VIBRATIONAL ANALYSIS OF CARBON NANOTUBES AND GRAPHENE SHEETS USING MOLECULAR STRUCTURAL MECHANICS APPROACH

Abstract In this article, the vibrational properties of two kinds of single-layered graphene sheets and single-wall carbon nanotubes (SWCNT) are studied. The simulations are carried out for two types of zigzag carbon nanotubes (6,0), (12,0), armchair carbon nanotubes (4,4), (6,6) and zigzag and armchair graphene sheets with free-fixed and fixed–fixed end conditions. Fundamental frequency is determined by means of molecular structural mechanics approach. In this approach, carbon nanotubes (CNTs) and grapheme sheets are considered as space frames. By constructing equality between strain energies of each element in structural mechanics and potential energies of each bond, equivalent space frames can be achieved. Carbon atoms are considered as concentrated masses placed in beam joints (bond junctions). Results are presented as diagrams stating fundamental frequencies of nanotubes and graphene sheets with respect to aspect ratios. The results indicate that fundamental frequency decreases as aspect ratio increases. So it is preferred to use nanotubes and graphene sheets with lower aspect ratios for dynamic applications in order to prevent resonance and dynamic damage. Fundamental frequency of nanotubes is larger than that of graphene sheets. The results are in good agreement with results of previous researches.

[1]  R. Naghdabadi,et al.  Nanoscale vibrational analysis of a multi-layered graphene sheet embedded in an elastic medium , 2005 .

[2]  Lin Wang,et al.  Dynamical behaviors of double-walled carbon nanotubes conveying fluid accounting for the role of small length scale , 2009 .

[3]  R. Gibson,et al.  VIBRATIONS OF CARBON NANOTUBES AND THEIR COMPOSITES: A REVIEW , 2007 .

[4]  William A. Goddard,et al.  Energetics, structure, mechanical and vibrational properties of single-walled carbon nanotubes , 1998 .

[5]  Hashem Rafii-Tabar,et al.  Computational modelling of the flow of viscous fluids in carbon nanotubes , 2007 .

[6]  Yan Yan,et al.  Dynamical behaviors of fluid-conveyed multi-walled carbon nanotubes , 2009 .

[7]  Ning Hu,et al.  Prediction of buckling characteristics of carbon nanotubes , 2007 .

[8]  A. Vafai,et al.  Application of Single-Layered Graphene Sheets as Mass Sensors and Atomistic Dust Detectors , 2007 .

[9]  William A. Goddard,et al.  Handbook of Nanoscience, Engineering, and Technology , 2002 .

[10]  M. Ghasemi-Nejhad,et al.  Analytical and numerical techniques to predict carbon nanotubes properties , 2006 .

[11]  A. Mioduchowski,et al.  VIBRATION OF AN EMBEDDED MULTIWALL CARBON NANOTUBE , 2003 .

[12]  Harold S. Park,et al.  Nano Mechanics and Materials: Theory, Multiscale Methods and Applications , 2006 .

[13]  Lin Wang,et al.  The thermal effect on vibration and instability of carbon nanotubes conveying fluid , 2008 .

[14]  A. Mioduchowski,et al.  Flow-induced flutter instability of cantilever carbon nanotubes , 2006 .

[15]  M. S. de Vries,et al.  Cobalt-catalysed growth of carbon nanotubes with single-atomic-layer walls , 1993, Nature.

[16]  Tsu-Wei Chou,et al.  Modeling of elastic buckling of carbon nanotubes by molecular structural mechanics approach , 2004 .

[17]  Chunyu Li,et al.  A STRUCTURAL MECHANICS APPROACH FOR THE ANALYSIS OF CARBON NANOTUBES , 2003 .

[18]  S. Iijima.  Helical microtubules of graphitic carbon , 1991, Nature.

[19]  A. Mioduchowski,et al.  Vibration and instability of carbon nanotubes conveying fluid , 2005 .

[20]  H. P. Lee,et al.  Application of nonlocal beam models for carbon nanotubes , 2007 .

[21]  Lin Wang,et al.  On vibration and instability of carbon nanotubes conveying fluid , 2008 .

[22]  Massoud Mir,et al.  A numerical study of vibrational properties of single-walled carbon nanotubes , 2008 .

[23]  Win-Jin Chang,et al.  Vibration analysis of a viscous-fluid-conveying single-walled carbon nanotube embedded in an elastic medium , 2009 .