Volume 21, Issue 1 (January 2021)                   Modares Mechanical Engineering 2021, 21(1): 29-37 | Back to browse issues page

XML Persian Abstract Print

Download citation:
BibTeX | RIS | EndNote | Medlars | ProCite | Reference Manager | RefWorks
Send citation to:

a_sadeghi@damavandiau.ac.ir. Modeling of Non-Linear Dynamic Behavior of Tapered Atomic Force Microscope Cantilevers Immersed in Different Liquids Based on Theoretical and Experimental Methods. Modares Mechanical Engineering. 2021; 21 (1) :29-37
URL: http://mme.modares.ac.ir/article-15-49389-en.html
Abstract:   (337 Views)
In this paper, the non-linear dynamic behavior of immersed AFM micro cantilever in liquid has been modeled. To increase the accuracy of the theoretical model, all necessary details for cantilever and sample surface have been taken into account. As for the theoretical model, the Timoshenko beam theory which takes the rotatory inertia and shear deformation effects into consideration has been adopted. For modeling the vibrational system, cantilever thickness, cantilever length and breadth, the angle between cantilever and sample surface, normal contact stiffness, lateral contact stiffness, tip height, breadth taper ratio, height taper ratio, time parameter and viscosity of the liquids have been considered. Differential quadrature method (DQM) has been used for solving the differential equations. During the investigation, the softening behavior was observed for all cases. Here, water, methanol, acetone and carbon tetrachloride has been supposed as immersion environments. Results show that increasing the liquid density reduces the resonant frequency. Time variable does not have any considerable effect on the non-linear resonant frequency. Theoretical modeling has been compared for a rectangular AFM cantilever with experimental works in both of the contact and non-contact modes in air and water environments. Results show good agreement.
Full-Text [PDF 700 kb]   (112 Downloads)    
Article Type: Original Research | Subject: Impact Mechanics
Received: 2021/01/21 | Accepted: 2021/01/19 | Published: 2021/01/19

1. Binnig G, Quate CF, Gerber C. Atomic force microscope. Physical review letters. 1986;56(9):930.
2. Rabe U, Janser K, Arnold W. Vibrations of free and surface‐coupled atomic force microscope cantilevers: Theory and experiment. Review of scientific instruments. 1996;67(9):3281-3293.
3. Turner JA, Wiehn JS. Sensitivity of flexural and torsional vibration modes of atomic force microscope cantilevers to surface stiffness variations. Nanotechnology. 2001;12(3):322
4. Dupas E, Gremaud G, Kulik A, Loubet JL. High-frequency mechanical spectroscopy with an atomic force microscope. Review of Scientific Instruments. 2001;72(10):3891-3897
5. Shen K, Turner JA. Finite element simulations of nonlinear vibrations of atomic force microscope cantilevers. InNondestructive Evaluation and Reliability of Micro-and Nanomaterial Systems. 2002; 4703: 93-104
6. Chen TY, Lee HL. Damping vibration of scanning near-field optical microscope probe using the Timoshenko beam model. Microelectronics journal. 2009;40(1):53-57.
7. Song Y, Bhushan B. Simulation of dynamic modes of atomic force microscopy using a 3D finite element model. Ultramicroscopy. 2006;106(8-9):847-873.
8. Song Y, Bhushan B. Finite-element vibration analysis of tapping-mode atomic force microscopy in liquid. Ultramicroscopy. 2007;107(10-11):1095-1104.
9. Korayem MH, Sharahi HJ, Korayem AH. Comparison of frequency response of atomic force microscopy cantilevers under tip-sample interaction in air and liquids. Scientia Iranica. 2012;19(1):106-112.
10. Sadeghi A. The flexural vibration of V shaped atomic force microscope cantilevers by using the Timoshenko beam theory. ZAMM‐Journal of Applied Mathematics and Mechanics/Zeitschrift für Angewandte Mathematik und Mechanik. 2012;92(10):782-800.
11. Zhang Y, Zhao H, Zuo L. Contact dynamics of tapping mode atomic force microscopy. Journal of sound and vibration. 2012;331(23):5141-5152.
12. Payam AF. Sensitivity of flexural vibration mode of the rectangular atomic force microscope micro cantilevers in liquid to the surface stiffness variations. Ultramicroscopy. 2013;135:84-88
13. Ghaderi R, Nejat A. Nonlinear mathematical modeling of vibrating motion of nanomechanical cantilever active probe. Latin American Journal of Solids and Structures. 2014;11(3):369-385.
14. Ansari R, Pourashraf T, Gholami R, Sahmani S, Ashrafi MA. Size-dependent resonant frequency and flexural sensitivity of atomic force microscope microcantilevers based on the modified strain gradient theory. International Journal of Optomechatronics. 2015;9(2):111-130.
15. Ahmadi M, Ansari R, Darvizeh M, Rouhi H. Effects of fluid environment properties on the nonlinear vibrations of AFM piezoelectric microcantilevers. Journal of Ultrafine Grained and Nanostructured Materials. 2017;50(2):117-123

Add your comments about this article : Your username or Email: