Elastic beam models for dynamics of multiwall carbon nanotubes

Since the discovery of carbon nanotubes (CNTs) in 1991, extensive research related to the nanotubes in the fields of physics, material science and mechanical and electrical engineering has been carried out. Most potential applications of CNTs are heavily based on a thorough understanding of their mechanical behavior. For this reason, numerous experiments and atomistic simulations have been conducted to study mechanical behavior of CNTs. Since these methods meet many difficulties, solid mechanics models offer an effective alternative method for CNTs. In this dissertation, several elastic beam models, which account for the interlayer van der Waals interaction and radial displacements, have been developed to study dynamics of multiwall CNTs (MWNTs), such as free vibration, sound wave propagation and flow-induced instability.; First, using a multiple-Euler-beam model, non-coaxial vibration of MWNTs is predicted for the first time in the literature. This novel phenomenon, first predicted by the present model, has been confirmed by more recent molecular dynamic simulations. Moreover, the multiple-Euler-beam model is used to study wave propagation in MWNTs. Our results show that sound wave propagation in MWNTs is essentially coaxial only when the frequency is much below a critical frequency.; When the aspect ratio of MWNTs is about or below 20, the wavelength of the higher-order modes is just few times the outermost diameter. In this case, rotary inertia and shear deformation would have a significant effect on dynamics of CNTs. For this reason, a multiple Timoshenko-beam model is developed to study vibration of short CNTs. The results predicted have been found to be in good agreement with more recent molecular dynamics simulations for wavelengths down to about 1nm. These results suggest that elastic beam models would be valid for CNTs even at very small scale provided some subtle factors can be further taken into account.; Finally, the influence of internal moving fluid on free vibration and flow-induced structural instability of CNTs is studied based on a simple Euler-beam model. The results indicate that internal moving fluid could substantially affect resonant frequencies especially for longer suspended CNTs of larger innermost radius at higher flow velocity, and the critical flow velocity for structural instability in some cases could fall within the range of practical significance.