Nonlocal effects on thermal buckling properties of double-walled carbon nanotubes

The thermal buckling properties of double-walled carbon nanotubes (DWCNTs) are studied using nonlocal Timoshenko beam model, including the effects of transverse shear deformation and rotary inertia. The DWCNTs are considered as two nanotube shells coupled through the van der Waals interaction between them. The geometric nonlinearity is taken into account, which arises from the mid-plane stretching. Considering the small-scale effects, the governing equilibrium equations are derived and the critical buckling temperatures under uniform temperature rise are obtained. The results show that the critical buckling temperature can be overestimated by the local beam model if the nonlocal effect is overlooked for long nanotubes. In addition, the effect of shear deformation and rotary inertia on the buckling temperature is more obvious for the higher-order modes. The investigation of the thermal buckling properties of DWCNTs may be used as a useful reference for the application and the design of nanostructures in which DWCNTs act as basic elements.

[1]  Dong Qian,et al.  Mechanics of carbon nanotubes , 2002 .

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

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

[4]  J. Bernholc,et al.  Nanomechanics of carbon tubes: Instabilities beyond linear response. , 1996, Physical review letters.

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

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

[7]  Reza Ansari,et al.  Evaluation of nonlocal parameter in the vibrations of single-walled carbon nanotubes with initial strain , 2010 .

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

[9]  R. Batra,et al.  Continuum models of multi-walled carbon nanotubes , 2007 .

[10]  C. Wang,et al.  Buckling analysis of micro- and nano-rods/tubes based on nonlocal Timoshenko beam theory , 2006 .

[11]  Quan Wang,et al.  A Review on the Application of Nonlocal Elastic Models in Modeling of Carbon Nanotubes and Graphenes , 2012 .

[12]  P. Bernier,et al.  Elastic Properties of C and B x C y N z Composite Nanotubes , 1998 .

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

[14]  Vasyl Harik,et al.  Mechanics of carbon nanotubes: applicability of the continuum-beam models , 2002 .

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

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

[17]  L. Girifalco.  Interaction potential for carbon (C60) molecules , 1991 .

[18]  Flexural Wave Propagation in Single-Walled Carbon Nanotubes , 2008 .

[19]  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 .

[20]  Gangan Prathap,et al.  Buckling Analysis of Carbon Nanotube Based on Nonlocal Timoshenko Beam Theory Using Differential Transform Method , 2010 .

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

[22]  L. Sudak,et al.  Column buckling of multiwalled carbon nanotubes using nonlocal continuum mechanics , 2003 .

[23]  Abdelouahed Tounsi,et al.  Sound wave propagation in single-walled carbon nanotubes with initial axial stress , 2008 .

[24]  A. Rubio,et al.  AB INITIO STRUCTURAL, ELASTIC, AND VIBRATIONAL PROPERTIES OF CARBON NANOTUBES , 1999 .

[25]  A. Maiti,et al.  Structural flexibility of carbon nanotubes , 1996 .

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

[27]  Boris I. Yakobson,et al.  High strain rate fracture and C-chain unraveling in carbon nanotubes , 1997 .

[28]  A. Eringen,et al.  On nonlocal elasticity , 1972 .

[29]  L. Girifalco,et al.  Energy of Cohesion, Compressibility, and the Potential Energy Functions of the Graphite System , 1956 .

[30]  C. Wang,et al.  Sanders shell model for buckling of single-walled carbon nanotubes with small aspect ratio , 2011 .

[31]  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 .

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

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

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

[35]  Vasyl Harik,et al.  Ranges of applicability for the continuum beam model in the mechanics of carbon nanotubes and nanorods , 2001 .

[36]  Volkov,et al.  Acoustoelectric effects in carbon nanotubes , 2000, Physical review letters.

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

[38]  A. Tounsi,et al.  Comment on “Free transverse vibration of the fluid-conveying single-walled carbon nanotube using nonlocal elastic theory” [J. Appl. Phys. 103, 024302 (2008)] , 2009 .

[39]  R. Batra,et al.  Buckling of multiwalled carbon nanotubes under axial compression , 2006 .

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

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

[42]  I. Mechab,et al.  Comment on ‘Vibration analysis of fluid-conveying double-walled carbon nanotubes based on nonlocal elastic theory’ , 2009, Journal of physics. Condensed matter : an Institute of Physics journal.

[43]  C. Siewert,et al.  Sound-wave propagation , 1977 .