Acta Mechanica Solida Sinica

, Volume 30, Issue 5, pp 520–530 | Cite as

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

  • Xilong Zhou
  • Pengfei Wen
  • Faxin Li


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


Nanomechanics Timoshenko model Forced vibration 


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Copyright information

© The Chinese Society of Theoretical and Applied Mechanics and Technology 2017

Authors and Affiliations

  1. 1.Department of Engineering Structure and Mechanics, School of ScienceWuhan University of TechnologyWuhanChina
  2. 2.Hubei Key Laboratory of Theory and Applications of Advanced Materials MechanicsWuhan University of TechnologyWuhanChina
  3. 3.Department of Mechanics & Engineering Science, College of EngineeringPeking UniversityBeijingChina

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