The modal frequencies of flexural vibration for an atomic force microscope (AFM)
cantilever have been evaluated using the Timoshenko beam theory, and a closed-form
expression for the frequencies of vibration modes has been obtained. In the analysis, the
effect of the ratios of different cantilever dimensions on frequency for the cantilever were
studied. The results show that increasing the ratio of cantilever thickness and
length decreases the vibration frequency. Increasing the ratio of the tip length
and cantilever length also increases the frequency. In addition, results using the
Bernoulli–Euler beam theory and the Timoshenko beam theory are compared. It can be
found that the Timoshenko beam theory is able to predict the frequencies of
flexural vibration of the higher modes with higher contact stiffness for the AFM
cantilever.