Volume 19, Issue 6 (June 2019)
Modares Mechanical Engineering 2019, 19(6): 1457-1466 |
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Saeedi B, Vatankhah R. Flexural Sensitivity Analysis of Atomic Force Microscope Made of Functionally Graded Materials Based on Modified Couple Stress Theory . Modares Mechanical Engineering 2019; 19 (6) :1457-1466
URL: http://mme.modares.ac.ir/article-15-22553-en.html
URL: http://mme.modares.ac.ir/article-15-22553-en.html
1- Mechanical Engineering Faculty, Shiraz University, Shiraz, Iran
2- Mechanical Engineering Faculty, Shiraz University, Shiraz, Iran , rvatankhah@shirazu.ac.ir
2- Mechanical Engineering Faculty, Shiraz University, Shiraz, Iran , rvatankhah@shirazu.ac.ir
Abstract: (3492 Views)
In this article, the sensitivity and resonant frequency of the atomic force microscope made of functionally graded materials is investigated by couple stress theory (MCST). In MCST, the size effect of the system is taking into account by means of the material length scale parameter. is made of a mixture of metal and ceramic with properties varying through the thickness following a simple In this work, due to the kinematic energy and potential energy of , the governing equations of motion and corresponding boundary conditions are derived on the basis of Hamilton principle by considering Euler-Bernoulli beam theory. Based on the results, it is clear that when the contact stiffness increases, the sensitivity of the system decreases, and resonant frequency increases. Moreover, when the thickness comes approximately close to material length scale parameter, the difference between MCST and classical continuum mechanic becomes significant. Furthermore, in low contact stiffness, increasing the power reduces the sensitivity of , while in high contact stiffness, increasing the power 
increases the sensitivity of the system. Results also show that at each value of contact stiffness, as ceramic volume fraction increases the resonant frequency will be increased, too.
increases the sensitivity of the system. Results also show that at each value of contact stiffness, as ceramic volume fraction increases the resonant frequency will be increased, too.
Keywords: Functionally Graded Materials, Modified Couple Stress Theory, Length Scale Parameter, Atomic Force Microscop
Article Type: Original Research |
Subject:
Micro & Nano Systems
Received: 2018/06/29 | Accepted: 2018/12/1 | Published: 2019/06/1
Received: 2018/06/29 | Accepted: 2018/12/1 | Published: 2019/06/1
References
1. Arafat HN, Nayfeh AH, Abdel-Rahman EM. Modal interactions in contact-mode atomic force microscopes. Nonlinear Dynamics. 2008;54(1):151-166. [Link] [DOI:10.1007/s11071-008-9388-5]
2. Binnig G, Quate CF, Gerber C. Atomic force microscope. Physical Review Letters. 1986;56(9):930-933. [Link] [DOI:10.1103/PhysRevLett.56.930]
3. Davis ZJ, Abadal G, Hansen O, Borise X, Barniol N, Perez-Murano F, et al. AFM lithography of aluminum for fabrication of nanomechanical systems. Ultramicroscopy. 2003;97(1-4):467-472. [Link] [DOI:10.1016/S0304-3991(03)00075-5]
4. Lee HL, Chang WJ. Coupled lateral bending-torsional vibration sensitivity of atomic force microscope cantilever. Ultramicroscopy. 2008;108(8):707-711. [Link] [DOI:10.1016/j.ultramic.2007.10.012]
5. Fang TH, Chang WJ. Effects of AFM-based nanomachining process on aluminum surface. Journal of Physics and Chemistry of Solids. 2003;64(6):913-918. [Link] [DOI:10.1016/S0022-3697(02)00436-5]
6. Garcıa R, Perez R. Dynamic atomic force microscopy methods. Surface Science Reports. 2002;47(6-8):197-301. [Link] [DOI:10.1016/S0167-5729(02)00077-8]
7. Basak S, Raman A. Dynamics of tapping mode atomic force microscopy in liquids: Theory and experiments. Applied Physics Letters. 2007;91(6):064107. [Link] [DOI:10.1063/1.2760175]
