چكيده به لاتين
Analyzing transverse free vibrations, torsional vibrations and transverse-torsional couple vibrations of single-walled armchair carbon nanotubes under various environmental factors including thermal stresses and viscoelastic substrate using nonlocal elasticity theory is the main goal of this research. In Eringen's theory of nonlocal elasticity, the effect of the small scale of structures is considered and it can be easily included in the equations of motion. Therefore, in this research, Euler-Bernoulli beam theory is combined with nonlocal elasticity theory, and motion equations in different directions are presented in a nonlocal form. More precisely, it can be stated that the analysis of transverse, torsional, and transverse-torsional coupling vibrations of carbon nanotubes using the theory of nonlocal elasticity and taking into account the effect of thermal stress, crack, magnetic force, elastic medium or substrate, damping caused by the viscoelastic substrate or layer and linear and nonlinear geometries is the main goal of this research. In this doctoral thesis, at first, some of the researches related to the vibrations of beams and rods will be introduced. In the following, linear and nonlinear transverse vibrations will be briefly investigated with the effect of several parameters such as thermal stresses, cracks, magnetic force, elastic and viscoelastic substrates or layers, and linear and nonlinear geometries using Euler-Bernoulli beam theory and nonlocal elasticity theory. Then, the necessary equations to investigate the effect of the same parameters plus the damping effect caused by the viscoelastic substrate or layer on the linear and nonlinear torsional vibrations of carbon nanotubes will be created using the relations of rods. Then, the transverse-torsional couple vibrations of carbon nanotubes will be investigated under the effect of factors such as thermal stresses, magnetic force, viscoelastic substrate, and nonlinear geometry. In transverse-torsional couple vibrations, Euler angles are used to obtain the curviture and the angular velocity vectors that are needed in the strain and kinetic energy equations. Then, by applying Hamilton's principle, the transverse and torsional equations of motion that include the coupling terms will be extracted. The obtained results and graphs will be presented and discussed, and at the end, the findings of the current research, innovations of this research and suggestions for future research will be mentioned. Some assumptions have been considered in this research that some of which are: non-dependence of mechanical and magnetic properties of nanotube and viscoelastic substrate on temperature changes, and taking into account the stretching effect of the middle plane and neutral axis. The results indicate that a carbon nanotube exposed to torsional vibrations will simultaneously vibrate in the transverse direction, but the amplitude of transverse oscillations is much lower than the amplitude of torsional oscillations. This causes torsional frequencies in a coupled mode to be less affected by transverse vibrations. But torsional vibrations have a noticeable effect on nonlinear transverse frequencies and vibrations. In general, the results show that in some cases the coupling effect of transverse and torsional vibrations cannot be ignored.
