Modeling the tip-sample interaction in atomic force microscopy with Timoshenko beam theory

Julio R. Claeyssen; Teresa Tsukazan; Leticia Tonetto; Daniela Tolfo

Nanoscale Systems: Mathematical Modeling, Theory and Applications (2013)

  • Volume: 2, page 124-144
  • ISSN: 2299-3290

Abstract

top
A matrix framework is developed for single and multispan micro-cantilevers Timoshenko beam models of use in atomic force microscopy (AFM). They are considered subject to general forcing loads and boundary conditions for modeling tipsample interaction. Surface effects are considered in the frequency analysis of supported and cantilever microbeams. Extensive use is made of a distributed matrix fundamental response that allows to determine forced responses through convolution and to absorb non-homogeneous boundary conditions. Transients are identified from intial values of permanent responses. Eigenanalysis for determining frequencies and matrix mode shapes is done with the use of a fundamental matrix response that characterizes solutions of a damped second-order matrix differential equation. It is observed that surface effects are influential for the natural frequency at the nanoscale. Simulations are performed for a bi-segmented free-free beam and with a micro-cantilever beam actuated by a piezoelectric layer laminated in one side.

How to cite

top

Julio R. Claeyssen, et al. "Modeling the tip-sample interaction in atomic force microscopy with Timoshenko beam theory." Nanoscale Systems: Mathematical Modeling, Theory and Applications 2 (2013): 124-144. <http://eudml.org/doc/266710>.

@article{JulioR2013,
abstract = {A matrix framework is developed for single and multispan micro-cantilevers Timoshenko beam models of use in atomic force microscopy (AFM). They are considered subject to general forcing loads and boundary conditions for modeling tipsample interaction. Surface effects are considered in the frequency analysis of supported and cantilever microbeams. Extensive use is made of a distributed matrix fundamental response that allows to determine forced responses through convolution and to absorb non-homogeneous boundary conditions. Transients are identified from intial values of permanent responses. Eigenanalysis for determining frequencies and matrix mode shapes is done with the use of a fundamental matrix response that characterizes solutions of a damped second-order matrix differential equation. It is observed that surface effects are influential for the natural frequency at the nanoscale. Simulations are performed for a bi-segmented free-free beam and with a micro-cantilever beam actuated by a piezoelectric layer laminated in one side.},
author = {Julio R. Claeyssen, Teresa Tsukazan, Leticia Tonetto, Daniela Tolfo},
journal = {Nanoscale Systems: Mathematical Modeling, Theory and Applications},
keywords = {Atomic force microscopy; nanoscale materials and structures; chemical/biological sensors; nanomachining; microscaled Timoshenko beams; atomic force microscopy},
language = {eng},
pages = {124-144},
title = {Modeling the tip-sample interaction in atomic force microscopy with Timoshenko beam theory},
url = {http://eudml.org/doc/266710},
volume = {2},
year = {2013},
}

TY - JOUR
AU - Julio R. Claeyssen
AU - Teresa Tsukazan
AU - Leticia Tonetto
AU - Daniela Tolfo
TI - Modeling the tip-sample interaction in atomic force microscopy with Timoshenko beam theory
JO - Nanoscale Systems: Mathematical Modeling, Theory and Applications
PY - 2013
VL - 2
SP - 124
EP - 144
AB - A matrix framework is developed for single and multispan micro-cantilevers Timoshenko beam models of use in atomic force microscopy (AFM). They are considered subject to general forcing loads and boundary conditions for modeling tipsample interaction. Surface effects are considered in the frequency analysis of supported and cantilever microbeams. Extensive use is made of a distributed matrix fundamental response that allows to determine forced responses through convolution and to absorb non-homogeneous boundary conditions. Transients are identified from intial values of permanent responses. Eigenanalysis for determining frequencies and matrix mode shapes is done with the use of a fundamental matrix response that characterizes solutions of a damped second-order matrix differential equation. It is observed that surface effects are influential for the natural frequency at the nanoscale. Simulations are performed for a bi-segmented free-free beam and with a micro-cantilever beam actuated by a piezoelectric layer laminated in one side.
LA - eng
KW - Atomic force microscopy; nanoscale materials and structures; chemical/biological sensors; nanomachining; microscaled Timoshenko beams; atomic force microscopy
UR - http://eudml.org/doc/266710
ER -

