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Fundamental frequencies of a nano beam used for atomic force microscopy (AFM) in tapping mode

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Abstract

In this study we investigate the motion of a torsionally restrained beam used in tapping mode atomic force microscopy (TM-AFM), with the aim of manufacturing at nano-scale. TM-AFM oscillates at high frequency in order to remove material or shape nano structures. Euler-Bernoulli theory and Eringen’s theory of non-local continuum are used to model the nano machining structure composed of two single degree of freedom systems. Eringen’s theory is effective at nano-scale and takes into account small-scale effects. This theory has been shown to yield reliable results when compared to modelling using molecular dynamics.

The system is modelled as a beam with a torsional boundary condition at one end; and at the free end is a transverse linear spring attached to the tip. The other end of the spring is attached to a mass, resulting in a single degree of freedom spring-mass system. The motion of the tip of the beam and tip mass can be investigated to observe the tip frequency response, displacement and contact force. The beam and spring–mass frequencies contain information about the maximum displacement amplitude and therefore the sample penetration depth and this allows

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References

  1. Eringen, A. C., and Edelen, D. (1972) On nonlocal elasticity. Int. J. Eng. Sci. 10 (3): 233–248.

    Article  Google Scholar 

  2. Eringen, A. C., (2002) Nonlocal Continuum Field Theories, Springer-Verlag, New York.

    Google Scholar 

  3. Rahmanian, M., Torkaman-Asadi, M. A., Firouz-Abadi, R. D., and Kouchakzadeh, M. A. (2016) Free vibrations analysis of carbon nanotubes resting on Winkler foundations based on nonlocal models. Physica B 484: 83– 94.

    Article  CAS  Google Scholar 

  4. Rosa, M. A. D., and Lippiello, M. (2016) Nonlocal frequency analysis of embedded single-walled carbon nanotube using the Differential Quadrature Method. Compos. Part B: Eng. 84: 41–51.

    Article  Google Scholar 

  5. Wu, D. H. Chien, W. T., Chen, C. S., and Chen, H. H. (2006) Resonant frequency analysis of fixed-free single-walled carbon nanotube-based mass sensor. Sens. Actuators A 126: 117–121.

    Article  CAS  Google Scholar 

  6. Chiu, H. Y., Hung, P., Postma, H. W. C., and Bockrath, M. (2008) Atomic-scale mass sensing using carbon nanotube resonators. Nano Lett. 8: 4342–4346.

    Article  CAS  Google Scholar 

  7. Kiani, K. (2015) Nanomechanical sensors based on elastically supported double-walled carbon nanotubes. Appl. Math. Comput. 270: 216–241.

    Article  Google Scholar 

  8. Kiani, K., Ghaffari, H., and Mehri, B. (2013) Application of elastically supported single-walled carbon nanotubes for sensing arbitrarily attached nano-objects. Curr. Appl. Phys. 13: 107–120.

    Article  Google Scholar 

  9. Reddy, J. N., and Pang, S. N. (2008) Nonlocal continuum theories of beams for the analysis of carbon nanotubes. J. App. Phys. 103: 023511.

    Article  Google Scholar 

  10. Maurizi, M. J., Rossi, R. E., and Reyes, J. A. (1976) Vibration frequencies for a uniform beam with one end spring hinged and subjected to a translational restraint at the other end. J. Sound Vib. 48(4): 565–568.

    Article  Google Scholar 

  11. Laura, P. A. A., Grossi, R. O., and Alvarez, S. (1982) Transverse vibrations of a beam elastically restrained at one end and with a mass and spring at the other subjected to an axial force. Nuclear Eng. Design 74: 299–302.

    Article  Google Scholar 

  12. Zhou, D. (1997) The vibrations of a cantilever beam carrying a heavy tip mass with elastic supports. J. Sound Vib. 206: 275–279.

    Article  Google Scholar 

  13. Magrab, B. E. (2012) Magrab Vibrations of Elastic Systems: With Applications to MEMS and NEMS, New York, Springer.

    Book  Google Scholar 

  14. Gürgöze M. (1996) On the eigenfrequencies of a cantilever beam with attached tip mass and spring-mass system. J. Sound Vib. 190(2): 149–162.

    Article  Google Scholar 

  15. Azrar, A., Azrar, L., and Aljinaidi, A. A. (2011) Length scale effect analysis on vibration behaviour of single walled carbon nano tubes with arbitrary boundary conditions. Revue de Mecanique Appliquee et Theorique 2.5: 475–485.

    Google Scholar 

  16. Li, X.-F., Tang, G.-J., Shen, Z.-B., and Lee, K. Y. (2015) Resonance frequency and mass identification of zeptogram-scale nanosensor based on nonlocal theory beam theory. Ultrasonics 55: 75–84.

    Article  Google Scholar 

  17. Moutlana, M. K., and Adali, S. (2015) Vibration of a cantilever beam with extended tip mass and axial load subject to piezoelectric control. R & D J. South African Institution of Mech. Eng. 31: 60–65.

    Google Scholar 

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Authors and Affiliations

  1. Department of Mechanical Engineering, Durban University of Technology, Durban, South Africa

    Malesela K. Moutlana

  2. Discipline of Mechanical Engineering, University of KwaZulu-Natal, Durban, South Africa

    Sarp Adali

Authors
  1. Malesela K. Moutlana
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  2. Sarp Adali
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Correspondence to Malesela K. Moutlana.

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Moutlana, M.K., Adali, S. Fundamental frequencies of a nano beam used for atomic force microscopy (AFM) in tapping mode. MRS Advances 3, 2617–2626 (2018). https://doi.org/10.1557/adv.2018.321

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  • DOI: https://doi.org/10.1557/adv.2018.321

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