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Nonlinear vibration of rectangular atomic force microscope cantilevers by considering the Hertzian contact theory

Sadeghi, A ; Sharif University of Technology

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  1. Type of Document: Article
  2. DOI: 10.1139/P10-019
  3. Abstract:
  4. The nonlinear flexural vibration for a rectangular atomic force microscope cantilever is investigated by using Timoshenko beam theory. In this paper, the normal and tangential tip-sample interaction forces are found from a Hertzian contact model and the effects of the contact position, normal and lateral contact stiffness, tip height, thickness of the beam, and the angle between the cantilever and the sample surface on the nonlinear frequency to linear frequency ratio are studied. The differential quadrature method is employed to solve the nonlinear differential equations of motion. The results show that softening behavior is seen for most cases and by increasing the normal contact stiffness, the frequency ratio increases for the first mode, but for the second mode, the situation is reversed. The nonlinear-frequency to linear-frequency ratio increases by increasing the Timoshenko beam parameter, but decreases by increasing the contact position for constant amplitude for the first and second modes. For the first mode, the frequency ratio decreases by increasing both of the lateral contact stiffness and the tip height, but increases by increasing the angle α between the cantilever and sample surface
  5. Keywords:
  6. Atomic force microscope cantilevers ; Constant amplitude ; Contact position ; Contact stiffness ; Differential quadrature methods ; Flexural vibrations ; Frequency ratios ; Hertzian contact model ; Hertzian-contact theory ; Lateral contact ; Linear frequency ; Non-linear vibrations ; Nonlinear differential equation ; Nonlinear frequency ; Sample surface ; Softening behavior ; Timoshenko beam theory ; Timoshenko beams ; Tip-sample interaction ; Atomic force microscopy ; Differentiation (calculus) ; End effectors ; Equations of motion ; Nanocantilevers ; Particle beams ; Stiffness ; Nonlinear equations
  7. Source: Canadian Journal of Physics ; Volume 88, Issue 5 , 2010 , Pages 333-348 ; 00084204 (ISSN)
  8. URL: http://www.nrcresearchpress.com/doi/abs/10.1139/P10-019#.WJ-BprURJkw