The thermal effect on vibration of zigzag single walled carbon nanotubes using nonlocal Timoshenko beam theory

Abstract Based on nonlocal theory of thermal elasticity mechanics, a nonlocal elastic Timoshenko beam model is developed for free vibration analysis of zigzag single-walled carbon nanotube (SWCNT) considering thermal effect. The nonlocal constitutive equations of Eringen are used in the formulations. The equivalent Young’s modulus and shear modulus for zigzag SWCNT are derived using an energy-equivalent model. Results indicate significant dependence of natural frequencies on the temperature change as well as the chirality of zigzag carbon nanotube. These findings are important in mechanical design considerations of devices that use carbon nanotubes.

[1]  Abdelouahed Tounsi,et al.  Effect of small size on wave propagation in double-walled carbon nanotubes under temperature field , 2008 .

[2]  Charles M. Lieber,et al.  Nanobeam Mechanics: Elasticity, Strength, and Toughness of Nanorods and Nanotubes , 1997 .

[3]  A. Waas,et al.  Buckling analysis of carbon nanotubes modeled using nonlocal continuum theories , 2008 .

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

[5]  John Peddieson,et al.  Application of nonlocal continuum models to nanotechnology , 2003 .

[6]  Gui-Rong Liu,et al.  Free transverse vibrations of double-walled carbon nanotubes using a theory of nonlocal elasticity , 2005 .

[7]  A. A. Gusev,et al.  Finite element predictions for the thermoelastic properties of nanotube reinforced polymers , 2004 .

[8]  T. Murmu,et al.  Nonlocal transverse vibration of double-nanobeam-systems , 2010 .

[9]  V. Varadan,et al.  Torsional buckling of carbon nanotubes , 2007 .

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

[11]  S. C. Pradhan,et al.  Thermal effects on the stability of embedded carbon nanotubes , 2010 .

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

[13]  Sondipon Adhikari,et al.  Nonlocal effects in the longitudinal vibration of double-nanorod systems , 2010 .

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

[15]  R. Rajapakse,et al.  Torsional buckling of carbon nanotubes based on nonlocal elasticity shell models , 2010 .

[16]  K. M. Liew,et al.  Nonlocal shell model for elastic wave propagation in single- and double-walled carbon nanotubes , 2008 .

[17]  H. P. Lee,et al.  Dynamic properties of flexural beams using a nonlocal elasticity model , 2006 .

[18]  Tony Murmu,et al.  Thermo-mechanical vibration of a single-walled carbon nanotube embedded in an elastic medium based on nonlocal elasticity theory , 2009 .

[19]  J. N. Reddy,et al.  Nonlocal theories for bending, buckling and vibration of beams , 2007 .

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

[21]  C. Wang,et al.  Exact variational nonlocal stress modeling with asymptotic higher-order strain gradients for nanobeams , 2007 .

[22]  S. Kitipornchai,et al.  Nonlinear free vibration of embedded double-walled carbon nanotubes based on nonlocal Timoshenko beam theory , 2009 .

[23]  M. Oblak,et al.  Thermal vibrational analysis for simply supported beam and clamped beam , 2007 .

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

[25]  J. N. Reddy,et al.  Nonlocal continuum theories of beams for the analysis of carbon nanotubes , 2008 .

[26]  P. Avouris,et al.  Carbon Nanotube Inter- and Intramolecular Logic Gates , 2001 .

[27]  Elias C. Aifantis,et al.  Gradient Deformation Models at Nano, Micro, and Macro Scales , 1999 .

[28]  S. C. Pradhan,et al.  Small-scale effect on the vibration of nonuniform nanocantilever based on nonlocal elasticity theory , 2009 .

[29]  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 .

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

[31]  Kaihui Liu,et al.  Vibration of multi-walled carbon nanotubes with initial axial loading , 2007 .

[32]  T. Ebbesen,et al.  Exceptionally high Young's modulus observed for individual carbon nanotubes , 1996, Nature.

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

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

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

[36]  Xiaodong Wang,et al.  Effects of initial stress on non-coaxial resonance of multi-wall carbon nanotubes , 2006 .

[37]  S. Timoshenko,et al.  LXVI. On the correction for shear of the differential equation for transverse vibrations of prismatic bars , 1921 .

[38]  Q. Han,et al.  Torsional buckling and postbuckling equilibrium path of double-walled carbon nanotubes , 2008 .

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

[40]  Chien Ming Wang,et al.  Timoshenko beam model for vibration analysis of multi-walled carbon nanotubes , 2006 .

[41]  David Hui,et al.  The revolutionary creation of new advanced materials - Carbon nanotube composites , 2002 .

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

[43]  K. M. Liew,et al.  Nonlocal elastic beam models for flexural wave propagation in double-walled carbon nanotubes , 2009 .

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

[45]  K. M. Liew,et al.  Application of nonlocal continuum mechanics to static analysis of micro- and nano-structures , 2007 .

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

[47]  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 .

[48]  Abdelouahed Tounsi,et al.  Nonlocal elasticity effect on column buckling of multiwalled carbon nanotubes under temperature field , 2010 .

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

[50]  P. Lu.  Dynamic analysis of axially prestressed micro/nanobeam structures based on nonlocal beam theory , 2007 .

[51]  Baolin Wang,et al.  Vibrational modes of Timoshenko beams at small scales , 2009 .

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

[53]  Sarp Adali,et al.  Variational principles for multi-walled carbon nanotubes undergoing buckling based on nonlocal elasticity theory , 2008 .

[54]  Xu Han,et al.  TRANSVERSE VIBRATIONS OF DOUBLE-WALLED CARBON NANOTUBES UNDER COMPRESSIVE AXIAL LOAD , 2005 .

[55]  Xi Chen,et al.  Thermal vibration and apparent thermal contraction of single-walled carbon nanotubes , 2006 .

[56]  Abdelouahed Tounsi,et al.  The thermal effect on vibration of single-walled carbon nanotubes using nonlocal Timoshenko beam theory , 2008 .

[57]  F. Ahlers,et al.  Surface acoustic wave driven quantized current transport , 2004 .

[58]  Haiyan Hu,et al.  FLEXURAL WAVE PROPAGATION IN SINGLE-WALLED CARBON NANOTUBES , 2005 .

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