A semi-analytical beam model for the vibration of railway tracks

Abstract

The high frequency dynamic behaviour of railway tracks, in both vertical and lateral directions, strongly affects the generation of rolling noise as well as other phenomena such as rail corrugation. An improved semi-analytical model of a beam on an elastic foundation is introduced that accounts for the coupling of the vertical and lateral vibration. The model includes the effects of cross-section asymmetry, shear deformation, rotational inertia and restrained warping. Consideration is given to the fact that the loads at the rail head, as well as those exerted by the railpads at the rail foot, may not act through the centroid of the section. The response is evaluated for a harmonic load and the solution is obtained in the wavenumber domain. Results are presented as dispersion curves for free and supported rails and are validated with the aid of a Finite Element (FE) and a waveguide finite element (WFE) model. Closed form expressions are derived for the forced response, and validated against the WFE model. Track mobilities and decay rates are presented to assess the potential implications for rolling noise and the influence of the various sources of vertical-lateral coupling. Comparison is also made with measured data. Overall, the model presented performs very well, especially for the lateral vibration, although it does not contain the high frequency cross-section deformation modes. The most significant effects on the response are shown to be the inclusion of torsion and foundation eccentricity, which mainly affect the lateral response.

Numerical and experimental investigation into the mid- and high-frequency vibration behavior of a concrete box girder bridge induced by high-speed trains

“…(2016) used a three-layer Bernoulli beam model subjected to a harmonic load to compare vibrational behaviors under various track structures installed on a viaduct. In addition, the finite element method (FEM) and waveguide FEM have proven to be useful in predicting track structure vibrations (Kostovasilis et al., 2017; Nilsson et al., 2009).…”

Investigation of Concrete Base‐Roadbed Surface Contact Variation‐Induced Vibration Characteristics of Vehicle‐Slab Track‐Subgrade System considering Fluid‐Solid Interaction

“…Main numerical formulations modeling of the dynamic response of railway structure under moving train loads involves the finite element method and the semianalytical method [2][3][4][5][6][7][8][9]. For example, rail pad properties [10] on dynamic performance of railway track were analyzed numerically.…”

A Fast Analytic Method to Calculate the Dynamic Response of Railways Sleepers

“…Determining the dynamic response of the sleeper is important because it affects the stability of the railway track. Substantial research using analytical methods for rail track have been carried out, for example: the model of a railway track as periodically supported beam [1][2][3][4][5][6][7][8][9][10] or the model of an infinite beam placed on a continuous foundation [11][12][13][14]), the studies of each track component have been performed on the rail [15][16][17][18] or on the ballast [19,20].…”