The modal frequencies of flexural vibration for an atomic force microscope (AFM) cantilever immersed in fluids have been derived based on
Timoshenko beam theory, including the effects of rotary inertia and shear deformation, and a closed-form expression for the resonant
frequencies of vibration modes has been obtained. The effects of quality factor and contact stiffness on the modal frequency are analyzed.
The results show that the damping effect on the vibration frequency of AFM cantilever is obvious, especially for high-order modes and low
contact stiffness. The vibration frequency of AFM cantilever shows a marked decrease with low quality factors. In addition, the effects of
rotary inertia and shear deformation on the ratio of vibration frequency of a Timoshenko beam to that of an Euler beam are significant,
especially for high-order modes and low quality factors. It indicates that the Timoshenko beam theory is able to evaluate the frequencies of
flexural vibration of the higher modes for the AFM cantilever immersed in liquids.