Nonlinear Dynamics

, Volume 77, Issue 1–2, pp 87–98 | Cite as

Effects of the van der Waals force, squeeze-film damping, and contact bounce on the dynamics of electrostatic microcantilevers before and after pull-in

  • Mansour Abtahi
  • Gholamreza Vossoughi
  • Ali Meghdari
Original Paper


The operational range of microcantilever beams under electrostatic force can be extended beyond pull-in in the presence of an intermediate dielectric layer. In this paper, a systematic method for deriving dynamic equation of microcantilevers under electrostatic force is presented. This model covers the behavior of the microcantilevers before and after the pull-in including the effects of van der Waals force, squeeze-film damping, and contact bounce. First, a polynomial approximate shape function with a time-dependent variable for each configuration is defined. Using Hamilton’s principle, dynamic equations of microcantilever in all configurations have been derived. Comparison between modeling results and previous experimental data that have been used for validation of the model shows a good agreement.


Microcantilever beams Electrostatic force Dynamic modeling Floating Pinned and flat configurations 


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Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  • Mansour Abtahi
    • 1
  • Gholamreza Vossoughi
    • 1
  • Ali Meghdari
    • 1
  1. 1.Center of Excellence in Design, Robotics & Automation (CEDRA), Department of Mechanical EngineeringSharif University of TechnologyTehranIran

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