Reza Javidi - School of Mechanical Engineering, College of Engineering, University of Tehran, Tehran, Iran
Hamid Haghshenas Gorgani - Engineering Graphics Center, Sharif University of Technology, Tehran, Iran
Mohsen Mahdavi Adeli - Department of Mechanical Engineering, Sousangerd Branch, Islamic Azad University, Sousangerd, Iran

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.

consistent couple stress theory, atomic force microscope (AFM), Euler–Bernoulli beam, Hamilton’s principle, Sensitivity