Comprehensive analytical approximations of the pull-in characteristics of an electrostatically actuated nanobeam under the influences of intermolecular forces

Hassen M. Ouakad*, Jihad E. AlQasimi

*Corresponding author for this work

Research output: Contribution to journalArticle

1 Citation (Scopus)


In this paper, analytical closed-form expressions to accurately estimate the pull-in characteristics of an electrostatically-actuated doubly-clamped nanobeam are derived and examined. In this regard, a coupled electro-mechanical problem for the nano-actuator is first presented assuming a single mode approximation while taking into account all the possible structural, electrical and nanoscale effects: the fringing of the electrical actuating force, the geometric mid-plane stretching and intermolecular (van derWalls and Casimir) forces. The complicated nonlinear resultant equations are numerically approximated in order to derive the closed-form expressions for the important nano-actuator pull-in characteristics: i.e., the detachment length, the minimum reachable gap size before the collapse and the respective pull-in voltage. The resulting closed-form expressions are first quantitatively validated with other previously published results, and comparisons showed an acceptable agreement. Unlike the reported expressions in the literature, the proposed closed-form expressions in this work are proper approximations, fairly accurate and, more importantly, provide a quick estimate of the critical design pull-in parameters of the nano-actuator. In addition, the analysis of these expressions demonstrated that the consideration of the intermolecular forces together with the fringe effect tends to significantly reduce the threshold pull-in voltage, whereas the mid-plane stretching parameter tends to the contrary to increase the voltage at the pull-in collapse. The derived expressions of these analytical/approximate solutions could hopefully be appropriately used by NEMS engineers as simple/quick procedures for successful design and fabrication of electrostatically-actuated nano-devices.

Original languageEnglish
Article number3
Issue number1
Publication statusPublished - Mar 1 2018
Externally publishedYes


  • Actuator
  • Analytical solution
  • Casimir force
  • Mid-plane stretching
  • NEMS
  • Pull-in characteristics
  • Van der Waals force

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Control and Optimization

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