Variational principles for buckling and vibration of MWCNTs modeled by strain gradient theory  

作　　者：徐晓建 邓子辰 

机构地区：[1]Department of Engineering Mechanics,Northwestern Polytechnical University [2]State Key Laboratory of Structural Analysis for Industrial Equipment,Dalian University of Technology

出　　处：《Applied Mathematics and Mechanics(English Edition)》2014年第9期1115-1128,共14页应用数学和力学（英文版）

基　　金：supported by the National Basic Research Program of China(973 Program)(No.2011CB610300);the 111 Project(No.B07050);the National Natural Science Foundation of China(Nos.10972182,11172239,and 10902089);the Doctoral Program Foundation of Education Ministry of China(No.20106102110019);the Open Foundation of State Key Laboratory of Structural Analysis of Industrial Equipment(No.GZ0802);the Doctorate Foundation of Northwestern Polytechnical University(No.CX201111)

摘　　要：Variational principles for the buckling and vibration of multi-walled carbon nanotubes （MWCNTs） are established with the aid of the semi-inverse method. They are used to derive the natural and geometric boundary conditions coupled by small scale parameters. Hamilton＇s principle and Rayleigh＇s quotient for the buckling and vibration of the MWCNTs are given. The Rayleigh-Ritz method is used to study the buckling and vibration of the single-walled carbon nanotubes （SWCNTs） and double-walled carbon nanotubes （DWCNTs） with three typical boundary conditions. The numerical results reveal that the small scale parameter, aspect ratio, and boundary conditions have a profound effect on the buckling and vibration of the SWCNTs and DWCNTs.Variational principles for the buckling and vibration of multi-walled carbon nanotubes （MWCNTs） are established with the aid of the semi-inverse method. They are used to derive the natural and geometric boundary conditions coupled by small scale parameters. Hamilton＇s principle and Rayleigh＇s quotient for the buckling and vibration of the MWCNTs are given. The Rayleigh-Ritz method is used to study the buckling and vibration of the single-walled carbon nanotubes （SWCNTs） and double-walled carbon nanotubes （DWCNTs） with three typical boundary conditions. The numerical results reveal that the small scale parameter, aspect ratio, and boundary conditions have a profound effect on the buckling and vibration of the SWCNTs and DWCNTs.

关 键 词：variational principle strain gradient theory BUCKLING VIBRATION carbonnanotube 

分 类 号：TB383.1[一般工业技术—材料科学与工程]