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Numerical Analysis of the Tapping Atomic Force Microscopy on a Viscoelastic Sample

[+] Author Affiliations
Ben Carmichael, Gary Frey, S. Nima Mahmoodi

The University of Alabama, Tuscaloosa, AL

Paper No. DSCC2014-5896, pp. V002T29A003; 8 pages
  • ASME 2014 Dynamic Systems and Control Conference
  • Volume 2: Dynamic Modeling and Diagnostics in Biomedical Systems; Dynamics and Control of Wind Energy Systems; Vehicle Energy Management Optimization; Energy Storage, Optimization; Transportation and Grid Applications; Estimation and Identification Methods, Tracking, Detection, Alternative Propulsion Systems; Ground and Space Vehicle Dynamics; Intelligent Transportation Systems and Control; Energy Harvesting; Modeling and Control for Thermo-Fluid Applications, IC Engines, Manufacturing
  • San Antonio, Texas, USA, October 22–24, 2014
  • Conference Sponsors: Dynamic Systems and Control Division
  • ISBN: 978-0-7918-4619-3
  • Copyright © 2014 by ASME


Mechanical characterization of thin samples is now routine due to the prominence of the Atomic Force Microscope. Advances in amplitude modulation techniques have allowed for accurate measurement of a sample’s elastic properties by interpreting the changes in the vibration of a cantilevered beam in intermittent contact. However, the nonlinearities associated with contact complicate attempts to find an accurate time-history for the beam. Furthermore, the inclusion of viscous effects, common to soft samples, puts an explicit solution even farther from reach.

A numerical method is proposed that analyzes the time-history and frequency response of a microcantilever beam with a viscoelastic end-condition. The mathematics can be simplified by incorporating the viscoelastic end-condition into the equation of motion directly by modeling it as a distributed load. A forcing function can then be derived from the Standard Linear Solid model of viscoelasticity and implemented in the non-conservative work term of Hamilton’s principle. The Galerkin method can separate the resulting nonlinear equation of motion into time and space components. Performing a numerical analysis of the time factor equation provide the beam’s response over time. The results demonstrate the distinctive effects of viscoelasticity and periodic contact on the beam’s motion and provide the framework for the determination of viscous properties using dynamic techniques.

Copyright © 2014 by ASME



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