Rigid-Flexible Coupling Dynamic Modeling of a Tower Crane with Long Flexible Boom

A mathematical model of a tower crane with long flexible boom is given in this paper. Both the vertical deformation and the horizontal deformation of the boom which is modelled as an Euler–Bernoulli boom as well as the tie bars’ effects are considered in the model. The Lagaragian method and the assumed mode method are combined to formulate the rigid-flexible coupling model which could fully describe its different motions. The nonlinear coupled motion equations are solved numerically by using Maple. A simplified ADAMS simulation model for a tower crane is built to verify the mathematical model. The dynamic responses of both the boom and the payload got from simulation and that got from numerical solving are analyzed in a comparative way. Several effects of the boom’s deformations to the swing angles of the payload are proposed according to the results.