional current feedback is capable of simplifying the block diagram of the interaction system. Furthermore, considering the uncertainty of the bridge’s modal frequency, the stability of the interaction system is explored according to an improved root-locus technique. Motivated by the positive effects of the mechanical damping of bridges and the feedback channels’ difference between the levitation subsystem and the bridge subsystem, the increment of electrical damping by the additional feedback of vertical velocity of bridge is proposed and several related implementation issues are addressed. Finally, the numerical and experimental results illustrating the stability improvement are provided.

Random vibration analysis of train-slab track-bridge coupling system under earthquakes

This study aimed to investigate the random vibration characteristic of train-slab track-bridge interaction system subjected to both track irregularities and earthquakes by use of pseudo-excitation method (PEM). Each vehicle subsystem was modeled by multibody dynamics. A three-dimensional rail-slab- girder-pier finite element model was created to simulate slab track and bridge subsystem. The equations of motion for the entire system were established based on the constraint condition of no jump between wheel and rail. The random load vectors of equations of motion were formulated by transforming track irregularities and seismic accelerations into a series of deterministic pseudo-excitations according to their respective power spectral density (PSD) functions by means of PEM. The time-dependent PSDs of random vibration responses of the system were obtained by step-by-step integration method, and the corresponding extreme values were estimated based on the first-passage failure criterion. As a case study, an ICE3 high-speed train passing a fifteen-span simply supported girder bridge simultaneously excited by track irregularities and earthquakes is presented. The evaluated extreme values and the PSD characteristic of the random vibration responses of bridge and train are analyzed, and the influences of train speed and track irregularities (without earthquakes) on the random vibration characteristic of bridge and train are discussed.

Evaluation of vehicle-track-bridge interacted system for the continuous CRTS-II non-ballast track slab

Considering the CRTS-II track slab, which is commonly used in the Chinese high-speed railway system, a vehicle-track-bridge dynamic analysis method is proposed in which the vehicle subsystem equations are established by the rigid body dynamics method, the track subsystem and the bridge subsystem equations are established by the FEM, the wheel-rail contact relation is defined by the corresponding assumption in vertical direction and the Kalker linear creep theory in lateral direction. The in-span spring element is derived to model the track-bridge interaction; the equal-band-width storage is adopted to fit the track structure with multilayer uniform section beam; and the dynamic equilibrium equations are solved by the inter-history iteration method. As a case study, the response of a CRH2 high-speed train transverses a simply-supported bridge with successive 31.5 m double bound pre-stress beams is simulated. The result shows that using the vehicle-track-bridge interaction model instead of the vehicle-bridge interaction model helps predict the rotation angle at beam ends and choose an economic beam vertical stiffness.

Analysis on wind-vehicle-bridge dynamic interaction when trian pass through the tower region of long-span bridge

When the long-span bridge is in the strong wind environment, the shielding effects of the bridge tower will change the body-force of the train. This mutation effect of the wind force will change the dynamic response of train and bridge.In this paper, the Oujiang Long-span suspension is used as the engineering background, the fast spectral analysis is used to simulate wind field. In order to establish the motion equation of the wind-vehicle-bridge coupling system, the buffeting wind force on bridge subsystem, steady wind force on the train subsystem and relationship between the width of tower and length of the train are considered and an inter-system history integral procedure is used to solve this equation. The shielding effects of tower under different wind speed and vehicle speed are listed and the results show that the dynamic response of the train will increase with the increase of the wind speed and the length of the tower while the dynamic response of the bridge is very small under the shielding effects of the bridge tower.

Influences of Soil-Structure Interaction on Coupled Vibration of Train-Bridge System: Theoretical and Experimental Study

A numerical solution for the dynamic response of train-track-bridge coupled system taking into account the influence of soil-structure interaction is studied and verified by field experiments. A three-dimensional vehicle–track-bridge coupling dynamics model is developed, in which the vehicle subsystem, the track subsystem and the bridge subsystem are coupled through wheel-rail interaction and track-bridge interaction, respectively. The soil-structure interaction between the bridge foundation and the soil is simulated by spring stiffness exerted on group-pile foundation. In a case study, the dynamic responses of a high-speed train and a continuous beam bridge are calculated by three models, that is fixed-base model, equivalent-stiffness model and the proposed whole-pile model. The comparison of simulated and experimental results show that soil-structure interaction has significant influence on the lateral dynamic response of the bridge; The whole-pile model is proposed to study the coupled vibration of bridge and vehicle, which gives more reasonable simulation result than the other two models.