8. Loganathan M, Kodandarama SR, Bristow DA. Measurement sensitivity improvement in tapping-mode atomic force microscopy through bi-harmonic drive signal. Review of Scientific Instruments. 2011;82(10):103704. [Link] [DOI:10.1063/1.3648103]
9. Chang WJ, Fang TH, Chou HM. Effect of interactive damping on sensitivity of vibration modes of rectangular AFM cantilevers. Physics Letters A. 2003;312(3-4):158-165. [Link] [DOI:10.1016/S0375-9601(03)00620-0]
10. Chang WJ, Lee HL, Chen TYF. Study of the sensitivity of the first four flexural modes of an AFM cantilever with a sidewall probe. Ultramicroscopy. 2008;108(7):619-624. [Link] [DOI:10.1016/j.ultramic.2007.10.003]
11. Kahrobaiyan MH, Ahmadian MT, Haghighi P, Haghighi A. Sensitivity and resonant frequency of an AFM with sidewall and top-surface probes for both flexural and torsional modes. International Journal of Mechanical Sciences. 2010;52(10):1357-1365. [Link] [DOI:10.1016/j.ijmecsci.2010.06.013]
12. Lee HL, Chang WJ, Yang YC. Flexural sensitivity of a V-shaped cantilever of an atomic force microscope. Materials Chemistry and Physics. 2005;92(2-3):438-442. [Link] [DOI:10.1016/j.matchemphys.2005.01.046]
13. Mahdavi MH, Farshidianfar A, Tahani M, Mahdavi S, Dalir H. A more comprehensive modeling of atomic force microscope cantilever. Ultramicroscopy. 2008;109(1):54-60. [Link] [DOI:10.1016/j.ultramic.2008.08.003]
14. McFarland AW, Colton JS. Role of material microstructure in plate stiffness with relevance to microcantilever sensors. Journal of Micromechanics and Microengineering. 2005;15(5):1060-1067. [Link] [DOI:10.1088/0960-1317/15/5/024]
15. Vatankhah R, Kahrobaiyan MH, Alasty A, Ahmadian MT. Nonlinear forced vibration of strain gradient microbeams. Applied Mathematical Modelling. 2013;37(18-19):8363-8382. [Link] [DOI:10.1016/j.apm.2013.03.046]
16. Saeedi B, Vatankhah R. Nonlinear dynamic analysis of an atomic force microscope submerged in liquid based on strain gradient theory. Modares Mechanical Engineering. 2018;17(12):275-285. [Persian] [Link]
17. 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]
18. Abbasi M. Size dependent vibration behavior of an AFM with sidewall and top-surface probes based on the strain gradient elasticity theory. International Journal of Applied Mechanics. 2015;7(3):1550046. [Link] [DOI:10.1142/S1758825115500465]
19. Habibnejad Korayem M, Dehghani Ghahnaviyeh S, Ghasemi M, Taheri M. Effect of different geometrical parameters of atomic force microscope cantilevers in critical force and time based on manipulation with applying EFAST sensitivity analyses. Modares Mechanical Engineering. 2015;15(1):310-316. [Persian] [Link]
20. Lee HL, Chang WJ. Sensitivity analysis of rectangular atomic force microscope cantilevers immersed in liquids based on the modified couple stress theory. Micron. 2016;80:1-5. [Link] [DOI:10.1016/j.micron.2015.09.006]
21. 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]
22. Asghari M, Ahmadian MT, Kahrobaiyan MH, Rahaeifard M. On the size-dependent behavior of functionally graded micro-beams. Materials and Design. 2010;31(5):2324-2329. [Link] [DOI:10.1016/j.matdes.2009.12.006]
23. Yang F, 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]
24. Kong Sh, Zhou Sh, Nie Z, Wang K. The size-dependent natural frequency of Bernoulli-Euler micro-beams. International Journal of Engineering Science. 2008;46(5):427-437. [Link] [DOI:10.1016/j.ijengsci.2007.10.002]
25. Rahaeifard M, Kahrobaiyan MH, Ahmadian MT. Sensitivity analysis of atomic force microscope cantilever made of functionally graded materials. ASME 2009 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, 30 August-2 September, 2009, San Diego, California, USA. New York: American Society of Mechanical Engineers; 2009. [Link] [DOI:10.1115/DETC2009-86254]
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