Implementation of Timoshenko curved beam into train-track-bridge dynamics modelling

Abstract

Curved bridge has been widely applied in railway lines due to its strong terrain adaptability, a more refined model that could capture curved bridge vibrations in the train-track-bridge (TTB) dynamic interaction issues is urgently required. In this paper, an improved semi-analytical approach for the vibrations of a Timoshenko curved beam is newly proposed based on the Chebyshev-tau method, which considers the rotary inertia and shear deformation, and is firstly implemented into the train-track-curved bridge coupled dynamics modelling (TTCBCD). First, by utilizing Galerkin method to discretize the partial differential equation of the curved beam and employing modal superposition method to decouple its ordinary differential equation, the forced vibration equations of the curved beam subject to three-dimensional moving loads are derived. Then, comprehensive comparisons of the eigenvalue analyses and dynamic performance of a pinned-pinned curved beam with published literature and finite element method demonstrate the accuracy and reliability of the current scheme. Moreover, the natural frequencies of curved beams with variable boundary conditions (BC) are investigated to illustrate its strong versatility by supplementing BC formulas. Finally, the established model is further implemented into the dynamics analysis of the TTCBCD featured by the nonlinear wheel-rail contact, the spatial flexibility of the track structure and the track slab-curved bridge interactions. The numerical analyses indicate that the bridge modelling approach exhibits remarkable distinction between the conventional method (idealized as a straight beam) and the proposed method, and some new insights in the applicable ranges of the proposed model with variable bridge lengths are pointed out. This work could be beneficial to a more accurately evaluation of the curve effects induced by train-track-bridge dynamic interactions.