Dynamic Instability of Vibrating Carbon Nanotubes Near Small Layers of Graphite Sheets Based on Nonlocal Continuum Elasticity

2016 ◽  
Vol 57 (1) ◽  
Keyword(s):  
Carbon Nanotubes ◽  
Dynamic Instability ◽  
Nonlocal Continuum ◽  
Graphite Sheets ◽  
Continuum Elasticity

Buckling analysis of carbon nanotubes modeled using nonlocal continuum theories

2008 ◽  
Vol 103 (7) ◽  
pp. 073521 ◽  
Author(s):  
Devesh Kumar ◽  
Christian Heinrich ◽  
Anthony M. Waas
Keyword(s):  
Carbon Nanotubes ◽  
Buckling Analysis ◽  
Nonlocal Continuum ◽  
Continuum Theories

scholarly journals Dynamic instability of a compound nanocomposite shell

2021 ◽  
Vol 27 (5) ◽  
pp. 60-70
Author(s):  
N.H. Sakhno ◽  
◽  
K.V. Avramov ◽  
B.V. Uspensky ◽  
◽  
...  
Keyword(s):  
Carbon Nanotubes ◽  
Finite Element Analysis ◽  
Finite Element ◽  
Cylindrical Shell ◽  
Supersonic Flow ◽  
Uniform Distribution ◽  
Critical Pressure ◽  
Natural Frequencies ◽  
Dynamic Instability ◽  
Element Analysis

Free oscillations and dynamic instability due to supersonic airflow pressure are investigated in a functional-gradient compound composite conical-cylindrical shell made of a carbon nanotubes-reinforced material. Nanocomposite materials with a linear distribution of the volumetric fraction of nanotubes over the thickness are considered. Extended mixture rule is used to estimate nanocomposite’s mechanical characteristics. A high-order shear deformation theory is used to represent the shell deformation. The assumed-mode technique, along with a Rayleigh-Ritz method, is applied to obtain the equations of the structure motion. To analyze the compound structure dynamics, a new system of piecewise basic functions is suggested. The pressure of a supersonic flow on the shell is obtained by using the piston theory. An example of the dynamic analysis of a nanocomposite conical-cylindrical shell in the supersonic gas flow is considered. The results of its modal analysis using the Rayleigh-Ritz technique are close to the natural frequencies of the shell obtained by finite element analysis. In this case, finite element analysis can only be used for shells made of material with a uniform distribution of nanotubes over the thickness. The dependence of the natural frequencies of a compound shell on the ratio of the lengths of the conical and cylindrical parts is studied. The dependence of the critical pressure of a supersonic flow on the Mach numbers and the type of carbon nanotubes reinforcement is investigated. Shells with a concentration of nanotubes predominantly near the outer and inner surfaces are characterized by higher values of natural frequencies and critical pressure than the shells with a uniform distribution of nanotubes or with a predominant concentration of nanotubes inside the shell.

“Y Contrast” of Single Shell Carbon Nanotubes: Determination Of Young’s Modulus by Observing Thermal Vibrations

1999 ◽  
Vol 5 (S2) ◽  
pp. 676-677
Author(s):  
M.M.J. Treacy ◽  
A. Krishnan ◽  
E. Dujardin ◽  
P.N. Yianilos ◽  
T.W. Ebbesen
Keyword(s):  
Carbon Nanotubes ◽  
Elastic Modulus ◽  
Fiber Reinforced Composites ◽  
Reinforced Composites ◽  
Multiwalled Nanotubes ◽  
Carbon Molecules ◽  
Thermal Vibrations ◽  
Graphite Sheets ◽  
Single Shell

Single shell carbon nanotubes are members of the Fullerene family of carbon molecules. Typically, single shell carbon nanotubes measure about 0.7 — 3 nm in diameter and are usually several microns in length. Structurally, they can be thought of as narrow graphite sheets that have been bent around the long axis and joined at opposite edges to form long seamless hollow shells of carbon. Typically, a hemispheroidal cap that contains exactly six 5-rings terminates each end, as shown in Figure 1.Graphite is known to have an in-plane elastic modulus of ∼1 TPa, one of the highest values known. Consequently, it is expected that single shell nanotubes should be very stiff — a fact that makes them potentially useful in fiber reinforced composites. However, because of their small size, it is impractical to measure their stiffness directly by conventional mechanical means. Recently, we demonstrated that thermal vibrations in freestanding multiwalled nanotubes could be used to estimate their stiffness [1].

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