Study of Unstable Orbits of Stationary Oscillations in the Phenomenon Taut-Slack

JORDAN, MARIO ALBERTO; BUSTAMANTE, JORGE

Santiago de Cuba, Cuba

Conferencia; International Conference of the Faculty of Electrical Engineering, FIE’06; 2006

Universidad de Oriente, Santiago de Cuba, Cuba

In this paper we present new results of a mechanism for reproducing the phenomenon known as "taut-slack" in a cable-body system. The operation of the mechanism consists in forcing an oscillation of a point from which a body immersed in liquid is suspended by means of a cord. For particular values of ad-hoc design parameters of the mechanism, the body can oscillate nonlinearly mainly because the cable transits from a taut to a slack condition cyclically. Both body and suspension point positions are sensed in order to detect the periodicity of the resulting body motion. The modeling of the system dynamics yields a set of two Mathieu differential equations that are combined piecewise according to the cable taut-slack condition. The periodicity detection implemented in this work is based on the analysis of Cauchy series obtained from the Poincaré maps. From the experimental results it could be obtained period doubling with the presence of the taut-slack phenomenon. Through comparison with simulated basins and Poincaré maps it could be noticed a good concordance between theoretical and experimental results with clear evidence of the behavior diversity.