The Study Of Dynamic Stability Of Carbon Nanotube Under Small-Scale Effect

Carbon nanotube possesses extremely high elastic modulus and toughness. Its elastic modulus can be up to about 1 TPa and elastic strain can be up to 5%, at most 12%. So the application foreground of carbon nanotubes will be great. On the aspect of engineering utilization, the special electronic, photophysical and mechanical characteristics of carbon nanotube make it very sensitive to its structural feature and deformation behavior. Because of this, the application result of carbon nanotube proub has a great relationship with the deformation character of carbon nanotube under external forces.In this paper, two dynamic stability models of carbon nanotube under small-scale effect are formulated respectively, based on non-local classical shell theory and non-local Donnell shell theory. Also the related dynamic stability basic equations of carbon nanotubes are derived. The solutions of the basic equations with the condition that axial periodic force equals zero are get in the real situation examples. Then the dynamic stability critical frequencies of carbon nanotube under the situation that axial periodic force does not equal zero are solved from the basic equations too. A kind of effective method for multi-walled carbon nanotubes is utilized to solve the dynamic stability problem of multi-walled carbon nanotubes. The solution of effective method and the accurate solution which considered van der Waals force are compared and discussed.Through the comparison of solutions based on the two different theories, the parameter condition under which non-local Donnell shell theory can replace non-local classical shell theory are get. Through the analysis of calculation results, we can find that when the axial periodic force equals zero, the small-scale effect on dynamic critical frequencies of carbon nanotube will gradually decrease with the increase of length-diameter ratio L / Rof carbon nanotube. When the amplitude of dynamic axial force increases proportionally, dynamic critical frequencies of carbon nanotube will basically increase proportionally too. Through the comparison between the calculation results of non-local Donnell shell theory and non-local classical shell theory, we can find that the result curve of these two theories are mainly the same. So for the study of dynamic stability of carbon nanotube, the calculation method of non-local Donnell shell theory can replace the calculation method of non-local classical shell theory in certain conditions, which can simplify the course of calculation and save time.This paper studies the dynamic stability calculation method and results of sngle-walled carbon nanotube and multi-walled carbon nanoTubes based on different non-local shell models. The study results possess certain theoretical and engineering application values for the application of carbon nanotube as probes in different engineering aspects.