Vibrational analysis of single-layered piezoelectric AFM microcantilever in amplitude mode by considering the capillary force
Robotic Research Laboratory, Center of Excellence in Experimental Solid Mechanics and Dynamics, School of Mechanical Engineering, Iran University of Science and Technology, Tehran, Iran
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Revised: 22 October 2014
Accepted: 5 November 2014
Published online: 5 December 2014
In this article, the vibrational behavior of a microcantilever (MC) with an extended piezoelectric layer in the air ambient undergoes examination. To model the vibrational motion of this type of cantilever, the Hamilton’s principle has been used. For this purpose, the MC vibrational equation has been derived by the assumption of the continuous beam based on the Euler-Bernoulli beam theory. By adopting the finite element method (FEM), the MC differential equation has been solved. In the present simulation not only van der Waals and contact forces but also the capillary forces resulting from the condensation of the water vapors in air on MC tip have been considered. The results illustrate that the force between the sample surface and the probe affects the MC amplitude; furthermore, it causes the reduction in the resonance frequency. In addition, to reduce the time delay during topography from the surface roughness, it is better to select MCs with larger width and length and smaller thickness. Furthermore, the results indicate that the best imaging takes place when the vibration is in its second vibrational mode. Finally, the effects of MC geometric parameters on the time delay between the starting moment of surface roughness and the moment of variation in the MC amplitude (surface roughness topography) have been analyzed.
© EDP Sciences, 2014