Static and dynamic response of CNT nanobeam using nonlocal strain and velocity gradient theory

Hassen M. Ouakad, Sami El-Borgi*, S. Mahmoud Mousavi, Michael I. Friswell

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

30 Citations (Scopus)


This paper examines the length-scale effect on the nonlinear response of an electrically actuated Carbon Nanotube (CNT) based nano-actuator using a nonlocal strain and velocity gradient (NSVG) theory. The nano-actuator is modeled within the framework of a doubly-clamped Euler–Bernoulli beam which accounts for the nonlinear von-Karman strain and the electric actuating forcing. The NSVG theory includes three length-scale parameters which describe two completely different size-dependent phenomena, namely, the inter-atomic long-range force and the nano-structure deformation mechanisms. Hamilton's principle is employed to obtain the equation of motion of the nonlinear nanobeam in addition to its respective classical and non-classical boundary conditions. The differential quadrature method (DQM) is used to discretize the governing equations. The key aim of this research is to numerically investigate the influence of the nonlocal parameter and the strain and velocity gradient parameters on the nonlinear structural behavior of the carbon nanotube based nanobeam. It is found that these three length-scale parameters can largely impact the performance of the CNT based nano-actuator and qualitatively alter its resultant response. The main goal of this investigation is to understand the highly nonlinear response of these miniature structures to improve their overall performance.

Original languageEnglish
Pages (from-to)207-222
Number of pages16
JournalApplied Mathematical Modelling
Publication statusPublished - Oct 2018
Externally publishedYes


  • Carbon nanotube (CNT) Euler–Bernoulli nanobeam
  • Differential quadrature method (DQM)
  • Material length scales
  • Nonlocal strain and velocity gradient theory
  • Static and eigenvalue problem

ASJC Scopus subject areas

  • Modelling and Simulation
  • Applied Mathematics


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