Numerical Simulation Of Vibration And Buckling Characteristics For Carbon Nanotubes

Due to their distinctive molecular structure and superior physical, chemical and mechanical properties,Carbon nanotubes(CNTs) possess significant application value. Molecular structure mechanics method can be an effective tool to investigate the mechanical behavior of CNTs. Based on the molecular structure mechanics method, this paper examines characteristics of vibration and buckling problems of CNTs. This paper is structured into three parts.The first part studies the cantilever single-walled carbon nanotubes' natural frequency; investigated the natural frequency of bending vibrations, torsional vibration, longitudinal vibration, radial direction vibration; and obtained the relation graphs between natural frequency and the diameter, and the aspect ratio. The results show that: The diameter presents significant effect on the carbon nanotubes' natural frequency of bending vibration, when the diameter is less than 1.5nm, a great influence on the radial breathing vibration, but does no effect on the nanotubes' natural frequency of torsional vibration, longitudinal vibration; when the aspect ratio of length to diameter increases, in turn, the natural frequency reduces. Different vibration types own different sensitive on aspect ratio. For the radial direction vibration, when the aspect ratio is less than 10, the natural frequency reduces suddenly if the aspect ratio increases; but, when it is greater than 10, the natural frequency is insensitive to the aspect ratio.The second part calculates natural frequency of CNTs by utilizing the relations between natural frequency of vibration and the elastic modulus, and the shear modulus of the single-wall carbon nanotubes, as well as adopting the molecular mechanics method. Then, based on the above frequency, the elastic modulus and the shear modulus of continuum mechanics model were calculated. The result obtained is close to the calculation in the references using other methods. The study shows that elastic modulus increases with the diameter when the tube diameters were smaller than 2nm. For tube diameters lager than 2nm, elastic modulus is almost independent of diameter, which is about 1.005 TPa. Shear modulus of the Armchair carbon nanotubes and Chiral carbon nanotubes increases with the diameter when the tube diameters were smaller than 2nm, while presents no changes when tube diameters were larger than 2nm, which is about 4.91TPa. The shear modulus of the Zigzag carbon nanotubes is always about 4.91TPa no matter how long the diameter is. The third part studies the axial compression elastic buckling of single-wall carbon nanotubes under three different boundary conditions. The effects of nanotubes diameter and aspect ratio on the buckling force are also investigated. The result shows that the critical load of the axial compression elastic buckling of single-wall carbon nanotubes decrease with its aspect ratio increases and linearly increase with its diameter increases.