On the origin and bifurcations of stick-slip oscillations
type: Item
instance of: scholarly article
title: On the origin and bifurcations of stick-slip oscillations
zbMATH Open document ID: 0963.70016
DOI: 10.1016/S0167-2789(99)00161-X
author: A. B. Nordmark
author: Harry Dankowicz
published in: Physica D
publication date: 2001-06-28T00:00:00Z
review text: A recently proposed model of macroscopic friction is investigated using methods of dynamical systems analysis. Particular emphasis is put on the bifurcations associated with the appearance of stick-slip oscillations. We show that the existence of these oscillations is a result of a periodic orbit straddling a discontinuity in the first derivative of the vector field. A local analysis tool is developed to discuss the stability of such an orbit and its bifurcations due to changes in system parameters. The analysis tool is found to be highly efficient in quantitatively predicting the location and type of bifurcations. It is argued that the method and the general results are applicable to a large class of friction models containing similar discontinuities and thus, hopefully, to actual frictional dynamics.
Mathematics Subject Classification ID: 70K50
Mathematics Subject Classification ID: 70F40
Mathematics Subject Classification ID: 37N05
zbMATH DE Number: 1394448
zbMATH Keywords: grazing bifurcations
zbMATH Keywords: discontinuity mappings
zbMATH Keywords: macroscopic friction model
zbMATH Keywords: stick-slip oscillations
zbMATH Keywords: periodic orbit
zbMATH Keywords: local analysis
zbMATH Keywords: stability
reviewed by: Jair Koiller
MaRDI profile type: Publication
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full work available at URL: s0167-2789(99)00161-x
OpenAlex ID: W2005988040
Wikidata QID: Q127814041
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description: scientific article; zbMATH DE number 1394448