Open AccessOn the axial vibration of carbon nanotubes with different boundary conditions
Author(s) -
Yayli Mustafa Özgür
Publication year - 2014
Publication title -
micro and nano letters
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.25
H-Index - 31
ISSN - 1750-0443
DOI - 10.1049/mnl.2014.0398
Subject(s) - fourier sine and cosine series , vibration , carbon nanotube , fourier series , boundary value problem , fourier transform , materials science , elasticity (physics) , sine , boundary (topology) , mathematical analysis , fourier analysis , mathematics , physics , composite material , geometry , acoustics , fractional fourier transform
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.