A MATHEMATICAL INVESTIGATION OF THE DYNAMICS OF DRIVE-SYSTEMS OF RAILWAY TRACTION VEHICLES UNDER STOCHASTIC TRACK EXCITATION
1992
In ZOBORY and NHUNG [10], some explicit conditions ensuring the existence of a stable
stationary forced vertical vibration of the railway vehicle dynamic system model (see
ZOBORY [7]) were derived. In this paper, we consider an elementary drive-system model.
Not only the vertical displacement in the translatory subsystem of the model will be
investigated, but also the angular displacements taking place in the torsional sub-system
of the model.
The elementary dynamics of drive-systems of railway traction vehicles under stochastic
track excitation may be described by an 8 X 8-system of random non-linear differential
equations whose linearized system has constant coefficients. To ensure the existence
and the stability of weakly stationary vertical and relative angular displacements in the
model, we apply the Routh-Hurwitz criterion (see e. g. ARNOLD [1]) and some theorems
elaborated by BUNKE [3] and NHUNG [4-6] to impose explicit conditions on the system
parameters in terms of algebraic inequalities. These conditions guarantee that the four
eigenvalues corresponding to the vertical displacements have negative real parts, and the
eigenvalue zero corresponding to the relative angular displacements is simple and the other
three eigenvalues have negative real parts.
The algebraic inequalities characterizing the existence and the stability of stationary
motions can be easily checked on computers.
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