New Data on the Flexural and Torsional Vibrations of Rectangular Atomic Force Microscope Cantilevers

The resonant frequency of flexural and torsional vibrations for an atomic force microscope (AFM) cantilever has been investigated using the Euler-Bernoulli beam theory. The results show that for flexural vibration the frequency is sensitive to the contact position, the first frequency is sensitive only to the lower contact stiffness, but high order modes are sensitive in a larger range of contact stiffness. By increasing the height H, for a limited range of contact stiffness the sensitivity to the contact stiffness increases. Furthermore, by increasing the angle between the cantilever and sample surface, the frequency decreases. For torsional vibration, the first mode is sensitive to the contact position, the first frequency is sensitive only to the lower lateral contact stiffness, but high order modes are sensitive in a larger range of lateral contact stiffness. All torsional modes are sensitive to the contact position.