Implementation of Timoshenko element local deflection for vertical track modelling

Abstract

A vertical track model suitable for the study of the dynamic response and the interaction between wheel and rail in the time domain is developed by using Timoshenko beam elements, and its performance is optimised by accounting for the local deflection of these type of elements. Implementation of the local system enables one to obtain an accurate description of the contact force in a more computationally efficient way than other numerical methods, and it leads to an almost total elimination of the discontinuities caused by the local displacement underestimation and the shear incompatibilities introduced by the conventional formulation with Timoshenko beam elements. The work presented here describes both static and dynamic approaches of the local system directly obtained through the resolution of the beam governing equations. The dynamic approach guarantees the shear rotation continuity and describes accurately the track frequency content. The method is tested for parametric excitation, in which it ensures the smoothness of the response. Secondly, it is tested for short-pitch corrugated rails, where overestimation of the contact force is avoided with a reduced model size when compared with conventional Timoshenko element formulation. The results are validated by comparison with those from previous studies.

Moving Element Analysis of High-Speed Train-Slab Track System Considering Discrete Rail Pads

“…35 Also note that a low-pass filter technique was applied to eliminate the oscillations in the wheel-rail contact force due to the finite element interpolation polynomials used for Timoshenko beam elements. 31,35 Although the MEM model does not encounter the motion of load points, the motion of the discrete supports relative to the rail beam also introduces some spurious fluctuations in the results. Therefore, the Butterworth low-pass filter 37 is employed to filter out these spurious fluctuations.…”

“…Studies have shown that the shear-deformable Timoshenko beam model is superior to the classic Euler-Bernoulli model in describing the rail vibrations especially in the high frequency range. [29][30][31] Therefore, it is important that the slab tracks are properly modelled to ensure a realistic analysis of the high-speed train-track system.…”

Semiactive dynamic model of the rail track–vehicle system to reduce the vertical contact force interaction using magnetorheological dampers

“…To avoid reflections at the end and to be able to integrate over a length of 500 m, the track model is closed regarding the boundary conditions (Ripke and Klaus, 1995). By using modal superposition method which is reported in many articles (Blanco et al, 2019), the equations are solved, and F si is expressed by the following equation…”

“…To avoid reflections at the end and to be able to integrate over a length of 500 m, the track model is closed regarding the boundary conditions (Ripke and Klaus, 1995). By using modal superposition method which is reported in many articles (Blanco et al, 2019), the equations are solved, and F si is expressed by the following equationwhere y si is the vertical displacement of the i th sleeper, c pi , k pi and c fi , k fi are the damping and stiffness coefficients of the i th pad and the fastener, respectively. Here, X w ( h , x i ) and V m are h th mode shape functions and mode time coefficients of the rail vertical deflection, respectively.…”

Development of innovative methodologies to reduce railway rolling noise through Genetic Algorithm-based shape optimization techniques

“…As a down side, they require a great number of steps during the problem solution computation if an appropriate precision if wanted, with the associated high computational cost. Examples of track modelling in the time domain can be found in [63][64][65], the latter case applied to the particular case of a sleeper. Due to the fact that the calculation time required would not be viable for the optimization procedures developed in the present Thesis, this section will focus on the several existing frequency domain-based models.…”