Modeling of system dynamics of a slewing flexible beam with moving payload pendulum

When a tower crane is handling payload via rotation and moving the carriage simultaneously the jib structure and the payload can be modeled as a system consisting of a slewing flexible clamed-free beam with the spherical payload pendulum that moves along the beam. The present work completes the dynamic modeling of the system mentioned above. The clamed-free beam attached to a rotating hub is modeled by Euler–Bernoulli beam theory. The payload is modeled as a sphere pendulum of point mass attached to via massless inextensible cable the carriage moving on the rotating beam. Non-linear coupled equations of motion of the in- and out-of-plane of the beam and the payload pendulum are derived by means of the Hamilton principle. Some remarks are made on the equations of motion.