Vibration analysis of atomic force microscope cantilevers in contact resonance force microscopy using Timoshenko beam model

Timoshenko beam model is employed to investigate the vibration of atomic force microscope (AFM) cantilevers in contact resonance force microscopy (CRFM). Characteristic equation with both vertical and lateral tip-sample contact is derived. The contact resonance frequencies (CRFs) obtained by the Timoshenko model are compared with those by the Euler−Bernoulli model. A method is proposed to correct the wave number obtained by the Euler−Bernoulli model. The forced vibration is compared between the two models. Results reveal that the Timoshenko model is superior to the Euler−Bernoulli model in predicting the vibration characteristics for cantilevers' higher eigenmodes.