Chaos identification of a colliding constrained body on a moving belt

Abstract

In this work, the combination of the 0-1 test for chaos and approximate entropy is applied to a newly established mechanical model instead of the Lyapunov exponent exploration on huge simulations reached on the supercomputer Salomon (Czech Republic). This procedure is applied to the mechanical systems modeled by a system of non-autonomous ordinary differential equations that detects the type of trajectories generated when the system parameters are changed. This new mechanical system is formed by an impact element hanging on a flexible rope, and a moving belt, etc. This contact system with impacts and dry friction is based on numerous industrial applications such as stones falling on a moving conveyor belt. The mathematical model's systems of equations have three degrees of freedom: two of them correspond to the position of the impact body center of gravity and the third one to the angular rotation. As the main aim, it is shown that the investigated systems exhibit a full range of trajectory types, meaning it can act in both a regular and irregular way. These results are supported by bifurcation diagrams and phase portraits for a suitable choice of drive parameters: the excitation frequency and amplitude.