Rotating electromechanical systems with bistable potential, hysteretic iron-core inductor and delay

Abstract

This thesis analyses the behaviour of rotating and pendulum rod like electromechanical arms. The goal ultimate is to design chaotic sieves and mixers. After the schematic representation and description of each prototype, the mathematical models are established and the appropriate theoretical methods are used to study their dynamical behaviours. The main results obtained are expressed in terms of design, modelling and dynamic characterization of new electromechanical devices. - The first device designed is an electromechanical system which rotates on an arc of a circle a rigid arm acting as a particle in a bistable potential due to three appropriately placed magnets. This first device is modelled, the analysis of the dynamics subjected to the action of a source of sinusoidal voltage and of a voltage source of square form is made. This analysis highlights the chaotic behaviour used in the mixing and sieving processes; - The second device designed differs from the first by the fact that its movement is framed by the symmetrically fixed springs and by the fact that the hysteresis of the inductance is taken into account through an inductance-intensity characteristic of the strongly nonlinear. Here again the reinforcement of the complexity of the dynamic behaviours is ensured on the one hand by the introduction of a bistability created by symmetrically arranged magnets and on the other hand by the introduction of a delay generated by feedback from a mechatronic device; - The third device designed has a pendula behaviour presenting both a translational movement through a horizontal rod and a pendulum movement through a second rod. This double movement gives the device several different functions in terms of applications. As in the case of the first two devices, complexification is ensured by the creation of bistability by magnets, the non-linear characteristic of the inductance and the use of a delayed feedback force.