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Experimental and analytical investigations of vibrational behavior of U-shaped atomic force microscope probe considering thermal loading and the modified couple stress theory

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Abstract.

In this study, experimental and analytical models of a U-shaped atomic force microscopic (AFM) probe are studied based on the modified couple stress theory (MCST). The experimental setup is a commercially fabricated U-shaped probe AN2-300 mounted in the atomic force microscope afm+ system. In the analytical model, the U-shaped probe of the AFM is simulated as a three-beam model (TBM). The governing equations of motion and boundary conditions are obtained by combination of basic equations of the modified couple stress theory and Hamilton’s principle. It is found that the natural frequencies of the AFM predicted by the MCST are size-dependent. The difference between the natural frequencies predicted by the MCST and the classical beam model is very significant when the ratio of characteristic size to internal material length scale parameter is approximately equal to one, but it is diminishing with increase in the ratio. In order to validate the results, the mathematical and experimental models have been compared with each other. It is seen that the analytical model based on MCST has excellent agreement with experimental results. Also, the natural frequencies of the probe have been obtained for different temperature values, aspect ratios, and small scale factor amounts. The results show, natural frequency decrease with increase in temperature value.

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References

  1. G. Binnig, C.F. Quate, C. Gerber, Phys. Rev. Lett. 56, 930 (1986)

    Article  ADS  Google Scholar 

  2. T. Junno, S.B. Carlsson, H. Xu, L. Montelius, L. Samuelson, Appl. Phys. Lett. 72, 548 (1998)

    Article  ADS  Google Scholar 

  3. E. Margeat, C. Le Grimellec, C.A. Royer, Biophys. J. 75, 2712 (1998)

    Article  Google Scholar 

  4. B.J. Rodriguez, C. Callahan, S.V. Kalinin, R. Proksch, Nanotechnology 18, 475504 (2007)

    Article  ADS  Google Scholar 

  5. W.P. King, T.W. Kenny, K.E. Goodson, G. Cross, M. Despont, U. Dürig, P. Vettiger, Appl. Phys. Lett. 78, 1300 (2001)

    Article  ADS  Google Scholar 

  6. W.P. King, S. Saxena, B.A. Nelson, B.L. Weeks, R. Pitchimani, Nano Lett. 6, 2145 (2006)

    Article  ADS  Google Scholar 

  7. W.P. King, J. Micromech. Microeng. 15, 2441 (2005)

    Article  ADS  Google Scholar 

  8. K. Park, J. Lee, Z.M. Zhang, W.P. King, Rev. Sci. Instrum. 78, 043709 (2007)

    Article  ADS  Google Scholar 

  9. W.P. King, E.O. Sunden, T.L. Wright, J. Lee, S. Graham, Appl. Phys. Lett. 88, 033107 (2006)

    Article  ADS  Google Scholar 

  10. O. Kolosov, A. Gruverman, J. Hatano, K. Takahashi, H. Tokumoto, Phys. Rev. Lett. 74, 4309 (1995)

    Article  ADS  Google Scholar 

  11. U. Rabe, K. Janser, W. Arnold, Rev. Sci. Instrum. 67, 3281 (1996)

    Article  ADS  Google Scholar 

  12. J.A. Turner, S. Hirsekorn, U. Rabe, W. Arnold, J. Appl. Phys. 82, 966 (1997)

    Article  ADS  Google Scholar 

  13. J.A. Turner, J.S. Wiehn, Nanotechnology 12, 322 (2001)

    Article  ADS  Google Scholar 

  14. W.J. Chang, S.S. Chu, Phys. Lett. A 309, 133 (2003)

    Article  ADS  Google Scholar 

  15. J.C. Hsu, H.L. Lee, W.J. Chang, Nanotechnology 18, 285503 (2007)

    Article  Google Scholar 

  16. M.H. Korayem, M. Damircheli, Precis. Eng. 38, 321 (2014)

    Article  Google Scholar 

