1 Introduction
1.1 Spatial variation of system geometric property
1.2 Spatial variation of system properties in physics and mechanics
1.3 Characterization of train–track interaction
1.4 Outline of this work
- In Sect. 2, the modelling method for the train–ballasted track interaction is presented with brevity.
- In Sect. 3, the spatial uncertainty of system excitations on geometry, physics and mechanics is illustrated and the quantification methods for these random excitations are elaborated. Besides the framework is formed by integrating the presented works on dynamics model construction and uncertain parameter simulation.
- In Sect. 4, numerical examples are conducted to validate the proposed method and to survey the influence of spatial uncertainty of system geometry and physics–mechanics property on train–track interaction.
- Finally in Sect. 5, some concluding remarks are presented.
2 Dynamics model for train–track interaction
2.1 Construction of matrices for the train system
2.2 Construction of matrices for the track system
2.3 Coupling method for train–track interaction
2.3.1 Wheel–rail vertical coupling matrices
2.3.2 Wheel–rail lateral coupling matrices
3 Spatial uncertainty and quantification of system excitation on geometries, physics and mechanics
3.1 Generation of correlated pseudo-random variables following arbitrary probability distribution function
3.2 Random simulation model for track irregularities
3.2.1 Spectral correlation of track irregularities
3.2.2 Random simulation of PSD with specific correlations
3.2.3 Random simulation of track irregularities
3.2.4 Model validations
3.3 Random simulation for system parameters
3.3.1 DEM-FEM model
3.3.2 Comparison with experimental results
3.3.3 Random field of system parameters
3.4 Framework for system stochastic analysis
4 Numerical examples
4.1 Uncertainty quantification of track geometric excitation
4.1.1 PDF comparison
- C1: Excitation of the measurement: a long length of track irregularities that are experimentally measured, as shown in Fig. 3, is used as the system excitation.
- C2: Excitation of the simulation: the track irregularities simulated by the random simulation method, in which the irregularity correlation and amplitude and wavelength characteristics are extracted from the measured irregularities of C1, is used as the system excitation.
4.1.2 PSD comparison
4.2 Influence of spatially uneven track parametric excitation
Track parameters | Mean parametric value |
---|---|
Support stiffness (MN/m) | |
Rail pad | 58 |
Track bed | 112.95 |
Density (kg/m3) | |
Track bed | 1800 |