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TECHNICAL PAPERS

Terahertz Vibration of Short Carbon Nanotubes Modeled as Timoshenko Beams

[+] Author and Article Information
J. Yoon, C. Q. Ru, A. Mioduchowski

Department of Mechanical Engineering, University of Alberta, Edmonton T6G 2G8, Canada

J. Appl. Mech 72(1), 10-17 (Feb 01, 2005) (8 pages) doi:10.1115/1.1795814 History: Received April 16, 2003; Revised May 15, 2004; Online February 01, 2005
Copyright © 2005 by ASME
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References

Rueckers,  T., Kim,  K., Joselevich,  E., Tseng,  G. T., Cheung,  C. L., and Lieber,  C. M., 2000, “Carbon Nanotube-Based Nonvolatile Random Access Memory for Molecular Computing,” Science, 289, 94–97.
Postma,  H. W. C., Teepen,  T., Yao,  Z., Grifoni,  M., and Dekker,  C., 2000, “Carbon Nanotube Single-Electron Transistors at Room Temperature,” Science, 293, 76–79.
Roschier,  L., Tarkiainen,  R., Ahlskog,  M., Paalanen,  M., and Hakonen,  P., 2001, “Multiwalled Carbon Nanotubes as Ultrasensitive Electrometers,” Appl. Phys. Lett., 78, 3295–3297.
Ahlskog,  M., Hakonen,  P., Paalanen,  M., Roschier,  L., and Tarkiainen,  R., 2001, “Multiwalled Carbon Nanotubes as Building Blocks in Nanoelectronics,” J. Low Temp. Phys., 124, 335–352.
Dai,  H., Hafner,  J. H., Rinzler,  A. G., Colbert,  D. T., and Smalley,  R. E., 1996, “Nanotubes as Nanoprobes in Scanning Probe Microscopy,” Nature (London), 384, 147–150.
Kim,  P., and Lieber,  C. M., 1999, “Nanotube Nanotweezers,” Science, 286, 2148–50.
Cumings,  J., and Zettel,  A., 2000, “Low-Friction Nanoscale Linear Bearing Realized From Multiwall Carbon Nanotubes,” Science, 289, 602–604.
Thostenson,  E. T., Ren,  Z., and Chou,  T. W., 2001, “Advances in the Science and Technology of Carbon Nanotubes and Their Composites: A Review,” Compos. Sci. Technol., 61, 1899–1912.
Qian,  D., Wagner,  G. J., Liu,  W. K., Yu,  M. F., and Ruoff,  R. S., 2002, “Mechanics of Carbon Nanotubes,” Appl. Mech. Rev., 55, 495–533.
Ru, C. Q., 2004, “Elastic Models For Carbon Nanotubes,” Encyclopedia of Nanoscience and Nanotechnology, Vol. 2, H. S. Nalwa, ed., American Scientific Publishers, Stevenson Ranch, CA, pp. 731–744.
Wong,  E. W., Sheehan,  P. E., and Lieber,  C. M., 1997, “Nanobeam Mechanics: Elasticity, Strength, and Toughness of Nanorods and Nanotubes,” Science, 277, 1971–75.
Treacy,  M. M. J., Ebbesen,  T. W., and Gibson,  J. M., 1996, “Exceptonally High Young’s Modulus Observed for Individual Carbon Nanotubes,” Nature (London), 381, 678–680.
Poncharal,  P., Wang,  Z. L., Ugarte,  D., and de Heer,  W. A., 1999, “Electrostatic Deflections and Electromechanical Resonances of Carbon Nanotubes,” Science, 283, 1513–16.
Harik,  V. M., 2001, “Ranges of Applicability for the Continuum Beam Model in the Mechanics of Carbon Nanotubes and Nanorods,” Solid State Commun., 120, 331–335.
Ru,  C. Q., 2000, “Column Buckling of Multiwalled Carbon Nanotubes With Interlayer Radial Displacements,” Phys. Rev. B, 62, 16962–67.
Yoon,  J., Ru,  C. Q., and Mioduchowski,  A., 2002, “Non-Coaxial Resonance of an Isolated Multiwall Carbon Nanotube,” Phys. Rev. B, 66, 233–402.
Yoon,  J., Ru,  C. Q., and Mioduchowski,  A., 2003, “Vibration of Embedded Multiwall Carbon Nanotubes,” Compos. Sci. Technol., 63, 1533–1542.
Dequesnes,  M., Rotkin,  S. V., and Aluru,  N. R., 2002, “Calculation of Pull-In Voltages for Carbon-Nanotube-Based Nanoelectromechanical Switches,” Nanotechnology, 13, 120–131.
Snow,  E. S., Campbell,  P. M., and Novak,  J. P., 2002, “Singlewall Carbon Nanotube Atomic Force Microscope Probes,” Appl. Phys. Lett., 80, 2002–4.
Ishikawa,  M., Yoshimura,  M., and Ueda,  K., 2002, “A Study of Friction by Carbon Nanotube Tip,” Appl. Surf. Sci., 188, 456–459.
Zhao,  Y., Ma,  C. C., Chen,  G., and Jiang,  Q., 2003, “Energy Dissipation Mechanisms in Carbon Nanotube Oscillators,” Phys. Rev. Lett., 91, 175–504.
Li,  C., and Chou,  T. W., 2004, “Vibrational Behaviors of Multiwalled-Carbon-Nanotube-Based Nanomechanical Resonators,” Appl. Phys. Lett., 84, 121–123.
Timoshenko, S., 1974, Vibration Problems in Engineering, Wiley, New York.
Rao,  S. S., 1974, “Natural Vibrations of Systems of Elastically Connected Timoshenko Beams,” J. Acoust. Soc. Am., 55, 1232–1237.
Cowper,  G. R., 1996, “The Shear Coefficient in Timoshenko’s Beam Theory,” ASME J. Appl. Mech., 33, 335–340.
Hutchinson,  J. R., 2001, “Shear Coefficients for Timoshenko Beam Theory,” ASME J. Appl. Mech., 68, 87–92.
Smith,  B. W., and Luzzi,  D. E., 2000, “Formation Mechanism of Fullerene Peapods and Coaxial Tubes: A Path for Large Scale Synthesis,” Chem. Phys. Lett., 321, 169–174.
Saito,  R., Matsuo,  R., Kimura,  T., Dresselhaus,  G., and Dresselhaus,  M. S., 2001, “Anomalous Potential Barrier of Double-Wall Carbon Nanotube,” Chem. Phys. Lett., 348, 187–193.
Bandow,  S., Takizawa,  M., Hirahara,  K., Yudasaka,  M., and Iijima,  S., 2001, “Raman Scattering Study of Double-Wall Carbon Nanotubes Derived From the Chains of Fullerenes in Single-Wall Carbon Nanotubes,” Chem. Phys. Lett., 337, 48–54.
Dresselhaus,  M. S., and Eklund,  P. C., 2000. “Phonons in Carbon Nanotubes,” Adv. Phys., 49, 705–814.

