Nonlinear vibration analysis of double-walled carbon nanotubes based on nonlocal elasticity theory

Abstract The nonlinear free vibration of double-walled carbon nanotubes based on the nonlocal elasticity theory is studied in this paper. The nonlinear equations of motion of the double-walled carbon nanotubes are derived by using Euler beam theory and Hamilton principle, with considering the von Karman type geometric nonlinearity and the nonlinear van der Waals forces. The surrounding elastic medium is formulated as the Winkler model. The harmonic balance method and Davidon–Fletcher–Powell method are utilized for the analysis and simulation of the nonlinear vibration. The simulation results show that the nonlocal parameter, aspect ratio and surrounding elastic medium play more important roles in the nonlinear noncoaxial vibration than those in the coaxial vibration of the double-walled carbon nanotubes. The noncoaxial vibration amplitudes of only considering nonlinear van der Waals forces are larger than those of considering both geometric nonlinearity and nonlinear van der Waals forces.

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

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

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

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

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

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

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

[8]  Lin Wang,et al.  VIBRATION AND INSTABILITY ANALYSIS OF TUBULAR NANO- AND MICRO-BEAMS CONVEYING FLUID USING NONLOCAL ELASTIC THEORY , 2009 .

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

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

[11]  Paul Calvert,et al.  Nanotube composites: A recipe for strength , 1999, Nature.

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

[13]  C. Q. Ru,et al.  Column buckling of multiwalled carbon nanotubes with interlayer radial displacements , 2000 .

[14]  Hui‐Shen Shen,et al.  Buckling and postbuckling of single-walled carbon nanotubes under combined axial compression and torsion in thermal environments , 2007 .

[15]  E. Snow,et al.  Single-wall carbon nanotube atomic force microscope probes , 2002 .

[16]  N. Aluru,et al.  Calculation of pull-in voltages for carbon-nanotube-based nanoelectromechanical switches , 2002 .

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

[18]  Jae Eun Jang,et al.  Carbon nanotube electron emitters with a gated structure using backside exposure processes , 2002 .

[19]  Lixiang Zhang,et al.  Dynamical mode transitions of simply supported double-walled carbon nanotubes based on an elastic shell model , 2008 .

[20]  S. Adali,et al.  Variational principles for multi-walled carbon nanotubes undergoing non-linear vibrations by semi-inverse method , 2009 .

[21]  R. Bi,et al.  Nonlinear dynamic instability of double-walled carbon nanotubes under periodic excitation , 2009 .

[22]  S. Tans,et al.  Room-temperature transistor based on a single carbon nanotube , 1998, Nature.

[23]  Xiaoqiao He,et al.  Flow-induced instability of double-walled carbon nanotubes based on an elastic shell model , 2007 .

[24]  Xiaoqiao He,et al.  Dynamic behavior of triple-walled carbon nanotubes conveying fluid , 2009 .

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

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

[27]  Xiaoqiao He,et al.  ANALYSIS OF NONLINEAR VIBRATIONS OF DOUBLE-WALLED CARBON NANOTUBES CONVEYING FLUID , 2009 .

[28]  M. Rasekh,et al.  Nonlinear vibration and stability analysis of axially loaded embedded carbon nanotubes conveying fluid , 2009 .

[29]  Yiming Fu,et al.  Analysis of nonlinear vibration for embedded carbon nanotubes , 2006 .

[30]  Q. Han,et al.  The thermal effect on axially compressed buckling of a double-walled carbon nanotube , 2007 .

[31]  C. Q. Ru,et al.  Vibration of a double-walled carbon nanotube aroused by nonlinear intertube van der Waals forces , 2006 .

[32]  E. Aifantis,et al.  Vibrations of Double-Walled Carbon Nanotubes With Different Boundary Conditions Between Inner and Outer Tubes , 2008 .

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

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