Grazing bifurcations in impact oscillators characterize the transition in asymptotic dynamics between impacting and nonimpacting motions. Several different grazing bifurcation scenarios under variations of a single system parameter have been previously documented in the literature. In the present paper, the transition between two characteristically different co-dimension-one grazing bifurcation scenarios is found to be associated with the presence of certain co-dimension-two grazing bifurcation points and their unfolding in parameter space. The analysis investigates the distribution of such degenerate bifurcation points along the grazing bifurcation manifold in examples of single-degree-of-freedom oscillators. Unfoldings obtained with the discontinuity-mapping technique are used to explore the possible influence on the global dynamics of the smooth co-dimension-one bifurcations of the impacting dynamics that emanate from such co-dimension-two points. It is shown that attracting impacting motion may result from parameter variations through a co-dimension-two grazing bifurcation of an initially unstable limit cycle in a nonlinear micro-electro-mechanical systems (MEMS) oscillator.
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October 2006
Research Papers
Co-dimension-Two Grazing Bifurcations in Single-Degree-of-Freedom Impact Oscillators Available to Purchase
Phanikrishna Thota,
Phanikrishna Thota
Department of Engineering Science and Mechanics, MC 0219,
e-mail: [email protected]
Virginia Polytechnic Institute and State University
, Blacksburg, VA 24061
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Harry Dankowicz
Harry Dankowicz
Department of Mechanical and Industrial Engineering,
e-mail: [email protected]
University of Illinois at Urbana-Champaign
, Urbana, IL 61801
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Phanikrishna Thota
Department of Engineering Science and Mechanics, MC 0219,
Virginia Polytechnic Institute and State University
, Blacksburg, VA 24061e-mail: [email protected]
Xiaopeng Zhao
Harry Dankowicz
Department of Mechanical and Industrial Engineering,
University of Illinois at Urbana-Champaign
, Urbana, IL 61801e-mail: [email protected]
J. Comput. Nonlinear Dynam. Oct 2006, 1(4): 328-335 (8 pages)
Published Online: April 18, 2006
Article history
Received:
January 8, 2006
Revised:
April 18, 2006
Citation
Thota, P., Zhao, X., and Dankowicz, H. (April 18, 2006). "Co-dimension-Two Grazing Bifurcations in Single-Degree-of-Freedom Impact Oscillators." ASME. J. Comput. Nonlinear Dynam. October 2006; 1(4): 328–335. https://doi.org/10.1115/1.2338658
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