Vehicle-Induced Lateral Vibration of Railway Bridges: An Analytical-Solution Approach

Abstract

The lateral vibration of railway bridges induced by moving trains has traditionally been solved through numerical integration. Although it provides practical prediction, the numerical approach does not explicitly reveal the underlying driving mechanism of the train–bridge interaction. In this paper, a closed-form solution is derived for the lateral vibration of a simply supported bridge subjected to hunting forces from running wheel sets. Through complex Fourier expansion, this solution leads to the formulation of three influential factors with explicit physical meanings, namely, the effective unit moving load on the bridge, the arrangement of all moving wheel sets, and the frequency response function of the bridge. On the basis of these factors, a simplified formula to estimate the maximum vibration of the bridge is proposed. The closed-form solution and the simplified formula are validated through comparison with results from numerical integration. The resonance conditions of the bridge due to moving hunting forces are derived using the simplified estimation.