References

top
  1. G. Binnig, C. F. Quate, C. Gerber, Physics Review Letters 56, 930–933 (1986). 
  2. Y. Song, B. Bhushan, Journal of Physics: Condensed Matter 20, 225012–225041 (2008). [Crossref] 
  3. N. Jalili, Piezoelectric-Based Vibration Control: From Macro to Micro/Nano Scale Systems. Springer-Verlag, (2010). [WoS] 
  4. S. Eslami, N. Jalili, Ultramicroscopy 117, 31–45 (2012). 
  5. A. Salehi-Khojin, S. Bashash, N. Jalili. Journal of Micromechanics and Microengineering 18, 11 pp (2008). 
  6. H. Jih-Lian, F. Rong-Fong, C. Sheng-Hsin. Journal of Sound and Vibration 289, 529–550 (2006). 
  7. V. K. W. Hoiles, B. Cornell, Nanoscale Systems MMTA Volume 1(ISSN 2299-3290 DOI: 10.2478/nsmmt-2012- 0009), 143–171 December (2012). [Crossref] 
  8. J. Hsu, H. L. Lee, W. Chang, Nanotechnology 18, 28503–28508 (2007). 
  9. J. W. Israelachvilli, Intermolecular and Surface Forces. Academic Press, 3rd edition, (2011). 
  10. M. Gurtin, J. Weissmuller, F. Larche, Philosophical Magazine A 75(5), 1093–1109 (1998). 
  11. J. R. Claeyssen„ G. Canahualpa, C. Jung, Applied Numerical Mathematics 30(1), 65–78 (1999). 
  12. J. Claeyssen, S. Costa, Journal of Sound and Vibration 296(4-5), 1053–1058 (2006). 
  13. F. Landolsi, F. Ghorbel, Smart Materials and Structures 19, 065028 (2010). 
  14. T. Fang, W. Chang, Journal of Physics and Chemistry of Solids 64, 913–918 (2003). 
  15. L. Calabri, N. Pugno, C. Menozzi, S. Valeri, Journal of Physics: Condensed Matter 20, 474208 (2008). [Crossref] 
  16. H. Butt, B. Cappella, M. Kappl, Surface Science Reports 59, 1–152 (2005). 
  17. M. Asghari, M. Kahrobaiyan, M. Ahmadian, International Journal of Engineering Science 48, 1749–1761 (2010). 
  18. S. Hasheminejad, B. Gheshlaghi, Applied Physics Letters 97, 253103 (2010). 
  19. B. On, E. Althus, E. Tadmor, International journal of solids and structures 47, 1243–1252 (2010). 
  20. P. Lu, H. P. Lee, C. Lu, Journal of Applied Physics 99(073510), 1–9 (2006). 
  21. H. Thai, International Journal of Engineering Science 52, 56–64–60 (2012). 
  22. S. Kong, S. Zhou, Z. Nie, K. Wang, International Journal of Engineering Science 47, 487–498 (2009). Zbl1213.74190
  23. L.L. Ke, Y.S. Wang, J. S.Kitipornchai. International Journal of Engineering Science 50, 256–267 (2012). 
  24. J. Schoeftner, H. Irschik, Smart Materials and Structures 20, 025007 (2010). 
  25. G. Wang, Journal of Intelligent Material Systems and Structures 24(6), 226–239 (2012). 
  26. G. Wang, X. Feng, Applied Physics Letters 90, 231904 (2007). 
  27. S. Abbasion, A. Rafsanjani, R. Avazmohammadi, A. Farshidianfar, Applied Physics Letters 95(14), 143122 (2009). 
  28. J. Ginsberg, Mechanical and Structural Vibrations. John Wiley, (2001). 
  29. T.C. Huang, Journal of Applied Mechanics 28, 579–584 (1961). Zbl0102.19005
  30. U. Rabe, E. Kester, W. Arnold, Surface and Interface Analysis 27, 386–391 (1999). 
  31. R. B. Guenther, J. W. Lee, Partial Differential Equations of Mathematical Physics and Integral Equations. Dover, (1988). 
  32. A. G. Butkovsky, Structural Theory of Distributed Systems. John Wiley, (1983). 
  33. H. K. Hong, J. T. Chen, Journal of Engineering Mechanics 114(6), 1028–1044 (1988). 
  34. F. J. Rubio-Sierra, R. VÃazquez, R. W. Stark, IEEE Transactions on Nanotechnology 5(6), 692–700 (2006). 
  35. A. Bhaskar, Proceedings the Royal of Society A- Mathematical, Physical & Engineering Sciences 465, 239–255 (2009). Zbl1186.74063
  36. N. G. Stephen, Journal of Sound and Vibration 292, 372–389 (2006). Zbl1243.74095
  37. M. Levinson, D. W. Cooke, Journal of Sound and Vibration 84(3), 319–326 (1982). Zbl0492.73058
  38. S.C. Stanton, B.P. Mann. Mechanical Systems and Signal Processing 24, 1409–1419 (2010). 
  39. T. Tsukazan, Journal of Sound and Vibration 281, 1175–1185 (2005). Zbl1236.74165
  40. M. Shirazi, H. Salarieh, A., Alasty, R. Shabani, Journal of Vibration and Control 117, 1–14 june (2012). 

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.