Open AccessAnalysis of nonlinear dynamic stability of single‐walled carbon nanotubes in thermal environments
Author(s) -
Fu Yiming,
Zhong Jun
Publication year - 2014
Publication title -
micro and nano letters
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.25
H-Index - 31
ISSN - 1750-0443
DOI - 10.1049/mnl.2013.0590
Subject(s) - galerkin method , nonlinear system , harmonic balance , partial differential equation , boundary value problem , carbon nanotube , ordinary differential equation , timoshenko beam theory , thermal , mechanics , stability (learning theory) , materials science , euler's formula , differential equation , mathematical analysis , beam (structure) , mathematics , physics , thermodynamics , computer science , composite material , quantum mechanics , machine learning , optics
Based on the non‐local Euler beam theory, the nonlinear dynamic stability of single‐walled carbon nanotubes (SWCNTs) embedded in an elastic medium including the thermal effects is presented. The nonlinear dynamic equations and the boundary conditions of the SWCNTs are obtained by using the Hamilton variation principle. By adopting the Galerkin procedure, the governing nonlinear partial differential equation is converted into a nonlinear ordinary differential equation, and then the incremental harmonic balance method is applied to obtain the principal unstable regions of the SWCNTs. In the numerical examples, the effects of the thermal loads, the non‐local parameters and the elastic medium on the nonlinear dynamic stability, respectively, are discussed.