Chemistry Reference
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behavior of CNTs using molecular dynamic simulation under pure short-
ening and twisting.
Ghavamian and Öchsner [43] were analyzed the effect of defects on
the buckling behavior of single and multiwalled CNT based on FE method
considering three most likely atomic defects including impurities, vacan-
cies (carbon vacancy) and introduced disturbance. The results demonstrate
that the existence of any type kinks in CNTs structure, conducts to lower
critical load and lower buckling properties.
Zhang et al. [44] performed an effort on the accuracy of the Euler Ber-
noulli beam model and Donnell shell model and their nonlocal counter-
parts in predicting the buckling strains of single-walled CNTs. Comparing
with MD simulation results, they concluded that the simple Euler-Ber-
noulli beam model is sufficient for predicting the buckling strains of CNTs
with large aspect ratios (i.e., length to diameter ratio L/d > 10). The refined
Timoshenko's beam model for nonlocal beam theory is needed for CNTs
with intermediate aspect ratios (i.e., 8 < L/d < 10). The Donnell thin shell
theory is unable to capture the length dependent critical strains obtained
by MD simulations for CNTs with small aspect ratios (i.e., L/d < 8) and
hence this simple shell theory is unable to model small aspect ratio CNTs.
Tables 9.4-9.6 summarizes some of theoretical simulations of buckling
behavior of CNTs.
9.5.2 VIBRATIONS ANALYSIS
Dynamic mechanical behaviors of CNTs are of importance in various ap-
plications, such as high frequency oscillators and sensors [56]. By adding
CNTs to polymer the fundamental frequencies of CNT reinforced polymer
can be improved remarkably without significant change in the mass den-
sity of material [57]. It is importance indicate that the dynamic mechanical
analysis confirms strong influence of CNTs on the composite damping
properties [58].
The simulation methods of CNT's vibrating were reviewed by Gib-
son et al. [59] in 2007. Considering wide applications of CNTs, receiving
natural frequencies and mode shapes by assembling accurate theoretical
model. For instance, the oscillation frequency is a key property of the reso-
nator when CNTs are used as nano mechanical resonators. Moreover, by
