Affiliations: Department of Mechanical Engineering, Universidade
Federal do Rio de Janeiro, COPPE, 21.941.972, Rio de Janeiro, RJ, P.O. Box
68.503, Brazil. E-mail: savi@ufrj.br | CSIRO Petroleum, Drilling Mechanics, Kensington WA
6151, P.O. Box 1130, Bentley WA 6102, Australia | Pontifícia Universidade Católica do Rio de
Janeiro, Department of Mechanical Engineering, 22.453.900, Rio de Janeiro, RJ,
Brazil
Abstract: 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.
