Journal of Theoretical
and Applied Mechanics

46, 3, pp. 641-664, Warsaw 2008

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

Silvio L.T. de Souza, Iberê L. Caldas, Ricardo L. Viana, José M. Balthazar
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.
Keywords: vibro-impact; chaos; control of chaos; non-ideal oscillators