Singular loss of stability due to hysteretic capillary forces in atomic force microscopy

Michael Katzenbach, Harry Dankowicz

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

This paper considers discontinuity-induced bifurcations due to the onset and termination of hysteretic, capillary tipsample interaction forces in a single-mechanical-mode model of intermittent-contact atomic-force microscopy. The theoretical analysis generalizes earlier results for a piecewise-linear hybrid dynamical system to establish the singular termination of branches of steady-state oscillations of the AFM cantilever at critical equilibrium separations corresponding to the grazing contact of the cantilever tip with a fluid layer deposited on the sample. It is shown that this termination is preceded by rapid changes in linearized stability characteristics with one characteristic multiplier going to plus or minus infinity in the deterministic model. The paper describes the application of a discontinuity-mapping technique that allows for unfolding the system response in the vicinity of the grazing condition and the critical equilibrium separation. Numerical simulations and results of parameter continuation are shown to closely agree with the predictions of the theoretical analysis.

Original languageEnglish (US)
Title of host publicationASME 2010 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC/CIE2010
Pages489-497
Number of pages9
Volume4
DOIs
StatePublished - 2010
EventASME 2010 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC/CIE2010 - Montreal, QC, Canada
Duration: Aug 15 2010Aug 18 2010

Other

OtherASME 2010 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC/CIE2010
CountryCanada
CityMontreal, QC
Period8/15/108/18/10

ASJC Scopus subject areas

  • Mechanical Engineering
  • Computer Graphics and Computer-Aided Design
  • Computer Science Applications
  • Modeling and Simulation

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