Track Effects Analysis on Dynamic Response of Bridge - Track - Train System

Railway is a major transportation system for mass transport at high speed to connect large cities. Recently many concerns have been focused on developing new type of train and increasing the maximum speed moreover to cope with the congested situations and environmental problems of railroads and roadways. One of the most important structural problems to meet the social demands would be to solve the dynamic interaction of vehicles, the rail and bridge, evaluate the running safety, and assume excellent riding comfort at high-speed operation.The dynamic response of railway bridge under moving load has been studied both theoretically and experimentally for many years. Recently, more sophisticated models that consider various dynamic characteristics of the moving vehicle have been used. Traditionally in studying the dynamic response of a vehicle-bridge system, two sets of equations of motion can be written, one for the vehicle and the other for the bridge or rail. It is interaction force existing at the contact point between the two subsystems that make the two sets of equation coupled. One feature with this kind of contact problem is that the contact points move from time to time. To solve these two sets of equations, procedures of an iterative nature can generally be followed one drawback of this approach is that the computation involved in the iteration process can be significantly large. The converge rate is likely to be low, when dealing with the more realistic case of a bridge bearing a series of vehicles in motion. From literature review, it is clear that most of the existing procedures cannot be efficiently adopted in the analysis of general vehicle-track-bridge systems. In this paper, a finite element formulation to solve the dynamic response of vehicles, the rail and a general bridge is presented. The interaction between wheel and rail is completely considered here. A mechanical model to describe the interaction between the wheel and the rail that is connected directly with the bridge is described. For the vertical and rolling motion, constraint equation to connect wheel-set and the rail are given. The equations become time-dependent since wheel-set move on the rail at high speed. For the transverse and yawing motions, constitutive equations to describe the relationship of interaction forces and relative velocities between wheel and rail are given in a form to be treated in the finite element solution procedure. The numerical method of solving the equation of the motions of vehicle-track-bridge systems effectively under the constraint and constitutive equation to express the interaction between the wheel and rail is discussed.A computer program, DTVBI has been developed for the nonlinear analysis on vehicle-track-bridge interactions. Numerical examples are demonstrated to assume the validity and effectiveness of the proposed method. Case study carried out on concrete three-span bridges with continuous girders by using mechanical model and presented analytical method. The results of calculations showed that a track effect on running comfort of passengers (lateral and vertical accelerations of rolling stocks) is very important. Track effects on bridge dynamic responses depend on their span length and in bridges with spans smaller than 25m have considerable effect, however, in bridges with larger spans have less effect.