TY - JOUR
T1 - On the origin and bifurcations of stick-slip oscillations
AU - Dankowicz, Harry
AU - Nordmark, Arne B.
N1 - Funding Information:
The authors gratefully acknowledge support from the Swedish Engineering Research Council. HD was further supported by a grant from the Swedish Foundation for Strategic Research.
Copyright:
Copyright 2019 Elsevier B.V., All rights reserved.
PY - 2000/2/15
Y1 - 2000/2/15
N2 - 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. In the model it is found 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 at 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.
AB - 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. In the model it is found 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 at 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.
KW - Discontinuity mappings
KW - Friction modeling
KW - Grazing bifurcations
KW - Stick-slip oscillations
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U2 - 10.1016/S0167-2789(99)00161-X
DO - 10.1016/S0167-2789(99)00161-X
M3 - Article
AN - SCOPUS:0346688041
VL - 136
SP - 280
EP - 302
JO - Physica D: Nonlinear Phenomena
JF - Physica D: Nonlinear Phenomena
SN - 0167-2789
IS - 3-4
ER -