Mathematical analysis of the transient loads for a deformed joint or welding in a railway track
The railway track is modeled as a continuous beam on elastic support. Train circulation is a random dynamic phenomenon and, according to the different frequencies of the loads it imposes, there exists the corresponding response of track superstructure. At the moment when an axle passes from the location of a sleeper, a random dynamic load is applied on the sleeper. The theoretical approach for the estimation of the dynamic loading of a sleeper demands the analysis of the total load acting on the sleeper to individual component loads-actions, which, in general, can be divided into:
• the static component of the load‚ and the relevant to it reaction/action per support point of the rail (sleeper)
• the dynamic component of the load, and the relevant to it reaction/action per support point of the rail (sleeper)
The dynamic component of the load of the track depends on the mechanical properties (stiffness, damping) of the system “vehicle-track”, and on the excitation caused by the vehicle’s motion on the track. The response of the track to the aforementioned excitation results in the increase of the static loads on the superstructure. The dynamic load is primarily caused by the motion of the vehicle’s Non-Suspended (Unsprung) Masses, which are excited by track geometry defects, and, to a smaller degree, by the effect of the Suspended (Sprung) Masses. In order to formulate the theoretical equations for the calculation of the dynamic component of the load, the statistical probability of exceeding the calculated load -in real conditions- should be considered, so that the corresponding equations refer to the standard deviation (variance) of the load.
In the present paper the dynamic component is investigated through the second order differential equation of motion of the Non Suspended Masses of the Vehicle and specifically the transient response of the reaction/ action on each support point (sleeper) of the rail. The case of a deformed or bent joint or welding is analyzed through the second order differential equation of motion and the solution is investigated.
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