Nonlinear Dynamics

, Volume 78, Issue 3, pp 1827–1837 | Cite as

Frequency response of primary resonance of electrostatically actuated CNT cantilevers

  • Dumitru I. Caruntu
  • Le Luo
Original Paper


This paper deals with electrostatically actuated carbon nanotube (CNT) cantilever over a parallel ground plate. Three forces act on the CNTs cantilever, namely electrostatic, van der Waals, and damping. The van der Waals force is significant for values of 50 nm or less of the gap between the CNT and the ground plate. As both forces electrostatic and van der Waals are nonlinear, and the CNTs electrostatic actuation is given by AC voltage, the CNT undergoes nonlinear parametric dynamics. The methods of multiple scales and reduced order model (ROM) are used to investigate the system under soft AC near half natural frequency of the CNT and weak nonlinearities. The frequency–amplitude response and damping, voltage, and van der Waals effects on the response are reported. It is showed that only five terms ROM predicts and accurately predicts the pull-in instability and the saddle-node bifurcation, respectively.


CNT cantilever resonators Electrostatic actuation  Primary resonance Frequency response 



This work was supported by the National Science Foundation under DMR Grant # 0934157 (PREM-The University of Texas Pan American/University of Minnesota - Science and Engineering of Polymeric and Nanoparticle-based Materials for Electronic and Structural Applications).


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Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  1. 1.Mechanical Engineering DepartmentUniversity of Texas-Pan AmericanEdinburgUSA

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