An application of the dynamic stiffness concept for vibration of three-dimensional cracked overhead crane

A simplified model is proposed for modal analysis of cracked 3D-framed overhead crane of H-form frame using the well-known dynamic stiffness method. First, the dynamic stiffness of a cracked beam is derived as the inverse of the frequency response function and used for establishing a model of the cracked beam called dynamic stiffness one. Then, the dynamic stiffness model of cracked beams is employed for representing two supporting beams in the H-form frame crane. So that a simplified model of the overhead crane is conducted as a beam with artificial elastic supports of stiffness obtained above for supporting beam. Finally, the free vibration problem of the simplified overhead crane is formulated and solved for the crane fundamental frequency analysis in dependence upon crack parameters and supporting positions. Numerical computation is accomplished for illustrating the proposed theory and providing some conclusions on the simplified model of 3D overhead cranes.