Vibration analysis of a flexible crane hoist beam under harmonic unbalance excitation

This study develops a three-degree-of-freedom nonlinear dynamic model for a flexible crane hoist system subjected to deterministic harmonic unbalance. The model integrates trolley displacement, payload swing, and the first bending mode response of the supporting beam to capture the key features of the coupled electromechanical–structural interaction. Lagrangian mechanics is used to derive the governing equations, and numerical simulations reveal low-amplitude, multi-frequency trolley motion, a dominant pendulum oscillation at low frequencies, and high-frequency beam bending effects associated with the unbalanced motor. Frequency analysis identifies distinct peaks related to the pendulum, beam, and excitation frequencies, illustrating the resonance mechanisms that appear when structural flexibility is taken into account. The results show that the beam’s flexibility significantly influences the dynamic response, modulates trolley motion, and amplifies high-frequency components during lifting. This study contributes to understanding the influence of deterministic excitation on the dynamics of overhead cranes and provides a structured framework for evaluating vibrations in flexible lifting systems.