Vibration Normal Modes of a Jib Crane Modeled as an Euler–Bernoulli boom using FEM

Abstract

In this paper, it was developed a method for determining the Vibration Normal Modes of a Jib Crane. A Finite Element Method modeling the Jib Crane as an Euler-Bernoulli boom has been used. We made the approximation of dividing the Boom into a limited number of elements, characterizing the weight distribution on the boom itself. This allowed us to obtain an analytical solution to the problem. The Jib Mass and Stiffness Matrices were calculated. Finally, the first natural frequencies are obtained as well as the first corresponding eigenvectors. From these results, we can derive the behavior of the structural dynamics of the Crane. This is particularly important for large tower cranes that show high structural dynamics, since this approach allows to reduce the vibrations of the crane structure. The advantage of this method is given by the fact that the set of eigen-frequencies can be recalculated using a supervisor Pc. This Pc sends the data of the same eigen-frequencies in real-time to the PLC that controls the crane according to the variable position of the trolley and payload on the Jib.