Dynamics and Stability of Train-Track-Systems,
POLISH ACADEMY OF SCIENCES WARSAW INST OF FUNDAMENTAL TECHNOLOGICAL RESEARCH
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The development of tracked high-speed transportation systems, e.g. fast wheel-rail-systems with operational speeds up to 260 kmh or fast magnetically levitated trains with speeds up to 400 kmh, is enforced in several countries. With increasing travelling speed the dynamic interaction between vehicles and guideway becomes more and more important. Thus, there is a strong need for simple but reliable models for such systems in order to study the dynamical effects. The aim of this paper is to introduce several linear and nonlinear models for train-track-systems and to investigate their dynamical behaviour. The models are useful to examine the vertical dynamics as well as the lateral dynamics. The track-subsystem is modelled as an infinite Bernoulli-Euler-beam on an elastic foundation, while the train-subsystems consists of different continuous or lumped models which are infinite or finite in length, respectively. Both subsystems are in relative motion to each other with constant velocity. The suspension is modelled by linear springs and in some cases also by nonlinear springs. The mathematical description of the different train-track-models depends on the modelling of the subsystems. It consists either of two coupled partial differential equations or a set or ordinary differential equations coupled with a partial differential equation. The solution is obtained applying the concept of travelling waves. Special attention is paid to the stationary solution and its stability.