Nonlinear Dynamics and Chaos in Systems with Discontinuous Support

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.