On the origin and bifurcations of stick-slip oscillations

Dankowicz, Harry; Nordmark, Arne

doi:10.1016/s0167-2789(99)00161-x

Cited by 208 publications

(110 citation statements)

References 39 publications

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“…There is ample literature where different aspects of the dynamics triggered by the presence of discontinuous nonlinearities have been treated, and in particular, bifurcations induced by the presence of discontinuity sets (Discontinuity Induced Bifurcations or DIBs for short) have been given much focus, see for example [5,6,7,8,9,10,11,12,13,14]. However, there is a number of important and intriguing questions that have not been answered as yet.…”

Section: Introductionmentioning

confidence: 99%

Attractors near grazing–sliding bifurcations

2012

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In this paper we prove, for the first time, that multistability can occur in 3-dimensional Fillipov type flows due to grazing-sliding bifurcations. We do this by reducing the study of the dynamics of Filippov type flows around a grazing-sliding bifurcation to the study of appropriately defined one-dimensional maps. In particular, we prove the presence of three qualitatively different types of multiple attractors born in grazing-sliding bifurcations. Namely, a period-two orbit with a sliding segment may coexsist with a chaotic attractor, two stable, period-two and period-three orbits with a segment of sliding each may coexist, or a non-sliding and period-three orbit with two sliding segments may coexist.

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Section: Introductionmentioning

confidence: 99%

Attractors near grazing–sliding bifurcations

2012

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“…Since, in the setup, both torsional and lateral vibrations appear, we are interested in the angular velocity ω l and radial displacement r of the lower disc in steady state for different constant input voltages u c . As already discussed before, when u c > u E p , ω l in steady state can be obtained by solving the first algebraic equation in (5). The corresponding radial displacement of the centre of the lower disc (in equilibrium) can be derived from the third and fourth equation in (4) …”

Section: Equilibrium Points and Equilibrium Setsmentioning

confidence: 99%

Interaction between torsional and lateral vibrations in flexible rotor systems with discontinuous friction

et al. 2007

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In this paper, we analyze the interaction between friction-induced vibrations and self-sustained lateral vibrations caused by a mass-unbalance in an experimental rotor dynamic setup. This study is performed on the level of both numerical and experimental bifurcation analyses. Numerical analyses show that two types of torsional vibrations can appear: frictioninduced torsional vibrations and torsional vibrations due to the coupling between torsional and lateral dynamics in the system. Moreover, both the numerical and experimental results show that a higher level of mass-unbalance, which generally increases the lateral vibrations, can have a stabilizing effect on the torsional dynamics, i.e. friction-induced limit cycling can disappear. Both types of analysis provide insight in the fundamental mechanisms causing self-sustained oscillations in rotor systems with flexibility, mass-unbalance and discontinuous friction which support the design of such flexible rotor systems.

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“…In switched systems the dynamical systems describing the evolution changes whenever some threshold (the switching surface) is crossed. Switched systems are common in control and digital applications, but examples are also found in more standard electronic circuits [1], biological modelling [3] and mechanical problems [7]. There is a growing body of results describing the bifurcations of deterministic models [4].…”

Section: Introductionmentioning

confidence: 99%

The Border Collision Normal Form with Stochastic Switching Surface

Glendinning

2014

SIAM J. Appl. Dyn. Syst.

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The deterministic border collision normal form describes the bifurcations of a discrete time dynamical system as a fixed point moves across the switching surface with changing parameter. If the position of the switching surface varies randomly, but within some bounded region, we give conditions which imply that the attractor close to the bifurcation point is the attractor of an Iterated Function System. The proof uses an equivalent metric to the Euclidean metric because the functions involved are never contractions in the Euclidean metric. If the conditions do not hold then a range of possibilities may be realized, including local instability, and some examples are investigated numerically.

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On the origin and bifurcations of stick-slip oscillations

Cited by 208 publications

References 39 publications

Attractors near grazing–sliding bifurcations

Attractors near grazing–sliding bifurcations

Interaction between torsional and lateral vibrations in flexible rotor systems with discontinuous friction

The Border Collision Normal Form with Stochastic Switching Surface

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