Dynamics of flexible overhead cranes: modeling and dynamic responses

Abstract

This study presents a nonlinear dynamic model of a flexible overhead crane operating in a vertical plane. The model simultaneously considers the flexural deformation of the main girder, the axial elongation of the hoisting cable, and the effects of internal damping. The equations of motion are formulated as a system of nonlinear ordinary differential equations (ODEs), allowing efficient simulation of the system’s dynamic response, vibration behavior and stability characteristics.Numerical analyses are conducted for both undamped and damped cases. The results show that the elastic deformation of the cable is the primary source of beam vibration, while the payload sway also contributes to the overall oscillation. Including cable elasticity slightly increases the maximum beam deflection but significantly amplifies elastic oscillations. When damping is introduced, both cable and beam oscillations are reduced, and can be reduced to static deformation with increasing damping. The study provides a compact yet accurate modeling framework and offers useful insights for the integrated control of elastic and sway vibrations in flexible overhead cranes.