Keywords: carbon nanotubes, mechanical properties, simulation methods, mechanical vibration, mode shapes, natural frequencies, zig-zag and arm-chair structures.

The structural components are becoming smaller and smaller from macro-to-micro-to-nano scales due to the enhanced properties of nano-scale structures. Additionally, the applications of nano-size structures are growing at a very rapid rate and the need for new methods to analyze and design with them requires considerable attention. These reasons have caused a kind of explosion in the research carried out in nano-technology throughout this world and the interest to grow further appears to remain very high.

Carbon nanotubes (CNTs) have been discovered in 1991 and found to possess extraordinary mechanical, thermal, and electronic properties. Since then a large number of researchers began investigating their behaviours from many different aspects. Manufacturing procedures were improved, properties of the carbon nanotubes were studied both experimentally and through mathematical modeling and in doing so many new applications of these in the fields of science, engineering and medicine were uncovered. Improvements are being made continuously on controlling the size and atomic structures of CNTs so that their mechanical properties can be enhanced. To understand the properties further, many experimental techniques such as atomic force microscopy, high resolution electron microscopy, and scanning electron microscopy have been used. Also, theoretical techniques such as, molecular dynamics, continuum shell and beam modeling, nonlocal theory of elasticity, and finite element methods have been used for the analysis of carbon nanotubes. The plate theories have been applied in modeling graphitic sheets in general to get into the details of the advanced elastic theories and imperfections of atomic structures. In this paper, a brief survey of the subject matter from a vibrational aspect is presented including some basic characterization of the carbon nanotubes and graphitic sheets.

Different molecular dynamic methods have been suggested to simulate the static, vibration and buckling behavior of carbon nanotubes. These techniques, beside their exceptional accuracy, are just able to model very short-duration phenomena and also, they cannot be used for systems with more than several hundred particles. Some researchers have used shell theories in their analyses. This approach has serious limitations with regards to defining the thickness and Young’s modulus of the shell. Therefore, treating a CNT as an elastic shell continuum may not be fully justified. Simplified models based on classical and shear deformable beam theories have also been used by many. Owing to the simplicity of beam theories, this analytical technique has relatively less computational and mathematical rigor. However, beam theories, like the shell theories, cannot model the atomic structure of carbon nano-structures in great detail. Moreover, beam models are unable to simulate cross-sectional deformation of carbon nanotubes. This paper provides some of the very basic concepts to researchers with a background in engineering mechanics.

purchase the full-text of this paper (price £20)

go to the previous paper
go to the next paper
return to the table of contents
return to Computational Technology Reviews
purchase this volume (price £80 +P&P)