A nonlocal Levinson beam model for free vibration analysis of zigzag single-walled carbon nanotubes including thermal effects

Abstract A nonlocal Levinson beam model is developed to study the free vibrations of a zigzag single-walled carbon nanotube (SWCNT) in thermal environments. The equivalent Young’s modulus and shear modulus for a zigzag SWCNT are derived using an energy-equivalent model. The present study illustrates that the vibration characteristics of an SWCNT are strongly dependent on the temperature change and on the chirality of a zigzag carbon nanotube. The investigation of the chirality and temperature effects on free vibration of carbon nanotubes may be used as a useful reference for the application and the design of nanoelectronic and nanodrive devices, nano-oscillators, and nanosensors, in which carbon nanotubes act as basic elements.

[1]  Bin Liu,et al.  Thermal Expansion of Single Wall Carbon Nanotubes , 2004 .

[2]  T. Yamabe.  Recent development of carbon nanotube , 1995 .

[3]  Quan Wang,et al.  Scale effect on wave propagation of double-walled carbon nanotubes , 2006 .

[4]  M. Şi̇mşek.  Forced vibration of an embedded single-walled carbon nanotube traversed by a moving load using nonlocal Timoshenko beam theory , 2011 .

[5]  M. Dresselhaus,et al.  Phonon modes in carbon nanotubules , 1993 .

[6]  A. C. Eringen,et al.  Nonlocal polar elastic continua , 1972 .

[7]  Tony Murmu,et al.  Buckling analysis of a single-walled carbon nanotube embedded in an elastic medium based on nonlocal elasticity and Timoshenko beam theory and using DQM , 2009 .

[8]  H. Qiang,et al.  Investigation of axially compressed buckling of a multi-walled carbon nanotube under temperature field , 2007 .

[9]  C. Wang,et al.  The constitutive relation and small scale parameter of nonlocal continuum mechanics for modelling carbon nanotubes , 2007, Nanotechnology.

[10]  Haosen Yang,et al.  Torsional buckling of multi-wall carbon nanotubes embedded in an elastic medium , 2007 .

[11]  Tony Murmu,et al.  SMALL SCALE EFFECT ON THE BUCKLING OF SINGLE-LAYERED GRAPHENE SHEETS UNDER BIAXIAL COMPRESSION VIA NONLOCAL CONTINUUM MECHANICS , 2009 .

[12]  Abdelouahed Tounsi,et al.  Deformation of short composite beam using refined theories , 2008 .

[13]  K. M. Liew,et al.  Buckling analysis of multi-walled carbon nanotubes: a continuum model accounting for van der Waals interaction , 2005 .

[14]  S. C. Pradhan.  Buckling of single layer graphene sheet based on nonlocal elasticity and higher order shear deformation theory , 2009 .

[15]  K. M. Liew,et al.  Analysis of wave propagation in carbon nanotubes via elastic shell theories , 2007 .

[16]  Vijay K. Varadan,et al.  Small scale effect on elastic buckling of carbon nanotubes with nonlocal continuum models , 2006 .

[17]  Abdelouahed Tounsi,et al.  Sound wave propagation in single-walled carbon nanotubes using nonlocal elasticity , 2008 .

[18]  A. Mioduchowski,et al.  Sound wave propagation in multiwall carbon nanotubes , 2003 .

[19]  R. Superfine,et al.  Bending and buckling of carbon nanotubes under large strain , 1997, Nature.

[20]  M. Levinson,et al.  A new rectangular beam theory , 1981 .

[21]  A. Eringen,et al.  Nonlocal Continuum Field Theories , 2002 .

[22]  C. Ru,et al.  Timoshenko-beam effects on transverse wave propagation in carbon nanotubes , 2004 .

[23]  M. Şi̇mşek,et al.  VIBRATION ANALYSIS OF A SINGLE-WALLED CARBON NANOTUBE UNDER ACTION OF A MOVING HARMONIC LOAD BASED ON NONLOCAL ELASTICITY THEORY , 2010 .

[24]  P Kim,et al.  ナノチューブナノピンセット | 文献情報 | J-GLOBAL 科学技術総合リンクセンター , 1999 .

[25]  Q. Han,et al.  Buckling Analysis of Multiwalled Carbon Nanotubes Under Torsional Load Coupling With Temperature Change , 2006 .

[26]  C. Dekker,et al.  Logic Circuits with Carbon Nanotube Transistors , 2001, Science.

[27]  M. Balkanski,et al.  ELASTIC PROPERTIES OF SINGLE-WALLED CARBON NANOTUBES , 2000 .

[28]  Vijay K. Varadan,et al.  Vibration of carbon nanotubes studied using nonlocal continuum mechanics , 2006 .

[29]  P. Kollman,et al.  A Second Generation Force Field for the Simulation of Proteins, Nucleic Acids, and Organic Molecules , 1995 .

[30]  M. Şi̇mşek,et al.  Nonlocal effects in the forced vibration of an elastically connected double-carbon nanotube system under a moving nanoparticle , 2011 .

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

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

[33]  Satish Nagarajaiah,et al.  Nanotube film based on single-wall carbon nanotubes for strain sensing , 2004 .

[34]  A. Tounsi,et al.  Scale effect on wave propagation of double-walled carbon nanotubes with initial axial loading , 2008, Nanotechnology.

[35]  Kong,et al.  Nanotube molecular wires as chemical sensors , 2000, Science.

[36]  Quan Wang,et al.  Wave propagation in carbon nanotubes via nonlocal continuum mechanics , 2005 .

[37]  A. Leung,et al.  An energy-equivalent model on studying the mechanical properties of single-walled carbon nanotubes , 2006 .

[38]  H. Dai,et al.  Nanotubes as nanoprobes in scanning probe microscopy , 1996, Nature.

[39]  A. Eringen.  On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves , 1983 .