Chaotic vibrations of a nonideal electro-mechanical system

Nonideal systems are those in which one takes account of the influence of t he oscillatory system on the energy supply with a limited power (Kononenko, 1969). In this paper, a particular nonideal system is investigated, consis ting of a pendulum whose support point is vibrated along a horizontal guide by a two bar linkage driven by a DC motor, considered to be a limited powe r supply. Under these conditions, the oscillations of the pendulum are anal yzed through the variation of a control parameter. The voltage supply of th e motor is considered to be a reliable control parameter. Each simulation s tarts from zero speed and reaches a steady-state condition when the motor o scillates around a medium speed. Near the fundamental resonance region, the system presents some interesting nonlinear phenomena, including multi-peri odic, quasiperiodic, and chaotic motion. The loss of stability of the syste m occurs through a saddle-node bifurcation, where there is a collision of a stable orbit with an unstable one, which is approximately located close to the value of the pendulum's angular displacement given by alpha (C)= pi /2 . The aims of this study are to better understand nonideal systems using nu merical simulation, to identify the bifurcations that occur in the system, and to report the existence of a chaotic attractor near the fundamental res onance. (C) 2001 Elsevier Science Ltd. All rights reserved.