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Modeling and Simulation of Dynamic Contact Atomic Force Microscope

  • Mohammad Reza BahramiEmail author
  • A. W. Buddimal Abeygunawardana
Conference paper
Part of the Lecture Notes in Mechanical Engineering book series (LNME)

Abstract

The aim of this article is modeling of the atomic force microscope as a lumped parameter system in its dynamic contact mode of operation. The Derjaguin–Muller–Toporov (DMT) force is considered as the interaction of the cantilever tip with the sample surface, and it introduces the nonlinearity to the model. The frequency response equation of the model is obtained by the method of multiple scales. As the results, effects of the nonlinearity, amplitude of excitation, and the damping coefficient on the frequency response are investigated.

Keywords

AFM Modeling Contact mode Vibration Lumped parameter model 

References

  1. 1.
    Binnig G, Quate CF, Geber Ch (1986) Atomic Force Microscope Phys Rev Lett 56(9):930CrossRefGoogle Scholar
  2. 2.
    Bahrami MR, Ramezani A, Osgouie K (2010) Modeling and simulation of non-contact atomic force microscope. In: Proceedings of the ASME 2010 10th conference on engineering system design and analysis, ESDA 2010. Vol. 5. pp 565–569Google Scholar
  3. 3.
    Materassi D, Basso M, Genesio R (2004) Frequency analysis of atomic force microscopes with repulsive-attractive interaction potentials. In: Proceedings of IEEE conference on decision and control. pp 3059–3061Google Scholar
  4. 4.
    Sebastian A, Salapaka MV, Chen DJ, Cleveland JP (2003) Harmonic analysis based modeling of tapping-mode AFM. In: Proceedings of American control conference. pp 232–236Google Scholar
  5. 5.
    Wang L (1998) Analytical descriptions of the tapping-mode atomic force microscopy response. Appl Phys Lett 73(25):3781–3783CrossRefGoogle Scholar
  6. 6.
    Gauthier M, Tsukada M (2000) Damping mechanism in dynamic force microscopy. Phys Rev Lett 85(25):5348–5351CrossRefGoogle Scholar
  7. 7.
    Belikov S, Magonov S (2009) Classification of dynamic atomic force microscopy control modes based on asymptotic nonlinear mechanics. In: Proceedings of American control conference. pp 979–984Google Scholar
  8. 8.
    Bahrami MR, Abeygunavardana VB (2018) Modeling and simulation of atomic force microscope through bond graph. Lecture notes mechanical engineering: advances in mechanical engineering, pp 9–15. Springer ISBN: 978-3-319-72928-2. 2018. PartF5Google Scholar
  9. 9.
    Nayfeh, AH, Mook DT (1995) Nonlinear oscillations, pp. 161–224. A Wiley-Interscience publication, New YorkGoogle Scholar
  10. 10.
    Bender CM, Orszag SA (1999) Advanced mathematical methods for scientists and engineers, pp 544–568. SpringerGoogle Scholar
  11. 11.
    Kevorkian J, Cole JD (1996) Multiple scale and singular perturbation methods, SpringerGoogle Scholar
  12. 12.
    Evgrafov AN, Petrov GN (2017) Computer simulation of mechanisms. Lecture notes in mechanical engineering. pp 45–56Google Scholar
  13. 13.
    Manzhula KP, Naumov AV (2017) Influence of flections’ radius value to local buckling of box-shaped beams with non-linear walls. Int Rev Mech Eng 11(5):326–331Google Scholar
  14. 14.
    Egorova OV, Shcherbinin DY (2015) 3D documents in the field of history of science and technology. In: 2015 IFToMM World Congress Proceedings, IFToMMGoogle Scholar
  15. 15.
    Eliseev KV (2018) Contact forces between wheels and railway determining in dynamic analysis. Numerical simulation. Lecture Notes in Mechanical Engineering pp. 61–70. PartF5Google Scholar
  16. 16.
    Eliseev VV (2006) Mechanics of a deformable solid. p 231. Publishing house Polytechnic UniversityGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Mohammad Reza Bahrami
    • 1
    Email author
  • A. W. Buddimal Abeygunawardana
    • 2
  1. 1.Innopolis UniversityInnopolisRussia
  2. 2.Peter the Great Saint-Petersburg Polytechnic UniversitySaint-PetersburgRussia

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