Dynamic Stress Analysis of Coupled Vehicle-Suspension Bridge System in Cross Wind

Dynamic stress computation of long suspension bridges under both railway and wind loading is required for either strength or fatigue assessment. However, the effect of dynamic coupling among bridge, railway vehicle and wind on bridge stress response is not well understood. This paper presents a method for predicting bridge dynamic stress responses with coupling effects included. The bridge model (bridge subsystem) and vehicle model (vehicle subsystem) are established using the finite element method, and they are related to each other through wheel-rail contact conditions. The spatial distribution of both buffeting forces and self-excited forces over the bridge deck surface is considered to facilitate the computation of local stress responses. The Tsing Ma suspension bridge in Hong Kong and the data recorded by a Wind and Structural Health Monitoring System (WASHMS) installed in the bridge are utilized as a case study to verify the proposed method to some extent. The railway loading and wind speed measured by the WASHMS are taken as input for the computation simulation. The computed local stress responses are compared with the measured ones. The results from the case study demonstrate that the proposed method could effectively predict the local stress responses of the coupled traffic vehicles and suspension bridge system in cross winds.

High-speed train–track–bridge dynamic interactions – Part I: theoretical model and numerical simulation

This paper presents a framework to systematically investigate the high-speed train–track–bridge dynamic interactions, aiming to provide a method for analysing and assessing the running safety and the ride comfort of trains passing through bridges, which are critically important for the design of new high-speed railway bridges. Train–track–bridge interactive mechanism is illustrated. A fundamental model is established for analysing the train–track–bridge dynamic interactions, in which the vehicle subsystem is coupled with the track subsystem through a spatially interacted wheel–rail model; and the track subsystem is coupled with the bridge subsystem by a track–bridge dynamic interaction model. Modelling of each subsystem and each interactive relationship between subsystems are presented. An explicit–implicit integration scheme is adopted to numerically solve the equations of motion of the large non-linear dynamic system in the time domain. Computer simulation software named the train–track–bridge interaction simulation software (TTBSIM) is developed to predict the vertical and lateral dynamic responses of the train–track–bridge coupled system.

Dynamic analysis of coupled vehicle–bridge system based on inter-system iteration method

An inter-system iteration method is proposed for dynamic analysis of coupled vehicle–bridge system. In this method, the dynamic responses of vehicle subsystem and bridge subsystem are solved separately, the iteration within time-step is avoided, the computation memory is saved, the programming difficulty is reduced, and it is easy to adopt the commercial structural analysis software for bridge subsystem. The calculation efficiency of the method is discussed by case study and an updated iteration strategy is suggested to improve the convergence characteristics for the proposed method.

Integral model for train-track-bridge interaction on the Sesia viaduct: Dynamic simulation and critical assessment

A 3-D dynamic analysis model for a coupled train-bridge system is established. The vehicle subsystem is modeled by multibody dynamics and each 4-axle coach is simulated as a 27-degree-of-freedom model. For the bridge subsystem a 3-D rail-ballast-beam finite element model is created, considering the elasticity and the continuity of the track system. The dynamic interaction between the bridge and the train is realized through the contact forces between the wheels and the track. Track irregularities and wheel hunting are included. The track irregularities are generated with the German high-speed track spectra, whereas the wheel hunting is simulated by a sinusoidal function with a random phase. The equations of motion of the coupled train-bridge system are derived by representing the bridge subsystem through its vibration modes. The proposed formulations are then applied to the Sesia viaduct located on the new Italian high-speed line between Torino and Milano. The dynamic responses of the bridge subjected to an Italian high-speed ETR500Y train are calculated and some results are compared with the measured data. The resonant train speed of the train-bridge system is discussed, and the running safety and the stability of the train vehicles on the bridge are evaluated. The results show that the Sesia viaduct is stiff enough in both vertical and lateral directions, fulfilling the design criteria for high-speed train passage. The numerical method proposed in this paper can be used to predict efficiently the dynamic behavior of coupled train-bridge systems with reasonable computational effort.

