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Title:Non-Smooth Dynamics and Control of Tapping Mode Atomic Force Microscopy
Author(s):Misra, Sambit
Doctoral Committee Chair(s):Dankowicz, Harry
Department / Program:Mechanical Engineering
Discipline:Mechanical Engineering
Degree Granting Institution:University of Illinois at Urbana-Champaign
Subject(s):Engineering, Mechanical
Abstract: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.
Issue Date:2009
Description:142 p.
Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 2009.
Other Identifier(s):(MiAaPQ)AAI3363041
Date Available in IDEALS:2015-09-25
Date Deposited:2009

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