Volume 19, Issue 4 (April 2019)
Modares Mechanical Engineering 2019, 19(4): 1029-1038 |
Back to browse issues page
Download citation:
BibTeX | RIS | EndNote | Medlars | ProCite | Reference Manager | RefWorks
Send citation to:
BibTeX | RIS | EndNote | Medlars | ProCite | Reference Manager | RefWorks
Send citation to:
Molavian Jazi M, Ghayour M, Ziaei-Rad S, Maani E. Effect of Fluid and Size on the Nonlinear Dynamic of Atomic Force Microscope Based on Modified Couple Stress Theory. Modares Mechanical Engineering 2019; 19 (4) :1029-1038
URL: http://mme.modares.ac.ir/article-15-24394-en.html
URL: http://mme.modares.ac.ir/article-15-24394-en.html
1- Department of Mechanical Engineering, Isfahan University of Technology, Isfahan, Iran
2- Department of Mechanical Engineering, Isfahan University of Technology, Isfahan, Iran , ghayour@cc.iut.ac.ir
3- School of Mechanical Engineering, College of Engineering, University of Tehran, Tehran, Iran.
2- Department of Mechanical Engineering, Isfahan University of Technology, Isfahan, Iran , ghayour@cc.iut.ac.ir
3- School of Mechanical Engineering, College of Engineering, University of Tehran, Tehran, Iran.
Abstract: (2921 Views)
The atomic force microscope (AFM) determines the topography of surfaces in nano scale based on the changes in the exited micro-cantilever’s dynamic characteristics. Therefore, it is essential to simulate and predict more accurately the dynamic behavior of cantilever beams for use in design and fabrication of AFM. Based on the experimental observations, in contrast to the classic theory, the normalized stiffness of structures is not constant with the reduction of dimensions in micro and nano scales. This change, which can be either softness or stiffness, results in size-dependent behavior, non-classic continuum theories. This paper studies the effect of size on the dynamic behavior of AFM based on modified couple stress theory, and compares the results with those obtained from classic theory. The nonlinear partial differential governing equation of the system is derived, considering intermolecular and hydrodynamic forces, based on the modified couple stress theory. By applying Galerkin projection method, partial differential equations are transformed into ordinary equations and the discrete system is extracted. It is shown that considering size effect leads to enlargement of expected working domain of AFM, and also predicted amplitude and frequency of oscillations decreases and increases, respectively. Moreover, two theories predict different start point of bi-stability region. Solution approach is verified by comparing the results with two degrees-of-freedom model and analogue equations method. Furthermore, effect of hydrodynamic forces of fluid on dynamic behaviour of AFM is investigated.
Keywords: Atomic Force Microscope, Size Effect, Modified Couple Stress Theory, Stability Analyses, Nonlinear Dynamic
Article Type: Original Research |
Subject:
Micro & Nano Systems
Received: 2018/08/23 | Accepted: 2018/11/26 | Published: 2019/04/6
Received: 2018/08/23 | Accepted: 2018/11/26 | Published: 2019/04/6
References
1. Binnig G, Quate CF, Gerber Ch. Atomic force microscope. Physical Review Letters. 1986;56(9):930-934. [Link] [DOI:10.1103/PhysRevLett.56.930]
2. Martin Y, Williams CC, Wickramasinghe HK. Atomic force microscope-force mapping and profiling on a sub 100-Å scale. Journal of Applied Physics. 1987;61(10):4723-4729. [Link] [DOI:10.1063/1.338807]
3. Jalili N, Laxminarayana K. A review of atomic force microscopy imaging systems: Application to molecular metrology and biological sciences. Mechatronics. 2004;14(8):907-945. [Link] [DOI:10.1016/j.mechatronics.2004.04.005]
4. Taheri M. 3D-Dynamic Modeling and simulation of biological nanoparticle motion using AFM nano-robot. Modares Mechanical Engineering. 2016;15(12):311-316. [Persian] [Link]
5. Zarei B, Bathaee SH, Taheri M, Momeni M. Second phase of nanomanipulation of particles by atomic force microscopy using Coulomb, HK, and LuGre Friction Models. Modares Mechanical Engineering. 2019;19(1):181-190. [Persian] [Link]
6. Zhong Q, Inniss D, Kjoller K, Elings VB. Fractured polymer/silica fiber surface studied by tapping mode atomic force microscopy. Surface Science Letters. 1993;290(1-2):L688-L692.
