TY - JOUR
T1 - On the Analysis of Chatter in Mechanical Systems with Impacts
AU - Dankowicz, Harry
AU - Fotsch, Erika
N1 - Funding Information:
This material is based upon work supported by the National Science Foundation under Grant No. 0855787. The authors gratefully acknowledge Alan Champneys for his hospitality and feedback on the pressure relief valve dynamics. The first author also wishes to acknowledge close to two decades of collaboration with Arne Nordmark.
Publisher Copyright:
© 2017 The Authors.
PY - 2017
Y1 - 2017
N2 - In rigid-body mechanics, models that capture collisional contact as an instantaneous exchange of momentum may exhibit dynamics that include infinite sequences of impacts accumulating in finite time to a state of persistent contact, often referred to as chatter. In this paper, we review theoretical tools for the analysis of transient and steady-state behavior in the vicinity of critical periodic orbits for which chatter terminates at a point corresponding to the imminent release from persistent contact, and illustrate the application of this theory to a simplified model of a mechanical pressure relief valve. A general theory for single-degree-of-freedom impact oscillators, previously described in an unpublished manuscript by Nordmark and Kisitu1, is shown to yield both qualitative and quantitative agreement with model simulation results. The predicted bifurcation structure shows that the border orbit unfolds supercritically into a universal cascade of local attractors with nontrivial scaling relationships.
AB - In rigid-body mechanics, models that capture collisional contact as an instantaneous exchange of momentum may exhibit dynamics that include infinite sequences of impacts accumulating in finite time to a state of persistent contact, often referred to as chatter. In this paper, we review theoretical tools for the analysis of transient and steady-state behavior in the vicinity of critical periodic orbits for which chatter terminates at a point corresponding to the imminent release from persistent contact, and illustrate the application of this theory to a simplified model of a mechanical pressure relief valve. A general theory for single-degree-of-freedom impact oscillators, previously described in an unpublished manuscript by Nordmark and Kisitu1, is shown to yield both qualitative and quantitative agreement with model simulation results. The predicted bifurcation structure shows that the border orbit unfolds supercritically into a universal cascade of local attractors with nontrivial scaling relationships.
KW - Accumulation of impacts
KW - Bifurcation analysis
KW - One-dimensional map
KW - Pressure relief valve
KW - Universal cascade
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U2 - 10.1016/j.piutam.2017.03.004
DO - 10.1016/j.piutam.2017.03.004
M3 - Conference article
AN - SCOPUS:85029759918
SN - 2210-9838
VL - 20
SP - 18
EP - 25
JO - Procedia IUTAM
JF - Procedia IUTAM
T2 - 24th International Congress of Theoretical and Applied Mechanics 2016
Y2 - 22 August 2016 through 24 August 2016
ER -