Numerical and experimental investigations of the nonlinear dynamics and chaos in non-smooth systems

Nature is full of non-smooth nonlinearities that are usually related to either friction phenomena or the discontinuous characteristics of intermittent contacts. In general, non-smooth characteristics cause difficulties in the modeling and simulation of natural systems. A smoothed switch model is used in this contribution in order to analyze non-smooth systems. The procedure is shown to be an effective method of dealing with this kind of system, and has advantages in numerical implementation. As an application of the general formulation, a single-degree of freedom oscillator with discontinuous support is analyzed. An experimental apparatus is developed in order to verify the capability of the mathematical formulation and the numerical procedure used to describe the system general behavior. This apparatus is instrumented to obtain all system state variables, making it possible to compare experimental results with those obtained through numerical simulations. The systemʹs dynamical behavior shows a rich response that includes dynamical jumps, bifurcations and chaos. Different aspects related to nonlinear dynamics are carried out showing that numerical simulations are in close agreement with experimental data.