Formulation of curved beam vibrations and its extended application to train-track spatial interactions

Abstract

This paper presents a semi-analytical solution to free and forced vibrations of a pinned–pinned Euler-Bernoulli curved beam, and extends it into train-track spatial interactions. The in-plane and out-of-plane modes of the curved beam are approximated by the partial sums of sinusoidal Fourier series, and the forced vibration equations in a generalized coordinate are formulated by utilizing the Galerkin method and mode orthogonality derived based on the reciprocal theorem of work. Comparisons of natural frequencies and dynamic responses with published results and finite element method (FEM) illustrate the reliability and advancement of current approach, which provides more accurate results for higher frequency analysis and possesses better adaptability to different boundary conditions by supplementing polynomials. Moreover, the influence of radius and subtended angle on the natural frequencies of rails simulated by the straight and curved beam models are also investigated. Finally, the established model is further extended to simulate the curved rails implemented in a train-track coupled dynamics system with consideration of a nonlinear wheel-curved rail contact model, since they used to be idealized as straight beams instead of taking the actual curvature into account. Some new recognitions are gained by examining the effect of rail modelling options and additional creepages on a curved track, which is conducive to more accurate evaluations on curve negotiation effects induced by train-track spatial interactions.