Sensitivity analysis of nonlinear vibration of AFM piezoelectric microcantilever in liquid
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Sensitivity analysis of nonlinear vibration of AFM piezoelectric microcantilever in liquid H. Korayem • R. Ghaderi
Received: 7 August 2013 / Accepted: 7 November 2013 Springer Science+Business Media Dordrecht 2013
Abstract In this paper sensitivity analysis of nonlinear vibrating motion of atomic force microscope (AFM) piezoelectric microcantilever (MC) is performed in liquid environment. With respect to the importance of resonance amplitude and system nonlinearity in AFM application, sensitivity analysis of nonlinear vibrating motion is performed on these two parameters. The sensitivity analysis is carried out based on the Sobol statistical method. Piezoelectric MC has geometrical discontinuities due to presence of piezoelectric layer and tip. Regarding these discontinuities, non-uniform beam model is chosen for the dynamic modeling. Vibrating motion of the MC is modeled in AFM non-contact mode. The sensitivity analysis is performed to study how the effective parameters affect nonlinear vibrating motion in liquid. The sensitivity analysis of piezoelectric MC in liquid was compared with the one performed in air to better specify the effect of liquid environment on motion. The obtained results show that sensitivity of piezoelectric MC to nonlinearity of interaction force in H. Korayem (&) Robotic Research Laboratory, Mechanical Engineering Department, School of Mechanical Engineering, Iran University of Science and Technology (IUST), Tehran, Iran e-mail: [email protected] R. Ghaderi Department of Mechanical and Aerospace Engineering, Science and Research Branch, Islamic Azad University, Tehran, Iran e-mail: [email protected]
air is greater than liquid and the sensitivity decreases with the increase of liquid density. With respect to the sensitivity analysis results, it can be concluded that the most effective geometrical parameters on nonlinearity in both air and liquid environments are thickness and length of piezoelectric layer and length of tip. The results of sensitivity analysis also show that the length of probe in liquid has a considerable effect on amplitude, whereas it has less effect on amplitude in air. Keywords Sensitivity analysis Nonlinear vibration AFM Piezoelectric microcantilever
1 Introduction The study of vibrating motion of microcantilever (MC) interacting with viscous liquids is of paramount importance to improve performance of AFM in liquid environment and some micro-electromechanical systems (MEMS), and other applications of MCs (Ahangar et al. 2011). In AFM, the rate of imaging and resolution of images depend on sensitivity of vibrating motion of AFM MC; therefore, study of AFM MC sensitivity is of paramount importance and it has been done by many researchers. Lee et al. (2005) studied flexural sensitivity of a V-shaped MC near a sample surface. They studied flexural sensitivity of MC against contact stiffness and compared the results with a rectangular MC. Ha et al. (2006) modeled a MC dynamically with two piezoelectric layers in base near
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H. Korayem, R. Ghaderi
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