Modeling and Nonlinear Resonance Characteristics of a Hoisting Structure in a Tower Gravity Energy Storage System

As a key energy-conversion component of tower gravity energy storage systems (T-SGESs), the hoisting structure is susceptible to large-amplitude coupled vibrations when the dominant frequency of a continuous external excitation approaches one of its natural frequencies, potentially compromising operational stability and safety. To characterize this behavior, a two-degree-of-freedom nonlinear dynamic model is developed based on Hamilton’s principle. Eigenvalue and modal analyses are performed to determine the natural frequencies and modal characteristics of the coupled system, while the second-mode primary resonance is further analyzed using the method of multiple scales and validated through numerical frequency-sweep simulations. Near the second-mode primary resonance, the system exhibits a pronounced hardening-type nonlinear response characterized by multistability, saddle-node bifurcations, jump transitions, and hysteresis. Parametric analysis indicates that greater attention should be paid to short-rope and low-payload operating conditions, under which the system tends to exhibit stronger nonlinear responses and larger payload swing amplitudes near the second-mode primary resonance. Meanwhile, the nonlinear resonance response of the hoisting structure can be effectively mitigated through enhanced equivalent stiffness and damping, which substantially narrow the multistable frequency interval. At a damping ratio of 0.04, the system transitions from a multivalued response to a single stable branch, with a marked reduction in payload swing amplitude. These findings identify the second-mode primary resonance as a critical nonlinear operating regime and provide a quantitative basis for resonance avoidance and parameter regulation in T-SGES hoisting systems.