Sizedependent on vibration and flexural sensitivity of atomic force microscope

In this paper, the free vibration behaviors and flexural sensitivity of atomic force microscope cantilevers with smallscale effects are investigated. To study the smallscale effects on natural frequencies and flexural sensitivity, the consistent couple stress theory is applied. In this theory, the couple stress is assumed skewsymmetric. Unlike the classical beam theory, the new model contains a materiallengthscale 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 materiallengthscale parameter and dimensionless thickness on the natural frequency and flexural sensitivity.