On the axial vibration of carbon nanotubes with different boundary conditions

Yayli M. Ö.

MICRO & NANO LETTERS, vol.9, no.11, pp.807-811, 2014 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 9 Issue: 11
  • Publication Date: 2014
  • Doi Number: 10.1049/mnl.2014.0398
  • Journal Name: MICRO & NANO LETTERS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.807-811
  • Keywords: vibrations, carbon nanotubes, elasticity, Fourier series, carbon nanotubes, free axial vibration response, arbitrary boundary conditions, nonlocal elasticity theory, Fourier sine series, Stokes transformation, general frequency determinant, rigid boundary conditions, Fourier series expansion, spring parameters, vibration frequencies, dynamic analyses, nanorods, restrained boundary conditions, C, NONLOCAL CONTINUUM-MECHANICS, ELASTICITY, MODELS
  • Bursa Uludag University Affiliated: No


In this reported work, the free axial vibration response of carbon nanotubes (CNTs) with arbitrary boundary conditions is studied based on the non-local elasticity theory. Using Fourier sine series together with Stokes'transformation, the general frequency determinant of CNTs is obtained. The main advantage of this method is its capability of dealing with rigid or restrained boundary conditions. Comparisons between the results of the presented method and previous works in the literature have been performed. Good agreement is obtained when enough terms are included in the Fourier series expansion. The effects of spring parameters on the vibration frequencies are discussed in detail. The proposed analytical method can be utilised for dynamic analyses of nanorods (CNTs) with arbitrary boundary conditions.