Three-dimensional modeling of container cranes with deformable boom

A three-dimensional model of container cranes accounting for the elastic interaction between the crane boom and the container dynamics is proposed. The container is modeled as a rigid body elastically suspended from the trolley moving on top of the crane boom. The Euler-Bernoulli beam model is adopted to describe the boom elasticity. The governing equations of motion are obtained employing the Euler-Lagrange equations whereby the boom kinetic and stored energies are introduced through a Galerkin discretization based on the mode shapes of the two-span crane boom taken as trial functions. Numerical investigations are carried out to evaluate the influence of the crane boom deformability on the dynamic response of the hoisted container especially when the response is nonlinearly excited by internal resonances. Comparisons with results obtained in a previous work where the boom dynamics were neglected are discussed.