On the origin and bifurcations of stick-slip oscillations

By H. Dankowicz, A. Nordmark. 2000

246 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/5d4e037edeb37e44c1fef266dcbc8902ad2dbd80

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Citations in the corpus

Local analysis of co-dimension-one and co-dimension-two grazing bifurcations in impact microactuators (2005, methodology): “We note that bifurcation scenarios similar to those observed here in the case of ΓI and ΓII have previously been documented in piecewise smooth dynamical systems, for example, in linear impact oscillators (Foale & Bishop [9]) and in friction oscillators (Dankowicz & Nordmark [6]).”
Bifurcations in Nonlinear Discontinuous Systems (2000, background): “Published bifurcation diagrams were often constructed from data obtained by brute force techniques and only show stable branches of periodic solutions [5, 6, 11, 20, 25, 29, 39, 43, 48, 52] (this list is far from complete).”
Bifurcations in piecewise-smooth feedback systems (2002, background): “A particularly useful concept in the derivation of normal form maps for grazing and sliding bifurcations is that of discontinuity mapping (Dankowicz and Nordmark 1999).”
Bifurcations in Nonsmooth Dynamical Systems (2008, methodology): “Before stating the results in the form of theorems (which are derived explicitly in [27, 37, 86]), we need to consider the geometry near the grazing point.”
Unveiling complexity of drill–string vibrations: Experiments and modelling (2015, unknown): “Different vibration modes, such as torsional, lateral and axial vibrations influence the dynamics of a drill–string, and their occurrence, especially stick–slip (torsional) vibrations [7–9], lead to a reduction of Rate Of Penetration (ROP).”
The nature of the normal form map for soft impacting systems (2008, background): “Dankowicz and Nordmark [20] considered a dry friction oscillator and showed that the map in this case will have a power of 3/2 term in one side which gives it some special features.”
Numerical sliding bifurcation analysis: an application to a relay control system (2003, background): “such as mechanical systems of the stick-slip type [7], [12], [15], [18] and linear systems with relay feedback controllers [3], [14].”
Bifurcations of piecewise smooth flows: Perspectives, methodologies and open problems (2012, background): “The key observation here, that study of discontinuity-induced bifurcations of a limit cycle can be reduced to local geometry, is attributable to Nordmark’s pioneering work on grazing bifurcations in impact and friction oscillators (see [76,28]).”