An Investigation On The Characteristics Of Buckling And Vibration Of Carbon Nanotubes

Carbon nanotubes(CNTs) hold numerous valuable applications due to their distinctive molecular structure and superior physical, chemistical and mechanical properties. Continuum mechanics model can be effectively used to investigate the mechanical behavior of CNTs. Based on the continuum mechanics model, this paper examines some characteristics of CNTs related to buckling and vibration problems utilizting 3-dimentional solid model, beam model and shell model, respectively. The work of this paper is divided into four parts as follows.In the first part, the local buckling and the reduction of bending stiffness during large angle bending of multiwalled carbon nanotubes (MWNTs) are simulated using solid elements of FEM(finite element method), and the nonlinear bending constitution of MWNTs is obtained. Next, a vibrating analysis of CNTs under an alternating electrical field using the beam model of FEM is carried out. The results can be used to explain the phenomenon of a decrease of Young's modulus of MWNTs with the increase of diameter in the resonance experiment measuring Young's modulus of MWNTs, and can provide a reference for further experiments probing the bending behavior of MWNTs.In the second part, an elastic multi-shell model is presented, which considers the van der Waals (vdW) interaction between two adjacent tubes of MWNTs. Based on this model, the torsional buckling of individual MWNTs and the eccentric compressed buckling of MWNTs embedded in an elastic matrix are investigated. The torsional buckling characteristics of individual MWNTs under two different forms of loading are examined, and the explicit expressions of critical torsional load are given. The result shows that the critical torque of MWNTs under torsional load applied on the outermost tube is higher than that of the same MWNTs twisted with the shear forces proportional to the radius of each layer. This conclusion is theoretically valuable for the design of nano-devices based on CNTs, such as nano-actuators and torsional oscillators.In the third part of this paper, based on the rigorous vdW interaction between any two layers of MWNTs, the radial breathing vibration of MWNTs embedded in an elastic matrix and the axial buckling of MWNTs under thermal environments are investigated. The results show that the mechanical characteristic of MWNTs based on the rigorous vdW model is different from that based on the simple vdW interaction between two adjacent tubes. The rigorous vdW interaction is dependent on the change of interlayer spacing and the radii of each layer. The highest radial breathing frequency considering the rigorous vdW interaction is higher than that considering the simple vdW interaction, and the critical axial stress considering the rigorous vdW interaction is higher than that considering the simple vdW interaction.In the fourth part, the coupling vibration of fluid-filled CNTs embedded in a matrix subject to axial load is examined using multi-beam model based on non-local continuum mechanics, where the small scale effect of CNTs is considered. Through some comparisons with the solutions based on the classical continuum mechanics model, the influences of small scale effect on the vibrating frequencies of CNTs under different parameters are obtained, and the applicable range of classical continuum mechanics is pointed out. From some comparisons with the results for CNTs without fluid, the effect of the coupling between the filling fluid and CNTs on the dynamic characteristics of fluid-filled CNTs are studied for various parameters including aspect ratio, density of the fluid, Winkler constant of the matrix, axial load, layer number, mode number, etc.The meaningful results derived in this paper reveal the new features related to the buckling and vibration of CNTs, and are helpful for the design and application of various nano-structures and nano-devices in which CNTs act as basic elements.