Size-dependent behavior of slacked carbon nanotube actuator based on the higher-order strain gradient theory

Iswan Pradiptya, Hassen M. Ouakad*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

20 Citations (Scopus)


This paper proposes to investigate the nonlinear size dependent behavior of electrically actuated carbon nanotube (CNT) based nano-actuator while including the higher-order strain gradient deformation, the geometric nonlinearity due to the von Karman nonlinear strain as well as the slack effect, and the temperature gradient effects. The assumed non-classical beam model adopts some internal material size scale parameters related to the material nanostructures and is capable of interpreting the size effect that the classical continuum beam model is unable to pronounce. The higher-order governing equations of motion and boundary conditions are derived using the so-called extended Hamilton principle. A Galerkin based reduced-order model (ROM) modal decomposition is developed to prescribe the non-classical nanotube mode shape as well as its static behavior under any applied DC actuation load. Results of the static analysis is compared with those obtained by both classical elasticity continuum and strain gradient theories. A Jacobian method is utilized to determine the variation of the natural frequencies of the nanobeam with the DC load as well as the slack level. A thorough parametric study is conducted to study the influences of the size scale dependent parameters, the geometric nonlinearity, the initial curvature, the gate voltage, and the temperature gradient effect on structural behavior of the CNT-based nano-actuator. It is found that the size effect based on the strain gradient deformation has significant influence on the fundamental nanotube natural frequency dispersion. Also, varying this size effect have revealed the offering of numerous possibilities of modes veering and crossing, all shown to be dependent of the strain gradient parameters as well as the CNT slack level.

Original languageEnglish
Pages (from-to)393-415
Number of pages23
JournalInternational Journal of Mechanics and Materials in Design
Issue number3
Publication statusPublished - Sept 1 2018
Externally publishedYes


  • Carbon nanotube
  • Electrostatic
  • Higher-order strain gradient theory
  • Slack
  • Temperature gradient

ASJC Scopus subject areas

  • General Materials Science
  • Mechanics of Materials
  • Mechanical Engineering


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