Nonlinear dynamics of viscoelastic time-varying vertical transport systems at multi-stage speeds

Steel belt-driven elevators have been increasingly adopted in high-rise buildings due to their compact structure and low noise. Unlike conventional wire ropes, steel belts exhibit strong viscoelasticity, which, together with the time-varying system length and multi-stage speeds operation, introduces a triple-coupling effect that fundamentally alters system dynamics, threatening the normal operation of an elevator. This study develops a nonlinear longitudinal dynamic model of viscoelastic belt-driven time-varying vertical transport systems using the Generalized Hamiltonian Principle, with model accuracy verified through experiments. A reduced-order Duffing oscillator is introduced to capture nonlinear behaviours such as bifurcation, phase trajectory, and Poincaré sections, which are further validated via Lyapunov spectra. Results reveal that viscoelastic damping can suppress vibrations during upward motion but may amplify responses during downward motion, and that mismatched dissipation at high speeds leads to energy accumulation and oscillatory shocks. The triple-coupling mechanism significantly affects both the stability boundaries and energy transfer characteristics of the system. Finally, the influence mechanism of the triple-coupling effect is discussed. This work provides new insights into the dynamic behaviours of viscoelastic traction systems and offers a theoretical foundation for vibration suppression and safe operation of belt-driven elevators, with potential applicability to winches, cranes, and robotic hoists.