Instability characteristics of free-standing nanowires based on the strain gradient theory with the consideration of casimir attraction and surface effects

Hamid M. Sedighi, Hassen M. Ouakad, Moosa Khooran

Research output: Contribution to journalArticle

3 Citations (Scopus)


Size-dependent dynamic instability of cylindrical nanowires incorporating the effects of Casimir attraction and surface energy is presented in this research work. To develop the attractive intermolecular force between the nanowire and its substrate, the proximity force approximation (PFA) for small separations, and the Dirichlet asymptotic approximation for large separations with a cylinder-plate geometry are employed. A nonlinear governing equation of motion for free-standing nanowires - based on the Gurtin-Murdoch model - and a strain gradient elasticity theory are derived. To overcome the complexity of the nonlinear problem in hand, a Garlerkin-based projection procedure for construction of a reduced-order model is implemented as a way of discretization of the governing differential equation. The effects of length-scale parameter, surface energy and vacuum fluctuations on the dynamic instability threshold and adhesion of nanowires are examined. It is demonstrated that in the absence of any actuation, a nanowire might behave unstably, due to the Casimir induction force.

Original languageEnglish
Pages (from-to)489-507
Number of pages19
JournalMetrology and Measurement Systems
Issue number3
Publication statusPublished - Sep 1 2017
Externally publishedYes


  • Casimir force
  • Dirichlet asymptotic approximation
  • Free-standing cylindrical nanowire
  • Proximity force approximation

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Instrumentation

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