Non-stationary resonance mechanism of non-uniform elevator traction strings based on space time finite element method

To investigate the mechanism underlying ‘sway-and-hit’ vibration risk of traction strings in super-high-rise elevators under mechanical degradation and non-stationary operation, an ALE-based Space Time Finite Element Method (STFEM) model is developed. A variable-density axially moving string model couples localized mass loss with stiffness degradation through a first-order evolution function. Using an Arbitrary Lagrangian-Eulerian (ALE) strategy and isoparametric mapping, time-varying material-following system matrices are derived for S-curve trajectories. Stiffness degradation drives a nonlinear frequency drift toward the low-frequency range and disrupts the car’s modal-tuning action. The prolonged dwell during S-curve deceleration enables wind-load energy accumulation and severe beat vibration. The resulting degradation-acceleration response surface provides a conditional map for interpreting aging-elevator vibration risk.