Signal and Model Based Analysis of Systems With Friction and Impacts

Abstract

Nonsmooth dynamical systems become increasingly important in engineering and other applied sciences since nonsmooth effects are taken into account and are no longer smoothed out. Due to the lack of smoothness, classical mathematical methods are not or only limited applicable and require often extensions in order to apply analytical and numerical methods. In mechanical systems the consideration of e.g. friction and impacts leads to discontinuities in the corresponding mathematical models. In the proposed paper different methods will be applied, based either on models or on measured or simulated time signals. The investigation comprises a friction oscillator with self- and external excitation and a simple impact oscillator. The methods under consideration are one-dimensional maps, bifurcation and stability analysis, the determination of Lyapunov exponents, and the phase-space reconstruction by the help of general mutual information and false nearest neighbours.