INSTABILITY OF VIBRATION OF A MOVING-TRAIN-AND-RAIL COUPLING SYSTEM

This paper presents the derivation of the governing equations for the stability of vibration of an integrated system comprising a moving train and the railway track. The train consists of a convoy of articulated two-axle wagons. The equations are applicable to any arbitrary number of axles at arbitrary spacing. Each axle is modelled as a mass–spring–damper vibration unit. The railway track is an infinitely long Euler beam subjected to an axial compressive force and rests on a visco-elastic foundation. The governing equations for the integrated system are coupled differential equations, which can be transformed to algebraic equations by Fourier and Laplace transforms. Subsequent inverse Fourier transform and contour integration yield the instability equation. Critical parameter is identified. It follows by parametric studies on the instability of vibration due to different train configurations. Illustrative examples for trains having up to 20 wagons or 40 axles are given.