Buckling Temperature of a Single-Walled Carbon Nanotube Using Nonlocal Timoshenko Beam Model

2010 ◽  
Vol 7 (11) ◽  
pp. 2367-2371 ◽  
Author(s):  
Win-Jin Chang ◽  
Haw-Long Lee
Keyword(s):  
Carbon Nanotube ◽  
Timoshenko Beam ◽  
Beam Model ◽  
Timoshenko Beam Model ◽  
Single Walled Carbon Nanotube ◽  
Single Walled Carbon

scholarly journals Free vibration of a single-walled carbon nanotube based on the nonlocal Timoshenko beam model

2021 ◽  
Vol 37 ◽  
pp. 616-635
Author(s):  
Yu-Chi Su ◽  
Tse-Yu Cho
Keyword(s):  
Carbon Nanotube ◽  
Free Vibration ◽  
Elastic Medium ◽  
Timoshenko Beam ◽  
Slenderness Ratio ◽  
Mode Shapes ◽  
Beam Model ◽  
Timoshenko Beam Model ◽  
Single Walled Carbon Nanotube ◽  
Single Walled Carbon

Abstract Free vibration of a single-walled carbon nanotube (SWCNT) embedded in an elastic medium is studied on the basis of the nonlocal Timoshenko beam model. Influences of the slenderness ratios, the boundary conditions, the atomic structures and the stiffness of the embedded medium on the natural frequencies and mode shapes of SWCNT are examined. The nonlocal effect is significant for the higher modes of SWCNT with a small slenderness ratio embedded in a soft elastic medium, and it softens the SWCNT except for the fundamental frequency of the clamped–free SWCNT.

Chaotic vibrations of a harmonically excited carbon nanotube with consideration of thermomagnetic filed and surface effects

2019 ◽  
Vol 233 (10) ◽  
pp. 3649-3658 ◽  
Author(s):  
H Ramezannejad Azarboni ◽  
SA Edalatpanah
Keyword(s):  
Carbon Nanotube ◽  
Dynamic Response ◽  
Governing Equation ◽  
Surface Effect ◽  
Time History ◽  
Integration Scheme ◽  
Beam Model ◽  
Single Walled Carbon Nanotube ◽  
Single Walled Carbon ◽  
Chaotic Vibrations

In the studies of the dynamic response of carbon nanotubes, the stability, predictable, and unpredictable chaotic vibrations are fundamental characteristics. In this paper, we investigate the chaotic and periodic vibrations of a single-walled carbon nanotube resting on the viscoelastic foundation, based on the nonlocal Euler–Bernoulli beam model. It is assumed that the single-walled carbon nanotube is subjected to an external harmonic excitation. The axial thermomagnetic field and the surface effect on the governing equation of single-walled carbon nanotube are taken into account. We also solve the nonlinear governing equation by using the Galerkin decomposition method along with the fourth-order Rung–Kutta numerical integration scheme. Furthermore, we analyze the effects of amplitude and frequency of excitation on the formation of chaotic and periodic regions using bifurcation diagrams and largest Lyapunov exponents. Moreover, we present the phase portrait, Poincare maps, and time history to observe the periodic and chaotic responses of the system. The results show that the nonlinear dynamic response of single-walled carbon nanotube is much more sensitive to both amplitude and frequency of excitation.

Effects of Axial Load and Elastic Matrix on Flexural Wave Propagation in Nanotube With Nonlocal Timoshenko Beam Model

2012 ◽  
Vol 134 (3) ◽  
Author(s):  
Yi-Ze Wang ◽  
Feng-Ming Li ◽  
Kikuo Kishimoto
Keyword(s):  
Wave Propagation ◽  
Carbon Nanotube ◽  
Timoshenko Beam ◽  
Axial Load ◽  
Elastic Matrix ◽  
Wave Number ◽  
Flexural Wave ◽  
Beam Model ◽  
Timoshenko Beam Model ◽  
Flexural Wave Propagation

In this paper, the effects of the axial load and the elastic matrix on the flexural wave in the carbon nanotube are studied. Based on the nonlocal continuum theory and the Timoshenko beam model, the equation of the flexural wave motion is derived. The dispersion relation between the frequency and the wave number is illustrated. The characteristics of the flexural wave propagation in the carbon nanotube embedded in the elastic matrix with the axial load are analyzed. The wave frequency and the phase velocity are presented with different wave numbers. Furthermore, the small scale effects on the wave properties are discussed.

Sign in / Sign up

Export Citation Format

Share Document