Implementation of variable cross-section curved beam in train-turnout dynamic interactions

Abstract

The abundance of variable cross-section curved rails in railway turnouts emphasizes the necessity of intricately modeling them, which facilitates a more accurate evaluation of train-turnout interactions. This study presents a general formulation for analyzing both free and forced vibrations of a variable cross-section curved Timoshenko beam and its implementation in train-turnout dynamic interactions. First, the natural frequencies and mode shapes for in-plane and out-of-plane free vibrations of the beam are determined through eigenvalue analysis, taking into careful consideration the characteristics of variable cross-section and curvature. Then, the forced vibration solution is derived using modal superposition and orthogonality. Furthermore, comparative analyses using finite element method (FEM) validate the natural frequencies and dynamic responses of a beam under various boundary conditions, confirming the reliability and accuracy of the proposed method. Finally, the developed beam model is then applied to simulate the switch rail and point rail under train-turnout interactions, revealing the differences from existing methods that modeled these components as uniform cross-section straight beams. Numerical analyses provide new insights by comparing wheel-rail forces and rail acceleration. Considering curve and variable cross section characteristics could contribute to a more accurate evaluation of train-turnout dynamic interactions.