Dynamics of oscillators with impact and friction

In the present paper two types of nonsmooth oscillators are investigated: an impact oscillator and a self-sustained friction oscillator. Both are nonsmooth one degree of freedom oscillators with harmonic external excitation. Here the different types of motion, bifurcation diagrams and Poincaré maps are determined from experiments. These results will be compared with numerical results on the basis of the identified impact and friction models. The nonsmooth third-order systems show rich bifurcational behaviour which is analysed by numerical simulations but also using mapping approaches. Two different formalisms for the calculation of the Lyapunov exponents are applied. The latter one requires special considerations in the given case of nonsmooth systems. Furthermore, the embedding dimension is gained applying the method of false nearest neighbours. In the case of coexisting solutions further analysis is done by means of bifurcation and stability analysis and the cell-mapping approach.