Iterative solution and numerical analysis of vehicle-track-bridge nonlinear coupled vibration considering viscoelasticity of rail pads

Abstract

To investigate the effect of rail pad viscoelasticity on vehicle-track-bridge coupled vibration, the fractional Voigt and Maxwell model in parallel (FVMP) was used to characterize the viscoelastic properties of the rail pad based on dynamic performance test results. The FVMP model was then incorporated into the vehicle-track-bridge nonlinear coupled model, and its dynamic response was solved using a cross-iteration algorithm with a relaxation factor. Results indicate that the nonlinear coupled model achieves good convergence when the time step is less than 0.001 s, with the cross-iteration algorithm adjusting the wheel-rail force. In particular, the best convergence is achieved when the relaxation factor is within the range of 0.3−0.5. The FVMP model effectively characterizes the viscoelasticity of rail pads across a temperature range of ±20 ℃ and a frequency range of 1−1000 Hz. The viscoelasticity of rail pads significantly affects high-frequency vibrations in the coupled system, particularly around 50 Hz, corresponding to the wheel-rail coupled resonance range. Considering rail pad viscoelasticity is essential for accurately predicting track structure vibrations.

1. Introduction

Bridges are widely used in high-speed railway lines due to their minimal land occupation and high smoothness [1−3]. When trains traverse bridges, they induce vibrations in the tracks and bridge structures. Excessive vibration poses risks to the integrity of the track structure, including issues such as rail wear [4] and track slab cracks [5]. Moreover, it can also affect the quality of life for residents along the railway line [6, 7].

Viscoelastic materials are used to mitigate vibrations in railway track structures. Fasteners serve as the primary components for reducing vibration in ballastless track systems [8−11]. ZHANG et al [12] proposed that higher fastener stiffness isolates vibrations above 50 Hz in the rail, track slab, and bridge. CHEN et al [13] revealed that reducing fastener stiffness increases the vertical deflection of the track and bridge, as well as high-frequency vibration energy. As viscoelastic materials, rail pads exhibit temperature- and frequency-dependent properties. Researchers have studied the viscoelastic properties and theoretical characterization of rail pads [14−16]. THOMPSON et al [17, 18] proposed an experimental method to measure the dynamic stiffness of fasteners within the 100−1000 Hz frequency range. MAES et al [19] conducted experiments to determine the stiffness and damping values of rail pads at various preloads within the frequency range of 20−2500 Hz. OREGUI et al [20] proposed dynamic mechanical analysis (DMA) and the time-temperature superposition principle (TTSP) to predict the dynamic properties of rail pads. The Prony series material model was introduced to describe this dynamic behavior. With advances in fractional derivative theory, researchers have found that fractional derivative models can more accurately characterize the viscoelastic properties of materials using fewer parameters [21]. WEI et al [22, 23] and LI et al [24] utilized the fractional derivative Kelvin-Voigt (KV) model to describe frequency-dependent behavior. ARIKOGLU [25] proposed a ten-parameter fractional derivative model to simulate the viscoelastic behavior of rail pads. LIU et al [26] demonstrated that the fraction Voigt and Maxwell mode in parallel (FVMP) model could accurately represent the viscoelastic behavior of rail pads.