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

• Published in: Applied mathematics and computation Vol. 217; no. 3; pp. 1246 - 1252
• Main Authors: Shubov, Marianna A., Rojas-Arenaza, Miriam
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier Inc 01.10.2010; Elsevier
• Subjects: 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; 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
• ISSN: 0096-3003; 1873-5649
• DOI: 10.1016/j.amc.2010.04.017

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.