Nonlinear size-dependent longitudinal vibration of carbon nanotubes embedded in an elastic medium

R. Fernandes, Sami El-Borgi, S. M. Mousavi, J. N. Reddy, A. Mechmoum

Research output: Contribution to journalArticle

28 Citations (Scopus)


In this paper, we study the longitudinal linear and nonlinear free vibration response of a single walled carbon nanotube (CNT) embedded in an elastic medium subjected to different boundary conditions. This formulation is based on a large deformation analysis in which the linear and nonlinear von Kármán strains and their gradient are included in the expression of the strain energy and the velocity and its gradient are taken into account in the expression of the kinetic energy. Therefore, static and kinetic length scales associated with both energies are introduced to model size effects. The governing motion equation along with the boundary conditions are derived using Hamilton's principle. Closed-form solutions for the linear free vibration problem of the embedded CNT rod are first obtained. Then, the nonlinear free vibration response is investigated for various values of length scales using the method of multiple scales.

Original languageEnglish
Pages (from-to)18-25
Number of pages8
JournalPhysica E: Low-Dimensional Systems and Nanostructures
Publication statusPublished - 1 Apr 2017



  • Embedded carbon nanotube rod
  • Linear and nonlinear free vibration
  • Method of Multiple Scales
  • Nonlinear von Kármán strain
  • Strain and velocity gradient theory

ASJC Scopus subject areas

  • Electronic, Optical and Magnetic Materials
  • Atomic and Molecular Physics, and Optics
  • Condensed Matter Physics

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