Vibration of Carbon Nanotubes with Defects and Their Composites: Reduced-Order Model and Damping
Open Access
- Author:
- Hudson, Robert Benjamin
- Graduate Program:
- Mechanical Engineering
- Degree:
- Doctor of Philosophy
- Document Type:
- Dissertation
- Date of Defense:
- June 21, 2018
- Committee Members:
- Alok Sinha, Dissertation Advisor/Co-Advisor
Alok Sinha, Committee Chair/Co-Chair
Reuben H Kraft, Committee Member
Adrianus C Van Duin, Committee Member
Mauricio Terrones Maldonado, Outside Member - Keywords:
- carbon nanotube
defect
vibration
phonon
composite
order reduction - Abstract:
- Carbon nanotubes, and the composites made from them, promise properties unrivaled by more traditional materials. To fully understand, predict, and tune those properties, a plethora of technical and theoretical challenges must be overcome. One such challenge is to find a technique with which to predict the dynamic behavior of carbon nanotubes containing defects. The dynamics of pristine carbon nanotubes are relatively well understood, but their analysis relies heavily on the periodic nature of their structure. When that structure is altered, these analyses are no longer valid. A new model is therefore needed that can incorporate these defects but is still computationally efficient enough to be coupled with a model of a composite matrix and have its vibrational characteristics analyzed under a range of conditions. In this dissertation, a model of a metallic matrix carbon nanotube composite is developed by first examining the dynamics of two well-known damping models --- the microslip and macroslip models. This analysis focuses on the implications of substituting the simpler macroslip models in place of the more mathematically complex microslip model. Specifically, the ability of these two damping models to predict the stability of a system subjected to self-exciting aeroelastic interactions (flutter) is considered. It is discovered that the microslip damper, while capable of stabilizing this system within a certain range of amplitudes, will always dissipate less energy than an equivalent macroslip damper vibrating at the same amplitude. The energy dissipation/amplitude relationships developed here are later employed to characterize the nature of the damping provided by a carbon nanotube composite. This study of generalized damping models is followed by the application of order reduction methods to defect-bearing carbon nanotubes. First, isotope and Stone-Wales defects are considered, and two well-known order reduction methods, modal domain analysis and modified modal domain analysis, are adapted for use on these atomic-scale systems. These models are demonstrated to predict the natural frequencies and normal modes of the defect-bearing carbon nanotubes with high accuracy, while greatly decreasing the computational costs associated with these calculations. Furthermore, this analysis reveals that even defects as ubiquitous and insignificant as the variation of isotopes within a carbon nanotube can produce large changes in the mode shapes of the resulting structure. The third and final defect that is considered is a multi-vacancy defect, which results in an even greater change to the structure of a carbon nanotube. As this type of defect removes atoms from the system, previous methods of order reduction are not applicable to it. Instead, a novel method of order reduction is developed, called modal domain reduction that, by combining elements of modal domain analysis and dynamic reduction with a new technique for handling the decrease in the number of degrees of freedom in the system, permits the vibrational properties of the system to be calculated efficiently and accurately. Finally, these order reduction techniques for individual carbon nanotubes are incorporated into a model of an aluminum matrix carbon nanotube composite. The composite itself is represented by a reduced-order model, created by applying Guyan, or static, reduction to the full-order matrix model. The interactions between the carbon nanotube and the matrix are calculated using the Lennard-Jones model. Several models of composites, some with pristine carbon nanotubes and other with carbon nanotubes containing a Stone-Wales or a multi-vacancy defect, are subjected to cyclic loading to determine their damping properties. The validity of these models is established through comparisons to published experimental results, and the nature of the observed damping is characterized in terms of the microslip and macroslip damping.