• The FVMP model accurately characterizes rail pad viscoelasticity across ±20 °C and 1–1000 Hz.
• The nonlinear coupled model converges well for time steps below 0.001 s, with best convergence for relaxation factors 0.3–0.5.
• Rail pad viscoelasticity significantly affects high-frequency vibrations, especially around 50 Hz in the wheel-rail coupled resonance range.
• The cross-iteration algorithm with relaxation factor effectively solves the coupled nonlinear dynamic response and adjusts wheel-rail force.