Chaos in overhead travelling cranes load motion

Abstract

The paper presents the results of numerical investigations of the overhead travelling cranes load motion. The model studies assumes that the load is suspended on the inextensible rope. 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. The main objective was to evaluate the impact of individual mathematical model parameters on the dynamics of the transported load. The results were compared between two models: with/without crane structure vibrations included. The results were illustrated by multi-colored maps of the largest Lyapunov exponent, bifurcation diagrams, and Poincare cross-sections.

Multiple Solutions of the Tristable Energy Harvester

“…Chaos theory has many tools that can be used to identify zones of chaotic movement. In addition to commonly implemented methods such as: Poincaré cross-section [40,41], the largest Lyapunov exponent [42,43], bifurcation diagrams [44], test 0-1 [45,46], you can use relatively unknown tools such as diagrams of the number of phase stream intersections (NPSI) or a correlation dimension [47]. However, these methods are not capable of determining the number of co-existing solutions and the nature of the solution.…”