NONLINEAR VIBRATION AND BENDING INSTABILITY OF A SINGLE-WALLED CARBON NANOTUBE USING NONLOCAL ELASTIC BEAM THEORY

2011 ◽  
Vol 10 (03) ◽  
pp. 447-453 ◽  
Author(s):  
I. MEHDIPOUR ◽  
P. SOLTANI ◽  
D. D. GANJI ◽  
A. FARSHIDIANFAR
Keyword(s):  
Carbon Nanotube ◽  
Nonlocal Parameter ◽  
Elastic Beam ◽  
Beam Theory ◽  
Special Kind ◽  
Nonlocal Theory ◽  
Length Ratio ◽  
Single Walled Carbon Nanotube ◽  
Single Walled Carbon ◽  
Bending Modulus

Due to the nonlocal Euler–Bernoulli elastic beam theory, the effects of rippling deformation on the bending modulus and the structural bending instability of a single-walled carbon nanotube (SWCNT) are investigated. The nonlinear vibrational model of a cantilevered SWCNT is solved using the perturbation method of multiscales. The nonlinear resonant frequency and the associated effective bending modulus of the carbon nanotube (CNT) are derived analytically. The effects of the nonlocal parameter, the external harmonic force, and the diameter-to-length ratio on the effective bending modulus are discussed widely. Moreover, the model can predict special kind of structural instability due to the rippling deformation called rippling instability. The results show that the nonlocal theory forecasts larger values for the effective bending modulus compared with the classical beam theory, especially for the stubby CNTs. Meanwhile, the rippling instability threshold will move to the higher values of the diameter-to-length ratio based on the nonlocal beam theory comparing with the local ones.

Free and forced axial vibration of single walled carbon nanotube under linear and harmonic concentrated forces based on nonlocal theory

2020 ◽  
Vol 34 (08) ◽  
pp. 2050067 ◽  
Author(s):  
Farshad Khosravi ◽  
Seyyed Amirhosein Hosseini ◽  
Hasti Hayati
Keyword(s):  
Carbon Nanotube ◽  
Natural Frequencies ◽  
Constitutive Relations ◽  
Nonlocal Parameter ◽  
Nonlocal Theory ◽  
Axial Vibration ◽  
Single Walled Carbon Nanotube ◽  
Single Walled Carbon ◽  
Concentrated Forces

The aim of this paper is to investigate the free and forced axial vibrations under the two various linear and harmonic axial concentrated forces in zigzag single-walled carbon nanotube (SWCNT). Two different boundary conditions, namely clamped–clamped and clamped-free, are established. Eringen’s nonlocal elasticity is employed to justify the nonlocal behavior of constitutive relations. The governing equation and the associated boundary condition are derived based on Hamilton’s principle. In order to solve the derived equation numerically, the assumed modes method is utilized. In the free axial vibration section, the first three natural frequencies are obtained for the various values of the nonlocal parameter. The results are in good agreement in comparison with another study. The fundamental natural frequencies with respect to the nonlocal parameter of the case study as a semiconducting nanotube with boron nitride nanotube (BNNT) as a semiconducting nanotube and SWCNT (5,5) as a metallic nanotube are compared. The effects of the nonlocal parameter, thickness and ratio of the excitation-to-natural frequencies overtime on dimensional and nondimensional axial displacements are studied.

Nonlinear Dynamic Analysis of Single-Walled Carbon Nanotube Based Mass Sensor

2011 ◽  
Vol 2 (4) ◽  
Author(s):  
Anand Y. Joshi ◽  
Satish C. Sharma ◽  
S. P. Harsha
Keyword(s):  
Carbon Nanotubes ◽  
Carbon Nanotube ◽  
Dynamic Response ◽  
Beam Theory ◽  
Central Plane ◽  
Mass Sensor ◽  
Poincaré Maps ◽  
Single Walled Carbon Nanotube ◽  
Poincare Maps ◽  
Single Walled Carbon

In previous studies, experimentally measured resonance frequencies of carbon nanotubes have been used along with classical beam theory for straight beams. However, it is found that these carbon nanotubes are not straight, and that they have some significant surface deviation associated with them. This paper deals with the nonlinear vibration analysis of a wavy single-walled carbon nanotube based mass sensor, which is doubly clamped at a source and a drain. Nonlinear oscillations of a single-walled carbon nanotube excited harmonically near its primary resonance are considered. The carbon nanotube is excited by the addition of an excitation force. The modeling is carried out using the elastic continuum beam theory concept, which involves stretching of the central plane and phenomenological damping. This model takes into account the existence of waviness in carbon nanotubes. The equation of motion involves two nonlinear terms due to the curved geometry and the stretching of the central plane. The dynamic response of the carbon nanotube based mass sensor is analyzed in the context of the time response, Poincaré maps, and fast Fourier transformation diagrams. The results show the appearance of instability and chaos in the dynamic response as the mass on carbon nanotube is changed. Period doubling and mechanism of intermittency have been observed as the routes to chaos. The appearance of regions of periodic, subharmonic, and chaotic behavior is observed to be strongly dependent on mass and the geometric imperfections of carbon nanotube. Poincaré maps and frequency spectra are used to elucidate and to illustrate the diversity of the system behavior.

A Finite Element Analysis of Single-Walled Carbon Nanotube Deformation

2011 ◽  
Vol 78 (3) ◽  
Author(s):  
Chao Fang ◽  
Ajeet Kumar ◽  
Subrata Mukherjee
Keyword(s):  
Carbon Nanotubes ◽  
Finite Element ◽  
Carbon Nanotube ◽  
Dominant Mode ◽  
Element Analysis ◽  
Single Walled Carbon Nanotube ◽  
Single Walled Carbon ◽  
Bending Modulus ◽  
Cosserat Rod ◽  
Rod Model

Chandraseker et al. (2009, “An Atomistic-Continuum Cosserat Rod Model of Carbon Nanotubes,” J. Mech. Phys. Solids, 57, pp. 932–958), in a 2009 JMPS paper, proposed an atomistic-continuum model, based on Cosserat rod theory, for deformation of a single-walled carbon nanotube (SWNT). This model allows extension and twist, as well as shear and bending (in two directions) of a SWNT. This present paper proposes a finite element method (FEM) implementation of the above mentioned Cosserat rod model for a SWNT, subjected, in general, to axial and transverse loads, as well as bending moments and torques. The resulting FEM implementation includes both geometric and material nonlinearities. Numerical results for several examples are presented in this paper. Finally, a recent experimental paper on SWNTs (Xu, Y-.Q., et al., 2009, “Bending and Twisting of Suspended Single-Walled Carbon Nanotubes in Solution,” ASAP Nano Lett., 9, pp. 1609–1614) is revisited herein. It is pointed out in the present paper that Xu et al. attempted to determine the bending stiffness of a SWNT from an experiment in which the dominant mode of deformation is stretching, not bending. (Their model, Euler–Bernoulli beam bending, should perhaps have been extended to include stretching.) As a result, their measured deflection is nearly insensitive to the bending modulus.

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