Dynamic Responses of an Overhead Crane’s Beam Subjected to a Moving Trolley with a Pendulum Payload

An overhead crane with a flexible cable is an underactuated system; the vibration of the crane’s beam and the residual swinging of the payloads cause fatigue in the crane and affect the precise positioning of the payloads. In this paper, the coupling system of an overhead crane was simplified to that of a moving mass with pendulum swing passing beam model. The differential equation motion of a coupled overhead crane system was derived based on the Lagrange equation. Mathematical solution was carried out by using the Newmark-β integral method. The influences of the trolley’s acceleration and the parameters of the payloads on the vibration of the beam and the payloads’ swing were, respectively, analyzed. A numerical analysis of the results indicates that increasing the mass of the payloads leads to a larger deflection of the beam, whereas increasing the speed and acceleration of the trolley does not obviously influence the maximum deflection of the central beam.