This paper presents a framework to investigate the dynamics of overall vehicle-track systems with emphasis on theoretical modelling, numerical simulation and experimental validation. A three-dimensional vehicle-track coupled dynamics model is developed in which a typical railway passenger vehicle is modelled as a 35-degree-of-freedom multi-body system. A traditional ballasted track is modelled as two parallel continuous beams supported by a discrete-elastic foundation of three layers with sleepers and ballasts included. The non-ballasted slab track is modelled as two parallel continuous beams supported by a series of elastic rectangle plates on a viscoelastic foundation. The vehicle subsystem and the track subsystem are coupled through a wheel-rail spatial coupling model that considers rail vibrations in vertical, lateral and torsional directions. Random track irregularities expressed by track spectra are considered as system excitations by means of a time-frequency transformation technique. A fast explicit integration method is applied to solve the large nonlinear equations of motion of the system in the time domain. A computer program named TTISIM is developed to predict the vertical and lateral dynamic responses of the vehicle-track coupled system. The theoretical model is validated by full-scale field experiments, including the speed-up test on the Beijing-Qinhuangdao line and the high-speed running test on the Qinhuangdao-Shenyang line. Differences in the dynamic responses analysed by the vehicle-track coupled dynamics and by the classical vehicle dynamics are ascertained in the case of vehicles passing through curved tracks.

https://www.tandfonline.com/doi/pdf/10.1080/00423110802621561

Fundamentals of vehicle–track coupled dynamics

A Guide to Monte Carlo Simulations in Statistical Physics: Reweighting methods

http://ieeexplore.ieee.org/iel5/5/31196/01451889.pdf

Random differential equations in science and engineering

Dynamic modeling of gearbox faults: A review

Analyses of dynamic response of vehicle and track coupling system with random irregularity of track vertical profile

A new simple explicit two-step method and a new family of predictor–corrector integration algorithms are developed for use in the solution of numerical responses of dynamic problems. The proposed integration methods avoid solving simultaneous linear algebraic equations in each time step, which is valid for arbitrary damping matrix and diagonal mass matrix frequently encountered in practical engineering dynamic systems. Accordingly, computational speeds of the new methods applied to large system analysis can be far higher than those of other popular methods. Accuracy, stability and numerical dissipation are investigated. Linear and nonlinear examples for verification and applications of the new methods to large-scale dynamic problems in railway engineering are given. The proposed methods can be used as fast and economical calculation tools for solving large-scale nonlinear dynamic problems in engineering.

Two simple fast integration methods for large-scale dynamic problems in engineering

This paper presents a framework to systematically investigate the high-speed train–track–bridge dynamic interactions, aiming to provide a method for analysing and assessing the running safety and the ride comfort of trains passing through bridges, which are critically important for the design of new high-speed railway bridges. Train–track–bridge interactive mechanism is illustrated. A fundamental model is established for analysing the train–track–bridge dynamic interactions, in which the vehicle subsystem is coupled with the track subsystem through a spatially interacted wheel–rail model; and the track subsystem is coupled with the bridge subsystem by a track–bridge dynamic interaction model. Modelling of each subsystem and each interactive relationship between subsystems are presented. An explicit–implicit integration scheme is adopted to numerically solve the equations of motion of the large non-linear dynamic system in the time domain. Computer simulation software named the train–track–bridge interacti...

High-speed train-track-bridge dynamic interactions - Part I: theoretical model and numerical simulation

SUMMARY A new detailed model is developed to investigate the vertical interactions between railway vehicles and tracks. The model consists of two subsystems of vehicle and track in which the vehicle subsystem is modelled as a multi-body system with 10 DOFs running on the track with a constant velocity, and the track substructure as an infinite Euler beam supported on a discrete-continuous elastic foundation consisting of the three layers of rail, sleeper, and ballast. The interface between these two subsystems is the wheel / rail interaction described by Hertzian nonlinear elastic contact theory. In order to get numerical results of such a complex system, a new simple fast integration method is adopted. And typical numerical results are compared with field measured data to verify the detailed model. Finally, the model is applied to analysing the wheel / rail dynamic interactions in high-speed rail and in heavy haul railway.

Wanming Zhai

Papers

Fundamentals of vehicle–track coupled dynamics

Two simple fast integration methods for large-scale dynamic problems in engineering

High-speed train-track-bridge dynamic interactions - Part I: theoretical model and numerical simulation

A Detailed Model for Investigating Vertical Interaction between Railway Vehicle and Track

Modelling and experiment of railway ballast vibrations