Impact dampers for controlling chaos in systems with limited power supply

We investigate numerically the dynamical behavior of a non-ideal mechanical system consisting of a vibrating cart containing a particle which can oscillate back and forth colliding with walls carved in the cart. This system represents an impact damper for controlling high-amplitude vibrations and chaotic motion. The motion of the cart is induced by an in-board non-ideal motor driving an unbalanced rotor. We study the phase space of the cart and the bouncing particle, in particular the intertwined smooth and fractal basin boundary structure. The control of the chaotic motion of the cart due to the particle impacts is also investigated. Our numerical results suggests that impact dampers of small masses are effective to suppress chaos, but they also increase the final-state sensitivity of the system in its phase space. (C) 2004 Elsevier Ltd. All rights reserved.

A nonlinear and non-ideal wind generator supporting structure

We present a simple mathematical model of a wind turbine supporting tower. Here, the wind excitation is considered to be a non-ideal power source. In such a consideration, there is interaction between the energy supply and the motion of the supporting structure. If power is not enough, the rotation of the generator may get stuck at a resonance frequency of the structure. This is a manifestation of the so-called Sommerfeld Effect. In this model, at first, only two degrees of freedom are considered, the horizontal motion of the upper tip of the tower, in the transverse direction to the wind, and the generator rotation. Next, we add another degree of freedom, the motion of a free rolling mass inside a chamber. Its impact with the walls of the chamber provides control of both the amplitude of the tower vibration and the width of the band of frequencies in which the Sommerfeld effect occur. Some numerical simulations are performed using the equations of motion of the models obtained via a Lagrangian approach.

Control and chaos for vibro-impact and non-ideal oscillators

In the paper, we discuss dynamics of two kinds of mechanical systems. Initially, we consider vibro-impact systems which have many implementations in applied mechanics, ranging from drilling machinery and metal cutting processes to gear boxes. Moreover, from the point of view of dynamical systems, vibro-impact systems exhibit a rich variety of phenomena, particularly chaotic motion. In this paper, we review recent works on the dynamics of vibro-impact systems, focusing on chaotic motion and its control. The considered systems are a gear-rattling model and a smart damper to suppress chaotic motion. Furthermore, we investigate systems with non-ideal energy source, represented by a limited power supply. As an example of a non-ideal system, we analyse chaotic dynamics of the damped Duffing oscillator coupled to a rotor. Then, we show how to use a tuned liquid damper to control the attractors of this non-ideal oscillator.

Control and chaos for vibro-impact and non-ideal oscillators

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)