Identification of chaotic attractors of the overhead travelling crane model
In this work, model studies were carried out, which focused mainly on structures mapping the geometry of strange attractants - the mathematical pendulum model with the flexible rope and variable length. Such a dynamic system approximates the movement of the overhead travelling crane’s load to a large extent. Conversely, its motion is triggered by an external moment. In addition, energy losses in the construction node connecting the rope to the drum are included. At the same time, these losses were mapped through a linear viscous damper. On the basis of the formulated non-linear mathematical model, the ranges of variation of physical parameters of external dynamic excitation for which the system motion is chaotic were identified. The results were presented in the form of multi-coloured maps of the largest Lyapunov exponent. The classic Poincare section, supplemented with information on the density of the points distribution of the trajectory intersection with the control plane, was the basis for the evaluation of the evolution of geometrical structures of strange attractors. It has been shown that chaotic attractors depending on the swing angle of the pendulum and the mass displacement due to the non-linear characteristic of the rope have a distinctly different geometric form. The areas with the highest densification of the Poincaré cross section are usually located in places where the strange attractor is curved. In addition, it has been shown that the model does not have chaotic phenomena if the operator uses the hoist correctly and in accordance with the manufacturer’s guidelines.
KeywordsChaos Mechanical Vibration Cranes Modelling Lyapunov Exponent
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