Vibrational frequency distribution for nonconservative model of double-walled carbon nanotube

The paper presents the mathematical results for a double-walled carbon nanotube model with nonconservative boundary conditions, given in the form of two Timoshenko beams coupled through a distributed Van Der Waals force. The system is clamped at the left end and subject to a four-parameter family of...

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Published inApplied mathematics and computation Vol. 217; no. 3; pp. 1246 - 1252
Main Authors Shubov, Marianna A., Rojas-Arenaza, Miriam
Format Journal Article
LanguageEnglish
Published Amsterdam Elsevier Inc 01.10.2010
Elsevier
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Online AccessGet full text
ISSN0096-3003
1873-5649
DOI10.1016/j.amc.2010.04.017

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Abstract The paper presents the mathematical results for a double-walled carbon nanotube model with nonconservative boundary conditions, given in the form of two Timoshenko beams coupled through a distributed Van Der Waals force. The system is clamped at the left end and subject to a four-parameter family of dynamical boundary conditions at the right end. We also present the four-branch vibrational spectrum of the system. All the results are purely analytical; they will be complemented by numerical simulations in a forthcoming work.
AbstractList The paper presents the mathematical results for a double-walled carbon nanotube model with nonconservative boundary conditions, given in the form of two Timoshenko beams coupled through a distributed Van Der Waals force. The system is clamped at the left end and subject to a four-parameter family of dynamical boundary conditions at the right end. We also present the four-branch vibrational spectrum of the system. All the results are purely analytical; they will be complemented by numerical simulations in a forthcoming work.
Author Rojas-Arenaza, Miriam
Shubov, Marianna A.
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Cites_doi 10.1103/PhysRevLett.91.145504
10.3233/ASY-2010-0991
10.1063/1.1898445
10.1063/1.2141648
10.57262/die/1369056045
10.1103/PhysRevB.65.235402
10.1088/2058-7058/13/6/25
10.1002/mma.1001
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Issue 3
Keywords Carbon nanotube
Eigenvalue asymptotic representation
Matrix differential operator
Timoshenko beam model
Transcendental equation
Eigenvector
Numerical linear algebra
Eigenvalue
Boundary condition
Non linear equation
Numerical analysis
Applied mathematics
Algebraic equation
Distribution function
Numerical simulation
Differential operator
Language English
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Snippet The paper presents the mathematical results for a double-walled carbon nanotube model with nonconservative boundary conditions, given in the form of two...
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SubjectTerms Boundary conditions
Carbon nanotube
Carbon nanotubes
Dynamical systems
Dynamics
Eigenvalue asymptotic representation
Exact sciences and technology
Frequency distribution
Mathematical analysis
Mathematical models
Mathematics
Matrix differential operator
Nonlinear algebraic and transcendental equations
Numerical analysis
Numerical analysis. Scientific computation
Numerical linear algebra
Operator theory
Ordinary differential equations
Sciences and techniques of general use
Timoshenko beam model
Van der Waals forces
Title Vibrational frequency distribution for nonconservative model of double-walled carbon nanotube
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