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Nonlinear Distributed-Parameters Vibration Analysis of an AFM Microcantilever Beam in Dynamic Mode

Delnavaz, Aidin | 2009

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  1. Type of Document: Ph.D. Dissertation
  2. Language: Farsi
  3. Document No: 40072 (08)
  4. University: Sharif University of Technology
  5. Department: Mechanical Engineering
  6. Advisor(s): Zohoor, Hassan
  7. Abstract:
  8. Dynamic and vibration behavior of AFM microcantilever beam subject to the tip-sample interaction and/or contact is systematically investigated. An Euler-Bernoli microcantilever in 2D plane is considered with longitudinal and bending displacements. Inextensibility assumption and extended Hamilton’s principle is utilized to extract the single-variable integro partial equation of motion under: 1) tip-nanoparticle interactions, 2) tip-surface interactions in non-contact mode and 3) tip-surface interactions and contacts in intermittent-contact mode. Galerkin’s first mode approximation is then used to discretize the derived equations; and multiple time scales method is adopted to analyze the time-dependant part of the equations. The results are compared with the conventional point-mass and linear distributed-parameters models of the microcantilever which have been extensively studied in the literature so far. These comparisons reveal that the differences between linear and non-linear approaches are amplified inside the sample attraction region. In addition to these theoretical achievements, a commercial AFM was utilized to do experimental validations. Studying the theoretical and the experimental results demonstrate that the developed model not only predicts the free vibration amplitude and the instable region, but also is well fitted with the experimental amplitude-separation curves inside the sample attraction region either in the resonance or non-resonance condition. Some phenomena in experimental curves like sudden amplitude drop and hysteresis which are not predicted by theoretical model are also investigated. Furthermore, it is observed that in the intermittent-contact mode, nonlinear approach presents a better approximation in comparison with linear model towards the saturated amplitude as well as the frequency interval in which the contact occurs between the tip and the sample. In conclusion, the developed nonlinear distributed-parameters model of microcantilever subject to tip-sample interaction is a more effective and reliable method in predicting the dynamic behavior of AFM in imaging or nanomanipulation tasks
  9. Keywords:
  10. Atomic Force Microscopy (AFM) ; Vibrational Analysis ; Microcantiliver Vibration ; Nonlinear Distributed Parameter Model ; Dynamic Mode ; Tip-Sample Interaction

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