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

Published online by Cambridge University Press:  02 April 2018

MALESELA K. MOUTLANA  and
SARP ADALI
MALESELA K. MOUTLANA*
Affiliation:
Department of Mechanical Engineering, Durban University of Technology, Durban, South Africa
SARP ADALI
Affiliation:
Discipline of Mechanical Engineering, University of KwaZulu-Natal, Durban, South Africa
*
*Corresponding author: [email protected]
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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

Keywords

atom probe microscopynanoscalenanostructure
Type
Articles
Information
MRS Advances , Volume 3 , Issue 42-43: African Materials Research Society 2017 , 2018 , pp. 2617 - 2626
Copyright
Copyright © Materials Research Society 2018 

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References

Eringen, A. C., and Edelen, D. (1972) On nonlocal elasticity. Int. J. Eng. Sci. 10(3): 233–248.CrossRefGoogle Scholar
Eringen, A. C., (2002) Nonlocal Continuum Field Theories, Springer-Verlag, New York.Google Scholar
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.CrossRefGoogle Scholar
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.CrossRefGoogle Scholar
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.CrossRefGoogle Scholar
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.CrossRefGoogle ScholarPubMed
Kiani, K. (2015) Nanomechanical sensors based on elastically supported double-walled carbon nanotubes. Appl. Math. Comput. 270: 216–241.Google Scholar
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.CrossRefGoogle Scholar
Reddy, J. N., and Pang, S. N. (2008) Nonlocal continuum theories of beams for the analysis of carbon nanotubes. J. App. Phys. 103: 023511.CrossRefGoogle Scholar
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.CrossRefGoogle Scholar
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.CrossRefGoogle Scholar
Zhou, D. (1997) The vibrations of a cantilever beam carrying a heavy tip mass with elastic supports. J. Sound Vib. 206: 275–279.CrossRefGoogle Scholar
Magrab, B. E. (2012) Magrab Vibrations of Elastic Systems: With Applications to MEMS and NEMS, New York, Springer.CrossRefGoogle Scholar
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.CrossRefGoogle Scholar
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
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.CrossRefGoogle ScholarPubMed
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