Experimental Demonstration of the Oscillatory Phenomenon Taut-Slack

Abstract

In this paper a mechanism for reproducing the phenomenon known as "taut-slack" in a cable-body system is presented. 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 Poincare maps. From the experimental results it could be obtained period doubling with the presence of the taut-slack phenomenon. Through comparison with simulated bifurcation diagrams and Poincare maps it could be noticed a good concordance between the signal profiles and also a comparable evidence of the behavior diversity.