Effect of tip mass on modal flexural sensitivity of rectangular AFM cantilevers to surface stiffness variations

In this paper, the effect of the tip mass on the sensitivity of flexural vibration modes of an AFM rectangular cantilever has been studied and a characteristics equation for the AFM cantilever has been derived. Then, based on the characteristics equation, a closed form expression for the flexural modal sensitivity of the rectangular cantilever to the surface stiffness variations has been derived. Using numerical experiments, the effect of various tip masses on the sensitivity has been investigated. The results show that for low stiffness materials, the sensitivity of AFM cantilevers with smaller tip masses is more than the cantilever with greater tip masses. While for the materials with high stiffness, the difference in sensitivities is not significant. However, for the cantilevers with bigger tip masses sensitivity is higher.