Instability of Vibrations of Mass(es) Moving Uniformly on a Two-Layer Track Model: Parameters Leading to Irregular Cases and Associated Implications for Railway Design

Abstract

Ballasted railway tracks can be modeled using reduced/simplified models composed of several layers of discrete components. This paper deals with the two-layer model, which is very popular due to its computational efficiency. In order to provide some recommendations for track design, it is necessary to identify which set of parameters leads to some irregular/unexpected behavior. In this paper, irregularities are investigated at three levels, namely, (i) the critical velocity of a moving constant force, (ii) the instability of one moving mass, and (iii) the instability of two moving masses. All results are presented in a dimensionless form to cover a wide range of real parameters. Irregular cases are identified by sets of parameters leading to them, which is the main finding of this paper; then, general conclusions are drawn. Regarding the method, all results are obtained analytically or semi-analytically, where “semi” refers to solving the roots of a given polynomial using predefined numerical procedures in symbolic software. No numerical integration is involved in any of the results presented. This means that the results are highly accurate and refer to exact values, so any kind of parametric or sensitivity analyses is readily possible.

Keywords

• integral transforms
• contour integration
• ballasted railway track
• critical velocity
• instability of moving inertial objects