https://doi.org/10.1016/0039-6028(93)90582-5 [Link] [DOI:10.1016/0167-2584(93)90906-Y]
7. McCarty R, Mahmoodi SN. Dynamic mulitmode analysis of non-linear piezoelectric microcantilever probe in bistable region of tapping mode atomic force microscopy. International Journal of Non-Linear Mechanics. 2015;74:25-37. [Link] [DOI:10.1016/j.ijnonlinmec.2015.03.010]
8. Lin SM, Liauh CT, Lee SY, Ho SH, Wang WR. Frequency shifts and analytical solutions of an AFM curved beam. Measurement. 2014;47:296-305. [Link] [DOI:10.1016/j.measurement.2013.08.053]
9. Safikhani Mahmoudi M, Yusefpour A, Bahrami A. Higher-mode excitation in the non-contact atomic force microscopy. Modares Mechanical Engineering. 2018;18(7):149-158. [Persian] [Link]
10. Lee SI, Howell SW, Raman A, Reifenberger R. Nonlinear dynamics of microcantilevers in tapping mode atomic force microscopy: A comparison between theory and experiment. Physical Review B. 2002;66(11):115409. [Link] [DOI:10.1103/PhysRevB.66.115409]
11. Pishkenari HN, Behzad M, Meghdari A. Nonlinear dynamic analysis of atomic force microscopy under deterministic and random excitation. Chaos Solitons and Fractals. 2008;37(3):748-762. [Link] [DOI:10.1016/j.chaos.2006.09.079]
12. Zhang WM, Meng G, Zhou JB, Chen JY. Nonlinear dynamics and chaos of microcantilever-based TM-AFMs with squeeze film damping effects. Sensors. 2009;9(5):3854-3874. [Link] [DOI:10.3390/s90503854]
13. Jamitzky F, Stark M, Bunk W, Heckl WM, Stark RW. Chaos in dynamic atomic force microscopy. Nanotechnology. 2006;17(7):S213-S220. [Link] [DOI:10.1088/0957-4484/17/7/S19]
14. Habibnejad Korayem M, Habibnejad Korayem A, Taheri M, Rafee Nekoo S. Control of AFM nano-robot based on sliding mode control method in different biological environments. Modares Mechanical Engineering. 2017;16(11):369-377. [Persian] [Link]
15. Bircher BA, Krenger R, Braun T. Influence of squeeze-film damping on higher-mode microcantilever vibrations in liquid. EPJ Techniques and Instrumentation. 2014;1:10. [Link] [DOI:10.1140/epjti/s40485-014-0010-6]
16. Salgar M, Srinivas J. Modeling of AFM microcantilevers operating in tapping mode. International Journal of Applied Engineering Research. 2012;7(11):7-10. [Link]
17. Sami S, Damircheli M, Korayem MH. Frequency response of AFM nano robot in liquid by considering the effect of cantilever dimension and environmental parameters. International Journal of Advanced Design and Manufacturing Technology. 2014;7(4):55-66. [Link]
18. Korayem MH, Kavousi A, Ebrahimi N. Dynamic analysis of tapping-mode AFM considering capillary force interactions. Scientia Iranica. 2011;18(1):121-129. [Link] [DOI:10.1016/j.scient.2011.03.014]
19. Tang Ch, Alici G. Evaluation of length-scale effects for mechanical behaviour of micro-and nanocantilevers: I. Experimental determination of length-scale factors. Journal of Physics D Applied Physics. 2011;44(33):335501.
