Multiple spatially localized dynamical states in friction-excited oscillator chains. (17th March 2018) - Papangelo, A.; Hoffmann, N.; Grolet, A.; Stender, M.; Ciavarella, M.
Abstract: Friction-induced vibrations are known to affect many engineering applications. Here, we study a chain of friction-excited oscillators with nearest neighbor elastic coupling. The excitation is provided by a moving belt which moves at a certain velocity v d while friction is modelled with an exponentially decaying friction law. It is shown that in a certain range of driving velocities, multiple stable spatially localized solutions exist whose dynamical behavior (i.e. regular or irregular) depends on the number of oscillators involved in the vibration. The classical non-repeatability of friction-induced vibration problems can be interpreted in light of those multiple stable dynamical states. These states are found within a "snaking-like" bifurcation pattern. Contrary to the classical Anderson localization phenomenon, here the underlying linear system is perfectly homogeneous and localization is solely triggered by the friction nonlinearity. Highlights: A friction-excited oscillator chain is studied with periodic boundary conditions. Multiple, spatially localized vibrating states have been found. Multiplicity can explain the lack of repeatability of friction-induced vibrations. Different initial conditions lead to different localized patterns. In the bifurcation diagram "snaking-like" bifurcations have been obtained.