This paper presents the application of the discontinuity-mapping technique to the analysis of discontinuity-induced bifurcations of periodic trajectories in an example piecewise smooth system in which changes in the vector field associated with the crossing of a discontinuity-surface depend on the direction of crossing. The analysis is motivatived by a hysteretic model of the capillary force interactions between an atomic-force-microscope cantilever probe tip and a nanoscale sample surface in the presence of a thin liquid film on the tip and the surface and operating in intermittent-contact mode. The analysis predicts the sudden termination of branches of periodic system responses at parameter values corresponding to grazing contact with the onset of the hysteretic force interactions. It further establishes the increase beyond all bounds of the magnitude of one of the eigenvalues of the linearization of a suitably defined Poincare´ mapping indicating the destabilizing influence of near-grazing contact.
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ASME 2008 9th Biennial Conference on Engineering Systems Design and Analysis
July 7–9, 2008
Haifa, Israel
Conference Sponsors:
- International
ISBN:
978-0-7918-4836-4
PROCEEDINGS PAPER
Discontinuity-Induced Bifurcations in Systems With Hysteretic Force Interactions Available to Purchase
Harry Dankowicz,
Harry Dankowicz
University of Illinois at Urbana-Champaign, Urbana, IL
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Mark R. Paul
Mark R. Paul
Virginia Polytechnic Institute and State University, Blacksburg, VA
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Harry Dankowicz
University of Illinois at Urbana-Champaign, Urbana, IL
Mark R. Paul
Virginia Polytechnic Institute and State University, Blacksburg, VA
Paper No:
ESDA2008-59293, pp. 633-641; 9 pages
Published Online:
July 6, 2009
Citation
Dankowicz, H, & Paul, MR. "Discontinuity-Induced Bifurcations in Systems With Hysteretic Force Interactions." Proceedings of the ASME 2008 9th Biennial Conference on Engineering Systems Design and Analysis. Volume 2: Automotive Systems; Bioengineering and Biomedical Technology; Computational Mechanics; Controls; Dynamical Systems. Haifa, Israel. July 7–9, 2008. pp. 633-641. ASME. https://doi.org/10.1115/ESDA2008-59293
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