A vibration analysis of a cracked micro-cantilever in an atomic force microscope by using transfer matrix method

In this paper, the effects of crack size and its location have been investigated on the free vibration of an atomic force microscopy (AFM) cantilever applying transfer matrix method. By modeling the crack as a torsional spring and considering the boundary conditions at the contact point with sample's surface, the AFM cantilever vibration behavior has been formulated. Afterwards, the characteristic equation has been derived applying the transfer matrix. At the end, the effects of crack size and its location have been investigated on the flexural resonant frequency and sensitivity of the AFM cantilever. The results indicate that the frequency and sensitivity would be maximum when the crack is approximately in the middle of the cantilever. Growing the crack size can result in the variations of either resonant frequency or sensitivity especially for more stiff samples.