Analysis of Nonlinear Vibrations for Multi-walled Carbon Nanotubes Embedded in an Elastic Medium

Subject Areas : Engineering

A Ghorbanpour Arani ¹ , H Rabbani ² , S Amir ³ , Z Khoddami Maraghi ⁴ , M Mohammadimehr ⁵ , E Haghparast ⁶

1 - Faculty of Mechanical Engineering, University of Kashan--- Institute of Nanoscience & Nanotechnology, University of Kashan
2 - Faculty of Mechanical Engineering, University of Kashan
3 - Department of Mechanical Engineering, Kashan Branch, Islamic Azad University
4 - Faculty of Mechanical Engineering, University of Kashan
5 - Faculty of Mechanical Engineering, University of Kashan
6 - Faculty of Mechanical Engineering, University of Kashan

Received: 2011-07-03 Accepted : 2011-08-15 Published : 2011-09-30

Keywords:

References:

[1] Iijima S., 1991, Helical microtubes of graphitic carbon, Nature 354:56–58.

[2] Yoon J., Ru C.Q., Miodochowski A., 2003, Vibration of an embedded multiwalled carbon nanotubes, Composites Science and Technology 63:1533-1542.

[3] Fu Y.M., Hong J.W., Wang X.Q., 2006, Analysis of nonlinear vibration for embedded carbon nanotubes, Journal of Sound and Vibration 296: 746-756.

[4] Wang C.M., Tan V.B.C., Zhang Y.Y., 2006, Timoshenko beam model for vibration analysis of multi-walled carbon nanotubes, Journal of Sound and Vibration 294: 1060-1072.

[5] Aydogdu M., 2008, Vibration of multi-walled carbon nanotubes by generalized shear deformation theory, International Journal of Mechanical Sciences 50:837–844.

[6] Ke L. L., Xiang Y., Yang J., Kitipornchai S., 2009, Nonlinear free vibration of embedded double-walled carbon nanotubes based on nonlocal Timoshenko beam theory, Computational Materials Science 47: 409–417.

[7] Zhang Y., Liu G., Han X., 2005, Transverse vibrations of double-walled carbon nanotubes under compressive axial load, Physics Letters A 340: 258-266.

[8] Xia W., Wang L., Yin L., 2010, Nonlinear non-classical microscale beams: Static bending, postbuckling and free vibration, International Journal of Engineering Science 48 (12):2044-2053.

[9] Kuang Y. D., He X. Q., Chen C. Y., Li G. Q., 2009, Analysis of nonlinear vibrations of double-walled carbon nanotubes conveying fluid, Computational Materials Science 45: 875–880.

[10] Toshiaki N., Xiao-Wen L., Qing-Qing N., Endo M., 2010, Free vibration characteristics of double-walled carbon nanotubes embedded in an elastic medium, Physics Letters A 374: 2670–2674.

[11] Toshiaki N., Xiao-Wen L., Qing-Qing N., Endo M., 2010, Vibrational analysis of double-walled carbon nanotubes with inner and outer nanotubes of different lengths, Physics Letters A 374 (46): 4684-4689.

[12] Simsek M., 2010, Vibration analysis of a single-walled carbon nanotube under action of a moving harmonic load based on nonlocal elasticity theory, Physica E 43 (1): 182-191.

[13] Ghorbanpour Arani A., Mohammadimehr M., Arefmanesh A., Ghasemi A., 2010, Transverse vibration of short carbon nanotube using cylindrical shell and beam models, Proceeding ImechE, Part C: Journal of Mechanical Engineering. Science 224 (C3): 745-756.

[14] Ali Hasan N., Mook D.T., 1995, Nonlinear Oscillations. John Wiley & Sons Publication, USA.

[15] Timoshenco S., 1937, Vibration Problems in Engineering, 2nd Ed., New York.

[16] Han Q., Lu G.X., 2003, Torsional buckling of a Double-walled carbon nanotube embedded in an elastic medium, European Journal of Mechanics A/Solids 22: 875-883.

[17] Yao X., Han Q., 2007, The thermal effect on axially compressed buckling of a double-walled carbon nanotubes, European Journal of Mechanics A/Solids 26: 298-312.

[18] He X. Q., Kitipornchai S., liew K. M., 2005, Buckling analysis of multi-walled carbon nanotubes:a continuum model acconting for van der waals interaction, Journal of the Mechanics and Physics of Solids 53: 303-326.

[19] Timoshenko S. P., Goodier J. N., 1970, Theory of elasticity, 3rd Ed, Mc Graw-Hill, New York.

[20] Bulson P. S., 1958, Buried Structure, Chapman and Hall, London.

[21] Ru C.Q., 2000, Elastic buckling of single-walled carbon nanotube ropes under high pressure, Physics Review B 62: 10405–10408.

[22] Yoon J., Ru C. Q., Miodochowski A., 2003, Vibration of an embedded multiwall carbon nanotube, Composites Science and Technology 63: 1533-1542.