The dynamic response of the railway track modelled as a continuously supported beam on a Kelvin type foundation and subjected to an axial force and time dependent moving loads is studied. The transient and steady state solutions are found for the general case including all linear effects. This study shows the effects of axial force and damping on the dynamic response. The results also show that the effect of the velocity of the moving load on the dynamic response is small, and hence it is not necessarily to consider the wave type expression to study the effect of track elasticity on the dynamics of railway vehicles.

An analysis for the dynamics of a railway vehicle including the effect of vertical track elasticity is presented, with particular emphasis on the lateral stability and the response to vertical track irregularities. The model used in the analysis is that of a six-axle locomotive of the type commonly used in North America. Wheel tread profile parameters, gravity stiffness effects and creep forces are included in the mathematical model.

The results show that an increase in vertical track elasticity results in a small increase in the critical speed at which hunting instability occurs. The increase in track elasticity results in appreciable increase in the amplitude of the response to track irregularities especially at high frequencies.

A method for the minimization of the vibrations transmitted due to track irregularities using the minimax principle and mathematical programming techniques is suggested. The method is demonstrated by considering the minimization of the lateral cab acceleration within the frequency range of interest.

The analyses and digital computer simulations are viewed as analytical tools for studying the effect of changing the vehicle and/or track parameters on the dynamic response of both the vehicle and the track. The methods developed are general and can be used in the design stage to adjust geometry and/or suspension characteristics for any proposed design of a railway vehicle.