Non-Smooth Dynamics and Control of Tapping Mode Atomic Force Microscopy

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.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Mechanical Engineering

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2015

Author dc:creator

• Misra, Sambit

Contributors dc:contributor

• Dankowicz, Harry

• Engineering, Mechanical

Language dc:language

eng

Identifier

(MiAaPQ)AAI3363041

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/83929