Nonlinear vibration analysis of double-walled carbon nanotubes based on nonlocal elasticity theory

被引：112

作者：

Fang, Bo ^{[1
]}

Zhen, Ya-Xin ^{[1
]}

Zhang, Chi-Ping ^{[2
]}

Tang, Ye ^{[1
]}

机构：

[1] Harbin Inst Technol, Sch Astronaut, Harbin 150001, Peoples R China

[2] Harbin Inst Technol, Dept Math, Harbin 150001, Peoples R China

来源：

APPLIED MATHEMATICAL MODELLING | 2013年 / 37卷 / 03期

关键词：

Geometric nonlinearity; Nonlinear van der Waals forces; Nonlocal elasticity theory; Harmonic balance method; CONVEYING FLUID; DYNAMICAL BEHAVIORS; MODELS;

D O I：

10.1016/j.apm.2012.03.032

中图分类号：

T [工业技术];

学科分类号：

08 ;

摘要：

The nonlinear free vibration of double-walled carbon nanotubes based on the nonlocal elasticity theory is studied in this paper. The nonlinear equations of motion of the double-walled carbon nanotubes are derived by using Euler beam theory and Hamilton principle, with considering the von Karman type geometric nonlinearity and the nonlinear van der Waals forces. The surrounding elastic medium is formulated as the Winkler model. The harmonic balance method and Davidon-Fletcher-Powell method are utilized for the analysis and simulation of the nonlinear vibration. The simulation results show that the nonlocal parameter, aspect ratio and surrounding elastic medium play more important roles in the nonlinear noncoaxial vibration than those in the coaxial vibration of the double-walled carbon nanotubes. The noncoaxial vibration amplitudes of only considering nonlinear van der Waals forces are larger than those of considering both geometric nonlinearity and nonlinear van der Waals forces. (C) 2012 Elsevier Inc. All rights reserved.

引用

页码：1096 / 1107

页数：12

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