MODELING OF VIBRATIONS IN CARBON NANOTUBES

In the present paper the theoretical modeling of eigenfrequency extraction of single- and multi-walled carbon nanotubes has been described. The knowledge of the vibrational behavior of the carbon nanotubes is very important in the case of possible using them in the nanoelectronics, nanocomposites and nanodevices. Generally, the models have been divided into continuum, atomic and structural-atomic models. In the continuum modeling review a beam and shell models of carbon nanotubes have been analyzed. From the use of the beam model the flexural eigenfrequencies and modes can be obtained whereas from the shell model the radial, axial and circumferential eigenfrequencies and modes can be observed. From the engineering point of view using the atomic models has been not sufficient because of the scale and time limitation and in fact these models have been used only in the short carbon nanotubes analysis. Nowadays in the dynamic analysis of nanostructures the structuralatomic approaches basing on the continuum mechanics and molecular dynamics have been developed. The geometry of nanotube and the interatomic interactions have been taken into account in the structural- atomic models whereas in the continuum models these effects have been neglected. The typical eigenfrequencies of nanotubes are on the level of teraherz values and depends on the boundary conditions. The noncoaxial vibration of multi-wall carbon nanotubes has been emphasized.