Floquet Stability Analysis of Moving Railway Track Models With Lumped Parameters

Abstract

Abstract. This work presents a methodology for assessing the stability of moving railway track models represented as lumped parameter systems that travel with the vehicle and exhibit periodic variations in their properties due to the discrete support structure of the track. Under constant forward velocity conditions, these models are governed by a damped and forced Hill-type equation and are shown to accurately reproduce the theoretical vertical displacement of a moving load on a beam with discrete supports. Floquet theory and Hamiltonian dynamics are employed to assess and thoroughly understand the stability of these computationally efficient railway track models. As a numerical validation, the methodology is applied to the damped and forced Mathieu's equation, formulated in the context of railway track dynamics. The results demonstrate the effectiveness of the approach and the crucial role of the selected damping in suppressing regions of parametric instability, with those associated with high forward velocity conditions persisting the longest. These findings support the use of Floquet analysis as a valuable tool for identifying operating conditions and parameter combinations that lead to parametric instability in simplified moving track models.