  17. H.L. Lee, W.J. Chang, Ultramicroscopy 108, 707 (2008)

    Article  Google Scholar 

  18. M.H. Kahrobaiyan, M. Asghari, M. Rahaeifard, M.T. Ahmadian, Int. J. Eng. Sci. 48, 1985 (2010)

    Article  Google Scholar 

  19. A.F. Payam, M. Fathipour, Arab. J. Sci. Eng. 39, 1393 (2014)

    Article  MathSciNet  Google Scholar 

  20. J.P. Killgore, R.C. Tung, D.C. Hurley, Nanotechnology 25, 345701 (2014)

    Article  ADS  Google Scholar 

  21. E. Rezaei, J.A. Turner, J. Appl. Phys. 115, 174302 (2014)

    Article  ADS  Google Scholar 

  22. L.N. Liang, L.L. Ke, Y.S. Wang, J. Yang, S. Kitipornchai, Int. J. Struct. Stab. Dyn. 15, 1540025 (2015)

    Article  MathSciNet  Google Scholar 

  23. M. Abbasi, N. Abbasi, Int. J. Nano Dimension 7, 49 (2016)

    Google Scholar 

  24. E. Rezaei, J.A. Turner, J. Appl. Phys. 119, 034303 (2016)

    Article  ADS  Google Scholar 

  25. R.D. Mindlin, Arch. Ration. Mech. Anal. 16, 51 (1964)

    Article  MathSciNet  Google Scholar 

  26. R.M. Tiersten, Arch. Ration. Mech. Anal. 11, 415 (1962)

    Article  MathSciNet  Google Scholar 

  27. R.A. Toupin, Arch. Ration. Mech. Anal. 11, 385 (1962)

    Article  MathSciNet  Google Scholar 

  28. S.J. Zhou, Z.Q. Li, J. Shandong Univ. Technol. 31, 401 (2001)

    Google Scholar 

  29. N.A. Fleck, J.W. Hutchinson, Adv. Appl. Mech. 33, 296 (1997)

    Google Scholar 

  30. F.A.C.M. Yang, A.C.M. Chong, D.C.C. Lam, P. Tong, Int. J. Solids Struct. 39, 2731 (2002)

    Article  Google Scholar 

  31. S.K. Park, X.L. Gao, J. Micromech. Microeng. 16, 2355 (2006)

    Article  ADS  Google Scholar 

  32. L. Meirovitch, R.G. Parker, Appl. Mech. Rev. 54, 100 (2001)

    Article  Google Scholar 

  33. F.A.C.M. Yang, A.C.M. Chong, D.C.C. Lam, P. Tong, Int. J. Solids Struct. 39, 2731 (2002)

    Article  Google Scholar 

  34. C.M. Leech, Int. J. Mech. Eng. Educ. 5, 81 (1977)

    Google Scholar 

  35. J.N. Reddy, Energy Principles and Variational Methods in Applied Mechanics (John Wiley & Sons, 2002)

  36. X.L. Gao, S. Mall, Int. J. Solids Struct. 38, 855 (2001)

    Article  Google Scholar 

  37. X.L. Gao, S.K. Park, Int. J. Solids Struct. 44, 7486 (2007)

    Article  Google Scholar 

Download references

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Authors and Affiliations

  1. Faculty of Engineering, Department of Mechanics, Imam Khomeini International University, Postal code: 3414916818, Qazvin, Iran

    Mohsen Namvar & Majid Ghadiri

  2. Mechanical and Materials Engineering, W342 Nebraska Hall, University of Nebraska-Lincoln, 68588, Lincoln, Nebraska, USA

    Ehsan Rezaei

  3. Faculty of Engineering, Department of Mechanics, Zanjan University, Zanjan, Iran

    Seyed Amirhosein Hosseini

Authors
  1. Mohsen Namvar
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  2. Ehsan Rezaei
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  3. Seyed Amirhosein Hosseini
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  4. Majid Ghadiri
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Correspondence to Majid Ghadiri.

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Namvar, M., Rezaei, E., Hosseini, S.A. et al. Experimental and analytical investigations of vibrational behavior of U-shaped atomic force microscope probe considering thermal loading and the modified couple stress theory. Eur. Phys. J. Plus 132, 247 (2017). https://doi.org/10.1140/epjp/i2017-11518-5

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  • DOI: https://doi.org/10.1140/epjp/i2017-11518-5

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