Parameter study of global and cluster synchronization in arrays of dry friction oscillators

2017 ◽  
Vol 381 (15) ◽  
pp. 1286-1301 ◽  
Author(s):  
Michał Marszal ◽  
Andrzej Stefański
Keyword(s):  
Dry Friction ◽  
Cluster Synchronization ◽  
Parameter Study ◽  
Friction Oscillators

scholarly journals Cluster synchronization of dry friction oscillators

2018 ◽  
Vol 148 ◽  
pp. 10004
Author(s):  
Michał Marszal ◽  
Andrzej Stefański
Keyword(s):  
Dry Friction ◽  
Numerical Study ◽  
Excitation Frequency ◽  
Friction Model ◽  
Cluster Synchronization ◽  
Stick Slip ◽  
Closed Ring ◽  
Mass Spring ◽  
Friction Oscillators ◽  
Two Parameter

Synchronization is a well known phenomenon in non-linear dynamics and is treated as correlation in time of at least two different processes. In scope of this article, we focus on complete and cluster synchronization in the systems of coupled dry friction oscillators, coupled by linear springs. The building block of the system is the classic stick-slip oscillator, which consists of mass, spring and belt-mass friction interface. The Stribeck friction itself is modelled using Stribeck friction model with exponential non-linearity. The oscillators in the systems are connected in nearest neighbour fashion, both in open and closed ring topology. We perform a numerical study of the properties of the dynamics of the systems in question, in two-parameter space (coupling coefficient vs. angular excitation frequency) and explore the possible configurations of cluster synchronization.

scholarly journals SLIDING BIFURCATIONS: A NOVEL MECHANISM FOR THE SUDDEN ONSET OF CHAOS IN DRY FRICTION OSCILLATORS

2003 ◽  
Vol 13 (10) ◽  
pp. 2935-2948 ◽  
Author(s):  
M. DI BERNARDO ◽  
P. KOWALCZYK ◽  
A. NORDMARK
Keyword(s):  
Dry Friction ◽  
Sudden Onset ◽  
Stick Slip ◽  
Border Collision Bifurcations ◽  
Sliding Bifurcation ◽  
Nonsmooth Systems ◽  
Different Types ◽  
Nonsmooth Dynamical Systems ◽  
Sudden Jump ◽  
Friction Oscillators

Recent investigations of nonsmooth dynamical systems have resulted in the study of a class of novel bifurcations termed as sliding bifurcations. These bifurcations are a characteristic feature of so-called Filippov systems, that is, systems of ordinary differential equations (ODEs) with discontinuous right-hand sides. In this paper we show that sliding bifurcations also play an important role in organizing the dynamics of dry friction oscillators, which are a subclass of nonsmooth systems. After introducing the possible codimension-1 sliding bifurcations of limit cycles, we show that these bifurcations organize different types of "slip to stick-slip" transitions in dry friction oscillators. In particular, we show both numerically and analytically that a sliding bifurcation is an important mechanism causing the sudden jump to chaos previously unexplained in the literature on friction systems. To analyze such bifurcations we make use of a new analytical method based on the study of appropriate normal form maps describing sliding bifurcations. Also, we explain the circumstances under which the theory of so-called border-collision bifurcations can be used in order to explain the onset of complex behavior in stick-slip systems.

scholarly journals Micro-Slip as a Loss of Determinacy in Dry-Friction Oscillators

2019 ◽  
Vol 29 (06) ◽  
pp. 1930015 ◽  
Author(s):  
S. Webber ◽  
M. R. Jeffrey
Keyword(s):  
Differential Equations ◽  
Dry Friction ◽  
Dynamical Theory ◽  
Stick Slip ◽  
Friction Forces ◽  
Mechanical Oscillators ◽  
The Stability ◽  
Stick Slip Motion ◽  
Friction Oscillators ◽  
Slip Motion

Dry-friction contacts in mechanical oscillators can be modeled using nonsmooth differential equations, and recent advances in dynamical theory are providing new insights into the stability and uniqueness of such oscillators. A classic model is that of spring-coupled masses undergoing stick-slip motion on a rough surface. Here, we present a phenomenon in which multiple masses transition from stick to slip almost simultaneously, but suffer a brief loss of determinacy in the process. The system evolution becomes many-valued, but quickly collapses back down to an infinitesimal set of outcomes, a sort of “micro-indeterminacy”. Though fleeting, the loss of determinacy means masses may each undergo different microscopic sequences of slipping events, before all masses ultimately slip. The microscopic loss of determinacy is visible in local changes in friction forces, and in creating a bistability of global stick-slip oscillations. If friction forces are coupled between the oscillators then the effect is more severe, as solutions are compressed instead onto two (or more) macroscopically different outcomes.

A Historical Review on Dry Friction and Stick-Slip Phenomena

1998 ◽  
Vol 51 (5) ◽  
pp. 321-341 ◽  
Author(s):  
Brian Feeny ◽  
Arde´shir Guran ◽  
Nikolaus Hinrichs ◽  
Karl Popp
Keyword(s):  
Dry Friction ◽  
Historical Review ◽  
Review Article ◽  
Stick Slip ◽  
Daily Lives ◽  
Friction Forces ◽  
Sliding Surfaces ◽  
Highly Nonlinear ◽  
History Of ◽  
Friction Oscillators

This article gives a historical overview of structural and mechanical systems with friction. Friction forces between sliding surfaces arise due to complex mechanisms and lead to mathematical models which are highly nonlinear, discontinuous and nonsmooth. Humankind has a long history of magnificent usage of friction in machines, buildings and transportation. Regardless, our state of knowledge of the friction-influenced dynamics occurring in such systems as well as in our daily lives was, until recently, rather primitive. To represent our understanding of friction in nonlinear dynamics, we first trace examples from the earliest prehistoric technologies and the formulation of dissipation laws in mechanics. The work culminates with examples of friction oscillators and stick-slip. This review article contains 304 references.

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