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Theoretical description of the flexural vibration of dagger shaped atomic force microscope cantilevers

Sadeghi, A ; Sharif University of Technology

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  1. Type of Document: Article
  2. DOI: 10.1166/jspm.2009.1012
  3. Abstract:
  4. The resonant frequency of flexural vibration for a dagger shaped atomic force microscope (AFM) cantilever has been investigated using the Timoshenko beam theory. Generally, three distinct regions are considered for dagger shaped cantilevers, one region with constant cross section and height and two double tapered regions. In this paper, the effects of the contact position, contact stiffness, the height of the tip, thickness of the beam, the height and breadth taper ratios of cantilever and the angle between the cantilever and the sample surface based on Timoshenko beam theory on the non-dimensional frequency and sensitivity to the contact stiffness have been studied. The differential quadrature method (DQM) is applied to solve the nonlinear differential equations of motion. The results show that the resonant frequency decreases when Timoshenko beam parameter or cantilever thickness increases and high order modes are more sensitive to it. Central and right (double tapered) cantilever lengths are effective on the resonant frequency and sensitivity to the contact stiffness. The first frequency is sensitive only in the lower range of contact stiffness, but the higher order modes are sensitive to the contact stiffness in a larger range. Increasing the tip height increases the sensitivity of the vibrational modes in a limited range of normal contact stiffness. We show that the sensitivity to the contact stiffness can be increased by the variations of height taper ratio and this matter has never been investigated formally. Copyright © 2009 American Scientific Publishers All rights reserved
  5. Keywords:
  6. Afm cantilever ; Atomic force microscope ; Dagger shaped cantilever ; Differential quadrature method ; Double tapered cantilever ; Timoshenko beam ; AFM cantilevers ; Atomic force microscope cantilevers ; Atomic force microscopes ; Contact position ; Contact stiffness ; Cross section ; Differential quadrature methods ; Flexural vibrations ; High order mode ; Higher-order modes ; Non-dimensional frequency ; Nonlinear differential equation ; Resonant frequencies ; Sample surface ; Taper ratios ; Timoshenko beam theory ; Timoshenko beams ; Vibrational modes ; Atomic force microscopy ; Atoms ; Cantilever beams ; Differentiation (calculus) ; Equations of motion ; Microscopes ; Natural frequencies ; Nonlinear equations ; Particle beams ; Sensitivity analysis ; Stiffness ; Nanocantilevers
  7. Source: Journal of Scanning Probe Microscopy ; Volume 4, Issue 2 , 2009 , Pages 78-90 ; 15577937 (ISSN)
  8. URL: http://www.ingentaconnect.com/content/asp/jspm/2009/00000004/00000002/art00004