Figures

Grahic Jump Location
DWNT amplitude ratio (a1/a2) for fn2 using a double-Euler-beam model
Grahic Jump Location
DWNT amplitude ratio (a1/a2) for fn1 using a double-Euler-beam model
Grahic Jump Location
DWNT amplitude ratio (a1/a2) for fn2 using a double-Timoshenko-beam model
Grahic Jump Location
DWNT amplitude ratio (a1/a2) for fn1 using a double-Timoshenko-beam model
Grahic Jump Location
DWNT frequencies for the inner radius 3.5 nm and L/d=50
Grahic Jump Location
DWNT frequencies for the inner radius 3.5 nm and L/d=20
Grahic Jump Location
DWNT frequencies for the inner radius 3.5 nm and L/d=10
Grahic Jump Location
DWNT frequencies for the inner radius 0.35 nm and L/d=50
Grahic Jump Location
DWNT frequencies for the inner radius 0.35 nm and L/d=20
Grahic Jump Location
DWNT frequencies for the inner radius 0.35 nm and L/d=10
Grahic Jump Location
Vibration of a short doublewall carbon nanotube
Grahic Jump Location
DWNT amplitude ratio (γ/b) for fn2 using a single-Timoshenko-beam model
Grahic Jump Location
DWNT amplitude ratio (γ/b) for fn1 using a single-Timoshenko-beam model
Grahic Jump Location
DWNT amplitude ratio (γ2/b2) for fn4 using a double-Timoshenko-beam model
Grahic Jump Location
DWNT amplitude ratio (γ2/b2) for fn3 using a double-Timoshenko-beam model
Grahic Jump Location
DWNT amplitude ratio (γ2/b2) for fn2 using a double-Timoshenko-beam model
Grahic Jump Location
DWNT amplitude ratio (γ2/b2) for fn1 using a double-Timoshenko-beam model

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