Seismic response analysis of skew bridges with pounding deck–abutment joints

In this paper the seismic response of short skew bridges with deck–abutment pounding joints is revisited. The permanent deck rotations and transverse displacements of such bridges after the recent earthquake in Chile created an incentive to revisit their non-conventional behaviour. A novel non-smooth rigid body approach is proposed to analyze the seismic response of pounding skew bridges which involves oblique frictional multi-contact phenomena. The coupling of the response, due to contact, is analysed in depth. It is shown that the tendency of skew bridges to exhibit transverse displacements and/or rotate (and hence unseat) after deck–abutment collisions is not a factor of the skew angle alone, but rather of the plan geometry plus friction. This is expressed with proposed dimensionless criteria. The study also unveils that the coupling is more pronounced in the low range of the frequency spectrum (short-period excitations/flexible structures) and presents novel dimensionless response spectra for the transverse displacements and rotations, triggered by oblique contact in a skew bridge subsystem. Despite the complexity of the response, the proposed spectra highlight a clear pattern. The dimensionless rotations, arising from contact, decline as the ratio of the structural versus excitation frequency increases and become practically negligible in the upper range of the frequency spectrum. Finally, a pilot application to a typical skew bridge is presented.

A VEHICLE–BRIDGE LINEAR INTERACTION MODEL AND ITS VALIDATION

A linear wheel–rail interaction model for the vehicle–bridge coupling system is presented in this paper. The vehicle subsystem is modeled by the rigid-body dynamics method, the bridge subsystem by both the direct stiffness method and superposition method, and the wheel–rail interaction by the "corresponding assumption" and simplified Kalker creep theory. Based on the above modeling for the wheel–rail interaction system, linear simultaneous equations are established and solved. As a case study, the response of the Pioneer train traversing a 24 m simply–supported girder bridge is calculated. The proposed analysis procedure is validated through comparison of the calculated results with the measured ones. Also, some vibration characteristics of the system are discussed.

Computer-aided Nonlinear Vehicle-bridge Interaction Analysis

The interaction between railway vehicle and bridge is dynamic and nonlinear in nature. This paper aims to develop a computer-aided numerical method for analyzing coupled railway vehicle-bridge systems of nonlinear features. The finite element method is used to establish not only a bridge model (bridge subsystem) but also flexible vehicle models (vehicle subsystem). The connections between the two subsystems are considered through wheel-rail contact models with and without wheel jumps. All the nonlinear forces and concentrated damping forces in the two subsystems and the nonlinear contact forces at their interface are treated as pseudo forces to facilitate nonlinear analysis. The mode superposition method is then applied to the two subsystems, and both non-iterative and iterative computation schemes are utilized to find the best solution. The convergence of iterative computation schemes is investigated with and without wheel jumps. The explicit integration scheme is found to possess higher convergence than other schemes. The applicability and accuracy of the proposed numerical method are finally illustrated through numerical examples and comparisons with previous work.

Vehicle-bridge interaction analysis of heavy load railway

An inter-system iteration solution for the vehicle-bridge coupling model is studied, in which the iteration within time step is avoided. The solution consists of two steps. At the first step, the bridge subsystem is assumed rigid, the vehicle motion and wheel-rail force are solved by the independent vehicle subsystem, and the bridge motion is obtained by putting the wheel-rail force to the independent bridge subsystem. At the second step, the vehicle motion and the wheel-rail force are modified by the calculated bridge motion. As a case, the calculation process and the results of 30t heavy load cargo train traversing a 70+3×120+70 m continuous frame bridge are studied, and the numerical calculation technology for solving the interacted system and its convergence characteristics is discussed.