Double-wall nanotube as vibrational system: Mathematical approach

作者：Shubov Marianna A^*; Rojas Arenaza Miriam

来源：Mathematical Methods in the Applied Sciences, 2008, 31(16): 1887-1904.

DOI：10.1002/mma.1001

• carbon nanotubes
• Timoshenko system
• dynamics generator
• matrix differential operator
• compact resolvent

In this paper, we present a recently developed mathematical model for short double-wall carbon nanotubes. The model is governed by a system of four hyperbolic equations representing the two Timoshenko beams coupled through the Van der Waals forces. The system is equipped with a four-parameter family of the boundary conditions and can be reduced to an evolution equation. This equation defines a strongly continuous semi-group. Spectral properties of the semi-group generator are presented in the paper. We show that it is an unbounded non-selfadjoint operator with compact resolvent. Moreover, this operator is a relatively compact perturbation of a certain selfadjoint operator.

• 出版日期2008-11-10