Vibration analysis of atomic force microscope cantilevers in contact resonance force microscopy using Timoshenko beam model
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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. © 2017 Published by Elsevier Ltd on behalf of Chinese Society of Theoretical and Applied
KeywordsNanomechanics Timoshenko model Forced vibration
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