A New Insight into the Flexural Vibration of Rectangular Atomic Force Microscope Cantilevers by Consideration the Contact Position

Abstract

The resonant frequency of flexural vibration for an atomic force microscope (AFM) cantilever has been investigated using the Timoshenko beam theory. In this paper the dynamic behavior of vibrational modes based on Timoshenko beam theory by consideration the effects of contact position, the height of the tip, thickness of the beam, and the angle between the cantilever and the sample surface on the non-dimensional resonant frequency have been investigated for the rectangular AFM cantilevers. The results show that the frequency is sensitive to the contact position and also decreases by increasing Timoshenko beam parameter or cantilever thickness, the first frequency is sensitive only to the lower normal contact stiffness, but high order modes are sensitive in a larger range of normal contact stiffness. By increasing the height H, for a limited range of normal contact stiffness the sensitivity to the normal contact stiffness increases. Increasing the lateral contact stiffness increases the sensitivity to the normal contact stiffness after critical normal contact stiffness, but when the normal contact stiffness is lower than critical normal contact stiffness, the situation is reversed. Furthermore, by increasing the angle between the cantilever and sample surface, the frequency decreases.