چكيده به لاتين
Vibrations and buckling of spinning nano-tubes are two effective phenomena in the operation of nano-machines. Therefore in this thesis, exact methods are developed to analyze vibrations and buckling of spinning nanotubes. For this purpose, equations of continuum mechanics are combined with non-classical elasticity theories. In continuum field, three groups of geometrical equations as beam theories, thin shell theory and first order shear deformation shell theory are used. Also, in order to considering size effects, nonlocal elasticity and modified couple stress theories are added to the mentioned continuum theories. Combining these two categories of relations, has created various equations of motion which all of them are solved using an exact straight forward mathematical method. Additionally, present problem is modeled in molecular dynamics simulation’s software and its results are compared with mathematical model’s results to analyze validity and accuracy of the formulations. At first, Results of single wall carbon nanotubes show that nonlocal first order shear deformation theory is the most reliable and accurate method. So, these equations are generalized to the multi-layer structure and behavior of spinning multi-layer carbon nanotube is obtained based on this theory. Also, in this study, Van der Wales force is applied in the equations of multilayer nanotubes using a pressure distribution equation between the layers. During this study, effects of changing geometrical and size dependent parameters on the frequency and buckling load of nanotube are investigated for all of the mathematical models in different figures and tables.
