A MATHEMATICAL INVESTIGATION OF THE DYNAMICS OF DRIVE-SYSTEMS OF RAILWAY TRACTION VEHICLES UNDER STOCHASTIC TRACK EXCITATION

Abstract

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.