Effect of the Chirality on Critical Buckling Temperature of Zigzag Single-walled Carbon Nanotubes Using the Nonlocal Continuum Theory

Abstract

In this article, the thermal buckling properties of a zigzag single-walled carbon nanotube (SWCNT) with both chirality and small scale effects are studied. Based on the nonlocal continuum theory and the Timoshenko beam model, the governing equations are derived and the critical buckling temperatures are obtained. The equivalent Young's modulus and shear modulus for zigzag SWCNT are derived using an energy-equivalent model. The results show that the critical buckling temperature can be overestimated by the local beam model if the small-scale effect is overlooked for long nanotubes. In addition, significant dependence of the critical buckling temperatures on the chirality of zigzag carbon nanotube is confirmed. These findings are important in mechanical design considerations of devices that use carbon nanotubes.

An Investigation on the Characteristics of Bending, Buckling and Vibration of Nanobeams via Nonlocal Beam Theory

“…Earlier works on the vibration of nonlocal beams did not consider the effects of transverse shear deformation and rotary inertia [Lu et al (2006); Xu (2006)]. Many researchers have applied the nonlocal elasticity concept for the bending, buckling and vibration analyses of beam-like elements in micro-or nanoelectromechanical devices [Sudak (2003); Zhang et al (2004); Zhang et al (2005); Zhang et al (2006); Heireche et al (2008); Semmah et al (2013)]. It should be noted that the Euler-Bernoulli beam theory (EBT) is only applicable for slender beams where the shear deformation effect is negligible.…”

Free vibration modelling of Single-walled Carbon Nanotubes using the Differential Quadrature Method

“…Two equation of motion are obtained: longitudinal and transverse inertia, only transverse vibration equation containig the deflection w(x,t) is the aim of this study, expressed as : (8) By introducing the surrounding elastic medium law:…”

“…Considerable efforts has been devoted to invesitigate and understand the mechanical properties of CNT's using molecular dynamics [4] which need much time and high efficient computational resources, and Quantum mechanics by using the theory of non-local elsticity wich has been introduced by Eringen [5], this theory could investigate the dynamic behavior of nanoscale structures such as CNT's using the well-known beams models : Temoshenko beam and Euler-Bernoulli beam, Many studies have been done to understand the mechanical behaviour of CNT's [6,7,8,9,10].…”

Vibration analysis of orthotropic circular and elliptical nano-plates embedded in elastic medium based on nonlocal Mindlin plate theory and using Galerkin method

“…Since vibration analysis of nanostructures is an important issue for efficient design and use of many Nanoelectro-mechanical systems (NEMS) such as sensors and actuators, present study determines the vibration characteristics of embedded orthotropic circular and elliptical nano-plates based on the nonlocal theory of elasticity. There are already different studies on the use of nonlocal continuum modeling in vibration and dynamic analysis of Carbon nano-tubes (CNTs) and nano-beams [18][19][20][21][22][23][24][25][26][27][28][29]. Similar to nano-beams and nanotubes, nano-plates possess superior mechanical properties [30][31][32][33][34].…”