Journal of Computational Applied Mechanics

Size-dependent on vibration and flexural sensitivity of atomic force microscope

Document Type : Research Paper

Authors

1 School of Mechanical Engineering, College of Engineering, University of Tehran, Tehran, Iran

2 Engineering Graphics Center, Sharif University of Technology, Tehran, Iran

3 Department of Mechanical Engineering, Sousangerd Branch, Islamic Azad University, Sousangerd, Iran

Abstract

In this paper, the free vibration behaviors and flexural sensitivity of atomic force microscope cantilevers with small-scale effects are investigated. To study the small-scale effects on natural frequencies and flexural sensitivity, the consistent couple stress theory is applied. In this theory, the couple stress is assumed skew-symmetric. Unlike the classical beam theory, the new model contains a material-length-scale parameter and can capture the size effect. For this purpose, the Euler–Bernoulli beam theory is used to develop the AFM cantilever. The tip interacts with the sample that is modeled by a spring with constant of. The equation of motion is obtained through a variational formulation based on Hamilton’s principle. In addition, the analytical expressions for the natural frequency and sensitivity are also derived. At the end, some numerical results are selected to study the effects of material-length-scale parameter and dimensionless thickness on the natural frequency and flexural sensitivity.

Keywords

Main Subjects

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Journal of Computational Applied Mechanics
Volume 50, Issue 1
June 2019
Pages 191-196
  • Receive Date: 15 January 2018
  • Revise Date: 14 February 2018
  • Accept Date: 16 February 2018