Dynamic modeling and nonlinear vibration simulation of piezoelectric micro-beam in self sensing mode of atomic force microscope

Document Type : Persian

Authors

1 Faculty of Mechanical Islamic Azad University of Shahrekord

2 Faculty of Mechanical Islamic Azad University of Shahrekord, Iran.

Abstract

Nowadays, atomic force microscope is considered as a useful tool in the determination of intermolecular forces and surface topography with the resolution of nanometers. In this kind of microscope, micro cantilever is considered as the heart of the microscope and is used as a measuring tool.  This paper is aimed towards investigating the behavior of a piezoelectric micro cantilever with a triangular head, in self-measure mode and close proximity to the surface of a sample. Output charge from the piezoelectric layer and also the output current, in this mode, is considered as an effective factor in the measurement of the bending. The micro cantilever’s vibration behavior becomes nonlinear, as it approaches the surface of the sample. Surely the piezoelectric layer in the self-measure mode can be considered as a good measuring tool, only when it reflects the effects of the nonlinear interaction between the tip of the probe and the surface of the sample in its measurements. In order to investigate this matter, first the differential equations that are ruling over the vibrating movements of the piezoelectric micro cantilever with a triangular head, are transformed into normal nonlinear differential equations using the Galerkin method. Then the resulting nonlinear differential equation is solved using the multi-scale method. After solving the differential equation ruling over the problem, the micro cantilevers behavior in the proximity of the surface of the sample is simulated and the effect of factors such as balancing distance, oscillation modes and the substance of piezoelectric layer are investigated.

Keywords

References

[1]     Vigneswaran N., Samsuri F., Ranganathan B., Recent Advances in Nano Patterning and Nano Imprint Lithography for Biological Applications, Procedia Engineering, 97, 2014, pp. 1387-1398.
[2]     MuthukumarT., Prabhavathi S., Chamundeeswari M., Sastry T.P., Bio-modified carbon nanoparticles loaded with methotrexate possible carrier for anticancer drug delivery, Materials Science and Engineering: C, 36(1), 2014, pp. 14-19.
[3]     Grayeli-Korpi A-R., Savaloni H., Habibi M., Corrosion inhibition of stainless steel type AISI 304 by Mn coating and subsequent annealing with flow of nitrogen at different temperatures, Applied Surface Science, 276(1), 2013, pp. 269-275.
[4]     Jalili N., Laxminarayana K., A Review of Atomic Force Microscopy Imaging Systems: Application to Molecular Metrology and Biological Sciences, International Journal of Mechanics, 14 (8), 2004, pp. 907-914.
[5]     Moosapour M., Hajabasi M.A., Ehteshami H., Thermoelastic damping effect analysis in micro flexural resonator of atomic force microscopy, Applied Mathematical Modelling, 38 (11-12), 2014, pp. 2716-2733.
[6]     Kangarlou H., Aghgonbad M.M., Incidence angle dependence on structural and optical properties of UHV deposited copper nano layers, International Journal for Light and Electron Optics, 125(19), 2014, pp. 5532-5537.
[7]     Adams J.D., Parrott G., Bauer C., Sant T., Manning L., Jones M., Rogers B., McCorkle D., Ferrel T.L, Nanowatt chemical vapor detection with a self-sensing, piezoelectric microcantilever array, Applied Physics Letters, 83, 2003, pp. 3428-3440.
[8]     Salehi-Khojin A., Bashash S., Jalili N., Modeling and Experimental Vibration Analysis of Nanomechanical Cantilever Active Probes, Micromechanics and Microengineering, 18, 2008, 085008 (11pp).
[9]     Liqun D., Guiryong K., Fumihito A., Toshio F., Kou-ichi I., Yasunori T., Structure design of micro to-uch sensor array, Sensors and Actuators A, 107, 2003, pp. 7-13.
[10] Korayem M.H., Ghaderi R., Sensitivity analysis of nonlinear vibration of AFM piezoelectric MC in liquid, International Journal of Mechanics and Materials in Design, 10(2), 2014, pp. 121–131.
[11] Rogers B., Manning L., Sulchek T., Adams J.D., Improving tapping mode atomic force microscopy with piezoelectric cantilevers, Ultramicroscopy, 100, 2004, pp. 267-276.
[12] Mahmoodi S.N., Jalili N., Non-linear vibrations and frequency response analysis of piezoelectrically driven microcantilevers, International Journal of Non-Linear Mechanics, 42, 2007, pp. 577-587.
[13] Wolf K., Gottlieb O., Nonlinear dynamics of a noncontacting atomic force microscope cantilever actuated by a piezoelectric layer, Journal of Applied Physics, 91(7),2002, pp. 4701-4712.
[14] Fung R.F., Huang S.C., Dynamic modeling and vibration analysis of the atomic force microscope, ASME Journal of Vibration and Acoustics, 123, 2001, pp. 502–509.
[15] Mahmoodi S.N., Dagag M.F., Jalili N., On the nonli-near-flexural response of piezoelectrically driven microcantilever sensors, Sens. and Act. A, 153, 2009, pp. 171-179.
[16] Mahmoodi S.N., Jalili N., Ahmadian M., Subharm-onics analysis of nonlinear flexural vibrations of piezoelectrically actuated microcantilevers, Nonlinear Dynamics, 59, 2010, pp. 397-409.
[17] Ghaderi R., Nejat A., Nonlinear Mathematical Modeling of Vibrating Motion of Nanomechanical Cantilever Active Probe, Latin American Journal of Solids and Structures, 11, 2014, pp. 369-385.
[18] Shin Ch., Jeon I., Khim Z.G., Hong J.W., Nam H.J., Study of sensitivity and noise in the piezoelectric self-sensing and self-actuating cantilever with an integrated Wheatstone bridge circuit, Review of Scientific Instruments, 81, 2010, 035109.
[19] Dong W., Lu X., Cui Y., Wang J., Liu M., Fabrication and characterization of microcantilever integrated with PZT thin film sensor and actuator, Thin Solid Films, 515, 2007, pp. 8544–8548.
[20] Itoh T., Suga T., Self-excited force sensing mic-rocantilevers with piezoelectric thin films for dynamic scanning force, Sensors and Actuators A: Physics, 54, 1996, pp. 477–481.
[21] Lee C., Itoh T., Suga T., Self-excited piezoelectric PZT microcantilevers for dynamic SFM-with inh-erent sensing and actuating capabilities, Sensors and Actuators A., 72, 1999, pp. 179–188.
[22] Korayem M.H., Ghaderi R., Vibration response of a piezoelectrically actuated microcantilever subjected to tip–sample interaction, Scientia Iranica B, 20 (1), 2013, pp. 195–206.
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Journal of Simulation and Analysis of Novel Technologies in Mechanical Engineering
Volume 9, Issue 3 - Serial Number 27
Autumn 2016
Pages 531-542

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