Synchronization in arrays of coupled self-induced friction oscillators


We investigate synchronization phenomena in systems of self-induced dry friction oscillators with kinematic excitation coupled by linear springs. Friction force is modelled according to exponential model. Initially, a single degree of freedom mass-spring system on a moving belt is considered to check the type of motion of the system (periodic, non-periodic). Then the system is coupled in chain of identical oscillators starting from two, up to four oscillators. A reference probe of two coupled oscillators is applied in order to detect synchronization thresholds for both periodic and non-periodic motion of the system. The master stability function is applied to predict the synchronization thresholds for longer chains of oscillators basing on two oscillator probe. It is shown that synchronization is possible both for three and four coupled oscillators under certain circumstances. Our results confirmed that this technique can be also applied for the systems with discontinuities.


Słowa kluczowe

complete synchronization, synchronization thresholds, coupled oscillators, bifurcations, dynamical systems, Master Stability Function (MSF), friction, synchronizacja kompletna, progi synchronizacyjne, sprzężone oscylatory, bifurkacje, systemy dynamiczne, Nadrzędna Funkcja Stateczności, tarcie