Dynamic modelling of overhead crane

This paperwork deals with dynamics of overhead crane. Dynamically speaking, I considered the overhead crane beams as continuous medium with distributed elasticity and weight, simple supported at ends, stressed by distributed as well as focused forces. The distributed forces are the own weight and forces of inertia (mass forces) and focused forces are those produced by the carriage and transported load. Focused forces may travel along the overhead crane, so they have variable position and are, in their turn, variable in time as the carriage, always considered in contact with overhead crane, is, on one hand subject to the same accelerations as the beams oscillate in vertical plane in the place where the carriage is at the said moment, and produce variable inertia forces, and, on the other hand, a load is hanging on it, sustained by elastic cables, pulling down with a variable force, depending on how oscillations of the load and overhead crane beam mix up together. The overhead crane is a beam with variable profile subject to static and dynamic, focused and distributed loads. This makes the mathematic model of the overhead crane dynamics to be very complicated and the presentation that follows shall prove it. Analysing the results presented in this study it may come to the conclusion that monitoring and analyse of overhead crane dynamics is extremely important because it may highlight the potentially dangerous situations in operation of this equipment.