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oai:www.ideals.illinois.edu:2142/83929 2023-07-11 col_2142_5131 col_2142_14787 com_2142_5130 com_2142_9630 com_2142_234

Dankowicz, Harry Misra, Sambit 2015-09-25T21:12:45Z 2015-09-25T21:12:45Z 10000-01-01 2009 2009 The case of co-dimension two grazing characterized by simultaneous tangential contact of a solution trajectory as well as a solution branch with the discontinuity surface is also presented. Analytical conditions are formulated to locate the co-dimension two grazing point and discontinuity-mapping technique is used to obtain a normal form description of the near-grazing dynamics. In addition to the non-smooth vector field, the relative strength of the vector fields on either side of the discontinuity surface is shown to be critical in determining the occurrence of discontinuity-induced isola and branch-point bifurcations. This result motivates a feedback strategy which modifies the near-grazing dynamics to ensure the persistence of the grazing solution trajectory beyond grazing. The feedback scheme applied to a linear impacting oscillator, and a dynamic model of tapping-mode atomic force microscope ensures persistence of the grazing solution trajectory by preventing loss of stability through a discontinuity induced saddle-node bifurcation. Made available in DSpace on 2015-09-25T21:12:45Z (GMT). No. of bitstreams: 2 license.txt: 4848 bytes, checksum: 96035ab3f5e1c23cc7138a224ce498bd (MD5) 3363041.pdf: 2080727 bytes, checksum: d4558f2af9a74cb1c45a2f98d5bac8c6 (MD5) Previous issue date: 2009 Embargo set by: Seth Robbins for item 85210 Lift date: Forever Reason: Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs U of I Only 142 p. Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 2009. http://hdl.handle.net/2142/83929 (MiAaPQ)AAI3363041 eng Engineering, Mechanical Non-Smooth Dynamics and Control of Tapping Mode Atomic Force Microscopy text Mechanical Engineering Mechanical Engineering University of Illinois at Urbana-Champaign Dissertation Ph.D.