https://doi.org/10.1088/0022-3727/44/33/335502 [Link] [DOI:10.1088/0022-3727/44/33/335501]
20. Rezaei H, Sadeghi MH, Khosroabadi H. An experimental study into the size effect in micromilling process. Modares Mechanical Engineering. 2017;17(10):242-248. [Persian] 29- Karami Mohammadi A, Abbasi M. Investigation of the size effect on the vibrational behavior of an AFM microcantilever with a sidewall probe, using strain gradient elasticity theory. Modares Mechanical Engineering. 2014;13(13):90-99. [Persian] [Link]
21. Fleck NA, Muller GM, Ashby MF, Hutchinson JW. Strain gradient plasticity: Theory and experiment. Acta Metallurgica et Materialia. 1994;42(2):475-487. [Link] [DOI:10.1016/0956-7151(94)90502-9]
22. Stölken JS, Evans AG. A microbend test method for measuring the plasticity length scale. Acta Materialia. 1998;46(14):5109-5115. [Link] [DOI:10.1016/S1359-6454(98)00153-0]
23. Namazu T, Isono Y, Tanaka T. Evaluation of size effect on mechanical properties of single crystal silicon by nanoscale bending test using AFM. Journal of Microelectromechanical Systems. 2000;9(4):450-459. [Link] [DOI:10.1109/84.896765]
24. Yang FA, Chong ACM, Lam DCC, Tong P. Couple stress based strain gradient theory for elasticity. International Journal of Solids and Structures. 2002;39(10):2731-2743. [Link] [DOI:10.1016/S0020-7683(02)00152-X]
25. Lam DCC, Yang F, Chong ACM, Wang J, Tong P. Experiments and theory in strain gradient elasticity. Journal of the Mechanics and Physics of Solids. 2003;51(8):1477-1508. [Link] [DOI:10.1016/S0022-5096(03)00053-X]
26. Eringen AC. Nonlocal polar elastic continua. International Journal of Engineering Science. 1972;10(1):1-16. [Link] [DOI:10.1016/0020-7225(72)90070-5]
27. Lu P, He LH, Lee HP, Lu C. Thin plate theory including surface effects. International Journal of Solids and Structures. 2006;43(16):4631-4647. [Link] [DOI:10.1016/j.ijsolstr.2005.07.036]
28. Kahrobaiyan MH, Asghari M, Rahaeifard M, Ahmadian MT. Investigation of the size-dependent dynamic characteristics of atomic force microscope microcantilevers based on the modified couple stress theory. International Journal of Engineering Science. 2010;48(12):1985-1994. [Link] [DOI:10.1016/j.ijengsci.2010.06.003]
29. Karami Mohammadi A, Abbasi M. Investigation of the size effect on the vibrational behavior of an AFM microcantilever with a sidewall probe, using strain gradient elasticity theory. Modares Mechanical Engineering. 2014;13(13):90-99. [Persian] [Link]
30. Chang WJ, Yang YC, Lee HL. Dynamic behaviour of atomic force microscope-based nanomachining based on a modified couple stress theory. Micro and Nano Letters. 2013;8(11):832-835. [Link] [DOI:10.1049/mnl.2013.0493]
31. Abbasi M. A simulation of atomic force microscope microcantilever in the tapping mode utilizing couple stress theory. Micron. 2018;107:20-27. [Link] [DOI:10.1016/j.micron.2018.01.008]
32. Jazi MM, Ghayour M, Ziaei-Rad S, Maani Miandoab E. Effect of size on the dynamic behaviors of atomic force microscopes. Microsystem Technologies. 2018;24(4):1755-1765. [Link] [DOI:10.1007/s00542-017-3698-9]
33. Ashhab M, Salapaka MV, Dahleh M, Mezić I. Melnikov-based dynamical analysis of microcantilevers in scanning probe microscopy. Nonlinear Dynamics. 1999;20(3):197-220. [Link] [DOI:10.1023/A:1008342408448]
34. Mindlin RD, Tiersten HF. Effects of couple-stresses in linear elasticity. Archive for Rational Mechanics and analysis. 1962;11(1):415-448. [Link] [DOI:10.1007/BF00253946]
35. Fu Y, Zhang J, Jiang Y. Influences of the surface energies on the nonlinear static and dynamic behaviors of nanobeams. Physica E Low Dimensional Systems and Nanostructures. 2010;42(9):2268-2273. [Link] [DOI:10.1016/j.physe.2010.05.001]
Send email to the article author
| Rights and permissions | |
 |
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License. |