Nonlinear vibration of embedded single-walled carbon nanotube with geometrical imperfection under harmonic load based on nonlocal Timoshenko beam theory  

作　　者：王博 邓子辰 张凯 

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)》2013年第3期269-280,共12页应用数学和力学（英文版）

基　　金：Project supported by the National Basic Research Program of China (No. 2011CB610300);the National Natural Science Foundation of China (Nos. 10972182, 11172239, and 10902089);the 111 Project of China (No. B07050);the Ph. D. Programs Foundation of Ministry of Education 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. CX201224)

摘　　要：Based on the nonlocal continuum theory, the nonlinear vibration of an embedded single-walled carbon nanotube （SWCNT） subjected to a harmonic load is in- vestigated. In the present study, the SWCNT is assumed to be a curved beam, which is unlike previous similar work. Firstly, the governing equations of motion are derived by the Hamilton principle, meanwhile, the Galerkin approach is carried out to convert the nonlinear integral-differential equation into a second-order nonlinear ordinary differ- ential equation. Then, the precise integration method based on the local linearzation is appropriately designed for solving the above dynamic equations. Besides, the numerical example is presented, the effects of the nonlocal parameters, the elastic medium constants, the waviness ratios, and the material lengths on the dynamic response are analyzed. The results show that the above mentioned effects have influences on the dynamic behavior of the SWCNT.Based on the nonlocal continuum theory, the nonlinear vibration of an embedded single-walled carbon nanotube （SWCNT） subjected to a harmonic load is in- vestigated. In the present study, the SWCNT is assumed to be a curved beam, which is unlike previous similar work. Firstly, the governing equations of motion are derived by the Hamilton principle, meanwhile, the Galerkin approach is carried out to convert the nonlinear integral-differential equation into a second-order nonlinear ordinary differ- ential equation. Then, the precise integration method based on the local linearzation is appropriately designed for solving the above dynamic equations. Besides, the numerical example is presented, the effects of the nonlocal parameters, the elastic medium constants, the waviness ratios, and the material lengths on the dynamic response are analyzed. The results show that the above mentioned effects have influences on the dynamic behavior of the SWCNT.

关 键 词：embedded curved carbon nanotube nonlocal Timoshenko beam theory nonlinear vibration harmonic load precise integrator method 

分 类 号：O175[理学—数学]