Vibration of Single-Walled Carbon Nanotubes by Using Nonlocal Theory

Abstract

The free bending vibration of single-walled carbon nanotubes (SWCNTs) is investigated in the present paper. A continuum approach based on nonlocal theory of beam bending is used for natural frequency computation. Analytical solutions of frequency equations are given for four types boundary conditions: clamped-free (C-F), simply-simply supported (S-S), clamped-simply supported (C-S) and clamped-clamped (C-C). The graphical representations of numerical results are shown for the first case of boundary conditions clamped end -free end.

Vibration analysis of single-walled carbon nanotubes using wave propagation approach

“…At L = 10 to 20 nm, the frequencies decreased rapidly and for L = 20 to 30 nm, the frequencies are moderately parallel. The variations of natural frequencies (Hz) versus length L (nm) also shows a good agreement with those effects assessed by Bocko and Lengvarský (2014). All frequency curves meet at L = 70 nm for the boundary conditions where these curves figured by f Hz L(nm)…”

“…The Timoshenko beam model was used implicating rotatory inertia and shear deformation terms. Bocko and Lengvarský (2014) investigated vibration frequencies of CNTs for four end conditions viz. : clamped-clamped, simply supported-simply supported, clamped-simply supported and clamped-free by using the continuum approach.…”

Carbon Nanotube Structure Vibration Based on Non-local Elasticity

“…In 1977, Eringen [7] improves the relationship between the molecular dynamics (MD) and his theory of non-local elasticity, which are identical. Many researches had been elaborated based on non-local elasticity investigated the vibrational wave propagation of CNT's [8][9][10][11][12][13][14]; in this paper the bending vibration of a pinned-pinned SWCNT has been investigated.…”

Vibration Characteristics of Single-Walled Carbon Nanotubes Based on Nonlocal Elasticity Theory Using Wave Propagation Approach (WPA) Including Chirality

“…The beam model (BM) [30] is used to calculate the associated frequencies and shapes of MWCNT. Bocko and Lengvarský [31] investigate the bending free vibration of SWCNTs with four different boundary conditions. A continuum approach is used for the computation of natural frequency based on nonlocal theory of bending beam.…”