The response of a layered half-space to traffic loads moving along its surface

Abstract

The dynamic behaviour of a railway system is in¯uenced by the interaction of its three subsystems: the vehicles, the rail construction itself and the subsoil. In this paper, the subsoil is considered as a linear-elastic layered half-space. Integral transformations are used for the analysis of this system: Fourier transformation for the time/frequency domain and for the space/wavenumber domains with respect to the horizontal coordinates. One arrives at an ordinary differential equation for the vertical direction, by which different layers or continuously changing elastic properties can be taken into account in an ef®cient manner. The ef®-ciency of the transformation technique depends substantially on the effort necessary for the inverse transformation. A substantial reduction of data can be achieved in an error-controlled procedure if a wavelet transformation is applied as an additional transformation. The calculations are illustrated by solutions of several examples of moving time-dependent loads, particularly of a train model with four vehicles idealized by moving forces, time depending as if they were passing a rigid surface with a given roughness.

Diagnosis and prediction of vibration from railway trains

“…For low frequencies, the train-track interaction as well as the inertia of the rail and sleepers are not considered. The soil model frequently used for simulation (for example, in [19]) is similar to that developed by Jones and Petyt [20] and the track model by Jones et al [21]. The moving vertical excitation includes a constant component and a harmonic one simulating irregularities in the track (single frequency).…”

Numerical modelling of free field traffic-induced vibrations

“…Using the displacement decomposition (18) together with the result of Eq. (22), the force vector (17) can be elaborated as:…”

“…An extensive survey of calculation methods for solids or structures under moving loads is given by Fru Âba [16]. Grundmann et al [18] have recently applied the dynamic reciprocity theorem for the calculation of free ®eld vibrations due to a moving time-dependent load along the surface of a layered halfspace.…”

“…The application of the displacement decompositions (14) and (18) to the relaxed boundary condition (20) results in: f r xã r f sz x; z 0ã s 21…”

Finite Element Elastic Analysis of 3-D Flexible Pavements Under Moving Loads

“…Flexible pavements, modeled as elastic layered half-spaces under stationary or moving loads, have been analysed by various numerical methods such as the FEM, the boundary element method (BEM) or the layered system theory in matrix form [3][4][5][6][7][8].…”