Clamped nano-beams as adsorption induced sensors: Linear and non-linear effects

B. Bar-On, E. Altus

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


This work analyzes the deflection of clamped nano-beam due to stochastic surface stresses, induced by adsorption/desorption of surrounding particles. Both linear and non-linear effects (mid-plane stretching) are considered. A mechanical model for 1D nano-beam is first introduced and includes the surface effects via their effective cross sectional residual force and moment. The model considers local non-stationary surface residual stresses, governed by Langmuir's interaction model. Local adsorption relations are described by non-deterministic model, from which the statistics of the surface residual stresses are extracted and their time-space correlations are calculated. A straightforward perturbation method is used to evaluate the non-linear effects. In each order of the approximated solution, the nano-beam deflections are governed by a stochastic differential operator with a non-deterministic load. Equations are solved analytically by the Functional Perturbation method (FPM) and validated by Monte-Carlo simulations. It is found that the non-deterministic nature of the nano-beam deflections can be used for in situ sensing applications, in cases of very fast or slow adsorption schemes, for which the microscopic sensors are not sufficient. Geometric non-linear effects can be used in order to achieve fine tuning of the sensitivity.

Original languageEnglish
Pages (from-to)11-17
Number of pages7
JournalProbabilistic Engineering Mechanics
StatePublished - 1 Apr 2012
Externally publishedYes


  • Nano beams
  • Nano sensors
  • Surface stresses

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Civil and Structural Engineering
  • Nuclear Energy and Engineering
  • Aerospace Engineering
  • Condensed Matter Physics
  • Ocean Engineering
  • Mechanical Engineering


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