The Computing Of Young's Modulus And Interlayer Slips For Carbon Nanotube

Since carbon nanotube was discovered, it has been become a hotspot in modern science field. Carbon nanotube possessed excellent mechanical properties; so many researchers do a lot of experiments and theory analysis. This dissertation focuses on the Young's modulus and interlayer slips of carbon nanotube respectively. The former, we rationally explain the special phenomenon that Young's modulus behaves in experiment using the method of multiple scales in perturbation analysis. The latter, we treat Van Der Waals force as the spring and receive the curve of interlayer slips of double-walled, tri-walled and four-walled carbon nanotube.The research scope and the major outputs obtained in this dissertation are as follows.(1) We give an overview on the the researches of carbon nanotube; summarizing the achievements and developments of the study of carbon nanotube home and abroad in recent years; introducing basic methods for carbon nanotube's mechanics characteristic in theory research.(2) Basing on the special phenomenons that Young's modulus behaves in bend resonance experiment, we utilize the method of multiple scales in perturbation analysis and explain the reason. The carbon nanotube is regarded as a cantilever beam. We establish the motion equation using elasticity mechanics and obtain the curve of frequency-response and averaged equation in polar form of carbon nanotube. At last, we receive the ratio of effective Young's modulus and real Young's modulus. This result agrees well with the experimental phenomenon observed by Poncharal(3) About the effect of Van Der Waals force on interlayer slips, we firstly regard the double-walled carbon nanotube as the cantilever beam. Meanwhile, we discuss the selection of thickness of carbon nanotube. The Euler-Bernoulli equations of every layer are established and the solutions are obtained by using the elasticity mechanics theory. Based on the solutions, the every layer relation of the deflections and the length of double-walled carbon nanotube under external force are obtained(4) Basis on the double-walled carbon nanotube, we compute the intrelayer slips of tri-walled carbon nanotube and four-walled carbon nanotube. The result indicates that the effect of Van Der Waals force cannot be neglected at lower length-radii ratio.