Slab tracks are widely used worldwide in high-speed railways. In order to investigate the dynamic behavior of the train and slab track coupling system, a new approach, based on conceptions of the vehicle element and track element, is developed with finite elements in a moving frame of reference. By discretizing the slab track subsystem into track elements that flow with the moving vehicle, the proposed method eliminates the need for keeping track of the vehicle position with respect to the track model. The governing equations are formulated in a coordinate system traveling at a constant velocity, and the associated stiffness matrix, mass matrix and damping matrix for the track element in a moving frame of reference are derived. The vehicle element is introduced to model a car with primary and secondary suspension systems, which has 26 degrees of freedom, where 10 degrees of freedom are used to describe the vertical movement of the car, and 16 degrees of freedom are associated with the rail displacements. In the numerical study, four cases of application examples are presented taking into consideration the effects of track roughness, train speed and track parameters. The numerical solutions compare favorably with the results obtained by alternative methods. The method is shown to work for varying train speed and track parameters, and has several advantages over the conventional finite element method in a fixed system of reference.
A model for dynamic analysis of the vehicle-track-subgrade coupling system was developed by utilizing the finite-element method. Based on the model, new types of vehicle and track elements are presented and their associated stiffness matrix, mass matrix, and damping matrix are formulated. Computational software is coded with Matlab. As an application example, influences of four kinds of transition patterns - abrupt change, step-by-step change, linear change, as well as cosine change for track stiffness distributions in track transitions - on dynamic behaviour of the vehicle and the track are investigated. The computational results show that the transition pattern of the track stiffness has primary influence on the dynamic behaviour of the vehicle and the track, and smoothing of the track stiffness distribution can significantly reduce the wheel-rail interaction forces and the rail vertical accelerations. From abating wheel-rail impact and improving traffic operation's point of view, the cosine change has the most effect, the linear change is somewhat effective and the abrupt change is the least effective for the four kinds of transition patterns of the track stiffness. However, the transition patterns of the track stiffness have essentially no influence on the vehicle vertical accelerations, due to the excellent behaviour of vibration isolation resulting from the primary and the secondary suspension systems of the vehicle.
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