Abstract
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.
Highlights
The synchronization has been widely studied in various fields of natural sciences
We focus on the synchronization properties of the system by using the Master stability function (MSF) and average synchronization error as the research tools
We investigated the synchronization properties of coupled self-induced dry friction oscillators
Summary
The synchronization has been widely studied in various fields of natural sciences. The classical experiment by Huygens back in the 17th century, who described the synchronization of pendulum clocks coupled by a common support, was the first scientific report on that phenomena [1]. Having two networks of length m and n with respective synchronization thresholds σm, σn, and the largest non-zero eigenvalues γ1(m), γ1(n) of connectivity matrices Gm and Gn one obtains: σmγ1(m) = σnγ1(n) Some development of this approach allows us to explain an occurrence of discontinuous synchronous intervals in coupling coefficient space – the phenomenon called ragged synchronizability [14]. Where k is the stiffness constant, U amplitude of kinematic excitation, Ω angular excitation frequency, FN normal load force (note that the weight of mass m is already included in FN ), vr relative velocity between the contact surfaces and vb velocity of the belt vr vb dx dt Function f (vr) models the dry friction relationship with respect to vr. All oscillators are subjected to the same excitation amplitude and frequency, conveyor belt velocity and have the same friction properties (i.e. model, coefficients), which should ease the process of synchronization
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