Nonlinear free vibration of embedded double-walled carbon nanotubes based on nonlocal Timoshenko beam theory

Liaoliang Ke; Yang Xiang; Jie Yang; Sritawat Kitipornchai

doi:10.1016/j.commatsci.2009.09.002

Nonlinear free vibration of embedded double-walled carbon nanotubes based on nonlocal Timoshenko beam theory

Liaoliang Ke, Yang Xiang, Jie Yang, Sritawat Kitipornchai

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258 Citations (Scopus)

Abstract

Nonlinear free vibration of embedded double-walled carbon nanotubes (DWNTs) is studied in this paper based on EringenÃƒÂ¢Ã¢"šÂ¬Ã¢"žÂ¢s nonlocal elasticity theory and von KÃƒÆ’Ã†'Ãƒ"šÃ‚Â¡rmÃƒÆ’Ã†'Ãƒ"šÃ‚Â¡n geometric nonlinearity. The effects of the transverse shear deformation and rotary inertia are considered within the framework of Timoshenko beam theory. The surrounding elastic medium is described as the Winkler model characterized by the spring. The governing equations and boundary conditions are derived by using the HamiltonÃƒÂ¢Ã¢"šÂ¬Ã¢"žÂ¢s principle. The differential quadrature (DQ) method is employed to discretize the nonlinear governing equations, which are then solved by a direct iterative method to obtain the nonlinear vibration frequencies of nonlocal DWNTs with different boundary conditions. A detailed parametric study is conducted to investigate the influences of nonlocal parameter, length of the tubes, spring constant and end supports on the nonlinear free vibration characteristics of DWNTs.

Original language	English
Pages (from-to)	409-417
Number of pages	9
Journal	Computational Materials Science
Volume	47
Issue number	2
DOIs	https://doi.org/10.1016/j.commatsci.2009.09.002
Publication status	Published - 2009

Keywords

differential equations
elasticity
molecular dynamics
nanotubes
vibration

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10.1016/j.commatsci.2009.09.002

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title = "Nonlinear free vibration of embedded double-walled carbon nanotubes based on nonlocal Timoshenko beam theory",

abstract = "Nonlinear free vibration of embedded double-walled carbon nanotubes (DWNTs) is studied in this paper based on Eringen{\~A}ƒ{\^A}¢{\~A}¢{"}{\v s}{\^A}¬{\~A}¢{"}{\v z}{\^A}¢s nonlocal elasticity theory and von K{\~A}ƒ{\AE}{\textquoteright}{\~A}†'{\~A}ƒ{"}{\v s}{\~A}‚{\^A}¡rm{\~A}ƒ{\AE}{\textquoteright}{\~A}†'{\~A}ƒ{"}{\v s}{\~A}‚{\^A}¡n geometric nonlinearity. The effects of the transverse shear deformation and rotary inertia are considered within the framework of Timoshenko beam theory. The surrounding elastic medium is described as the Winkler model characterized by the spring. The governing equations and boundary conditions are derived by using the Hamilton{\~A}ƒ{\^A}¢{\~A}¢{"}{\v s}{\^A}¬{\~A}¢{"}{\v z}{\^A}¢s principle. The differential quadrature (DQ) method is employed to discretize the nonlinear governing equations, which are then solved by a direct iterative method to obtain the nonlinear vibration frequencies of nonlocal DWNTs with different boundary conditions. A detailed parametric study is conducted to investigate the influences of nonlocal parameter, length of the tubes, spring constant and end supports on the nonlinear free vibration characteristics of DWNTs.",

keywords = "differential equations, elasticity, molecular dynamics, nanotubes, vibration",

author = "Liaoliang Ke and Yang Xiang and Jie Yang and Sritawat Kitipornchai",

year = "2009",

doi = "10.1016/j.commatsci.2009.09.002",

language = "English",

volume = "47",

pages = "409--417",

journal = "Computational Materials Science",

issn = "0927-0256",

publisher = "Elsevier B.V.",

number = "2",

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T1 - Nonlinear free vibration of embedded double-walled carbon nanotubes based on nonlocal Timoshenko beam theory

AU - Ke, Liaoliang

AU - Xiang, Yang

AU - Yang, Jie

AU - Kitipornchai, Sritawat

PY - 2009

Y1 - 2009

N2 - Nonlinear free vibration of embedded double-walled carbon nanotubes (DWNTs) is studied in this paper based on EringenÃƒÂ¢Ã¢"šÂ¬Ã¢"žÂ¢s nonlocal elasticity theory and von KÃƒÆ’Ã†'Ãƒ"šÃ‚Â¡rmÃƒÆ’Ã†'Ãƒ"šÃ‚Â¡n geometric nonlinearity. The effects of the transverse shear deformation and rotary inertia are considered within the framework of Timoshenko beam theory. The surrounding elastic medium is described as the Winkler model characterized by the spring. The governing equations and boundary conditions are derived by using the HamiltonÃƒÂ¢Ã¢"šÂ¬Ã¢"žÂ¢s principle. The differential quadrature (DQ) method is employed to discretize the nonlinear governing equations, which are then solved by a direct iterative method to obtain the nonlinear vibration frequencies of nonlocal DWNTs with different boundary conditions. A detailed parametric study is conducted to investigate the influences of nonlocal parameter, length of the tubes, spring constant and end supports on the nonlinear free vibration characteristics of DWNTs.

AB - Nonlinear free vibration of embedded double-walled carbon nanotubes (DWNTs) is studied in this paper based on EringenÃƒÂ¢Ã¢"šÂ¬Ã¢"žÂ¢s nonlocal elasticity theory and von KÃƒÆ’Ã†'Ãƒ"šÃ‚Â¡rmÃƒÆ’Ã†'Ãƒ"šÃ‚Â¡n geometric nonlinearity. The effects of the transverse shear deformation and rotary inertia are considered within the framework of Timoshenko beam theory. The surrounding elastic medium is described as the Winkler model characterized by the spring. The governing equations and boundary conditions are derived by using the HamiltonÃƒÂ¢Ã¢"šÂ¬Ã¢"žÂ¢s principle. The differential quadrature (DQ) method is employed to discretize the nonlinear governing equations, which are then solved by a direct iterative method to obtain the nonlinear vibration frequencies of nonlocal DWNTs with different boundary conditions. A detailed parametric study is conducted to investigate the influences of nonlocal parameter, length of the tubes, spring constant and end supports on the nonlinear free vibration characteristics of DWNTs.

KW - differential equations

KW - elasticity

KW - molecular dynamics

KW - nanotubes

KW - vibration

UR - http://handle.uws.edu.au:8081/1959.7/502232

U2 - 10.1016/j.commatsci.2009.09.002

DO - 10.1016/j.commatsci.2009.09.002

M3 - Article

SN - 0927-0256

VL - 47

SP - 409

EP - 417

JO - Computational Materials Science

JF - Computational Materials Science

IS - 2

ER -

Nonlinear free vibration of embedded double-walled carbon nanotubes based on nonlocal Timoshenko beam theory

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