Effect of viscoelastic-plastic dynamic properties of rail pads on curved rail dynamic characteristics based on the modified SEM–SM hybrid method

To accurately and efficiently investigate the influence of the viscoelastic-plastic dynamic properties of rail pads on curved rail vibration characteristics, a spatial model of an infinitely curved track was developed by combining the spectral element method (SEM) and symplectic method (SM). Specifically, a fractional derivative Zener model combined with a Berg friction model was used to describe the dynamic properties of the rail pad. Subsequently, the curved rail mobility and decay rate (DR) were analyzed by accounting for the frequency, preload, and amplitude dependence of the rail pad. In conclusion, the frequency dependence mainly influenced the low- and medium-frequency vibrations of the curved rail and made the vibration within this range to shift to higher frequencies. In terms of the curved rail DRs of different degrees of freedom, because of their coupling effects, the wave modes were converted mutually at the cross frequency of their DR curves, and the torsional (axial) wave had the maximum (minimum) DR. The preload dependence had a significant effect on the vertical and torsional vibrations of the curved rail. As the preload increased, the cut-on frequencies of the first vertical and torsional waves increased; consequently, the curved rail vibrations were transmitted more in the downward.