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Shock and Vibration
Volume 13, Issue 4-5, Pages 315-326

Nonlinear Dynamics and Chaos in Systems with Discontinuous Support

Sandor Divenyi,1 Marcelo Amorim Savi,1 Luiz Fernando Penna Franca,2 and Hans Ingo Weber3

1Department of Mechanical Engineering, Universidade Federal do Rio de Janeiro, COPPE, 21.941.972, Rio de Janeiro, RJ, P.O. Box 68.503, Brazil
2CSIRO Petroleum, Drilling Mechanics, Kensington WA 6151, P.O. Box 1130, Bentley WA 6102, Australia
3Pontifícia Universidade Católica do Rio de Janeiro, Department of Mechanical Engineering, 22.453.900, Rio de Janeiro, RJ, Brazil

Received 19 July 2006; Revised 19 July 2006

Copyright © 2006 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Non-smooth systems are abundant in nature being usually related to physical systems with dry friction, impact and backlash. These systems operate in different modes, and the transition from one mode to another can often be idealized as an instantaneous or discrete transition. Since the time scale of this transition is much smaller than the scale of the individual modes dynamics, its mathematical modeling can be lead as non-smooth. This contribution uses a smoothened switch model to analyze non-smooth systems. The procedure seems to be effective to deal with this kind of system, presenting advantages for the numerical implementation. As an application of the general formulation, a single-degree of freedom oscillator with discontinuous support is analyzed. System dynamical behavior shows a rich response, presenting dynamical jumps, bifurcations and chaos.