Transverse Vibration Analysis of Single-Walled Carbon Nanotubes Embedded in an Elastic Medium Using Bernoulli-Fourier Method

Thin-Lin Horng^{*}

Show more

References

[1] A. Bianco, K. Kostarelos and M. Prato, “Applications of Carbon Nanotubes in Drug Delivery,” Current Opinion in Chemical Biology, Vol. 9, No. 6, 2005, pp. 674-679.
doi:10.1016/j.cbpa.2005.10.005

[2] R. S. Ruoff and D. C. Lorents, “Mechanical and Thermal Properties of Carbon Nanotubes,” Carbon, Vol. 33, No. 7, 1995, pp. 925-930. doi:10.1016/0008-6223(95)00021-5

[3] D. Srivastava, M. Menon and K. Cho, “Computational Nanotechnology with Carbon Nanotubes and Fullerenes,” Computing in Science & Engineering, Vol. 3, No. 4, 2001, pp. 42-55. doi:10.1109/5992.931903

[4] R. Saito, G. Dresselhaus and M. S. Dresselhaus, “Physical Properties of Carbon Nano-tubes,” Imperial College, London, 1998.

[5] P. J. F. Harris, “Carbon Nanotubes and Related Structures,” Cambridge University Press, Cambridge, 1999.
doi:10.1017/CBO9780511605819

[6] B. I. Yakobson, C. J. Brabec and J. Bernholc, “Nanome-chanics of Carbon Tubes: Instabilities beyond Linear Response,” Physical Review Letters, Vol. 76, No. 14, 1996, pp. 2511-2514. doi:10.1103/PhysRevLett.76.2511

[7] P. Zhang, H. Jiang, Y. Huang, P. H. Geubelle and K. C. Hwang, “An atomistic-Based Continuum Theory for Carbon Nanotubes: Analysis of Fracture Nucleation,” Journal of the Mechanics and Physics of Solids, Vol. 52, No. 5, 2004, pp. 977-998. doi:10.1016/j.jmps.2003.09.032

[8] E. W. Wong, P. E. Sheehan and C. M. Lieber, “Nanobeam Mechanics: Elasticity, Strength, and Toughness of Nano-rods and Nanotubes,” Science, Vol. 277, No. 5334, 1997, pp. 1971-1975. doi:10.1126/science.277.5334.1971

[9] O. Lourie, P. M. Co and H. D. Wagner, “Buckling and Collapse of Embedded Carbon Nanotubes,” Physical Review Letters, Vol. 81, No. 8, 1998, pp. 1638-1641.
doi:10.1103/PhysRevLett.81.1638

[10] Y. Q. Zhang, G. R. Liu and J. S. Wang, “Small-Scale Effects on Buckling of Multiwalled Carbon Nanotubes under Axial Compression,” Physical Review B, Vol. 70, No. 20. 2004, p. 205430.
doi:10.1103/PhysRevB.70.205430

[11] Y. Zhang, G. Liu and X. Han, “Transverse Vibrations of Double-Walled Carbon Nanotubes under Compressive Axial Load,” Physics Letters A, Vol. 340, No. 1-4, 2005, pp. 258-266. doi:10.1016/j.physleta.2005.03.064

[12] K. M. Liew and Q. Wang, “Analysis of Wave Propaga- tion in Carbon Nanotubes via Elastic Shell Theories,” International Journal of Engineering Science, Vol. 45, No. 2-8, 2007, pp. 227-241.
doi:10.1016/j.ijengsci.2007.04.001

[13] J. C. Hsu, R. P. Chang and W. J. Chang, “Resonance Frequency of Chiral Single-Walled Carbon Nanotubes Using Timoshenko Beam Theory,” Physics Letters A, Vol. 372, No. 16, 2008, pp. 2757-2759.
doi:10.1016/j.physleta.2008.01.007

[14] J. Yoon, C. Q. Ru and A. Mioduchowski, “Vibration of an Embedded Multiwall Carbon Nanotube,” Composites Science and Technology, Vol. 63, No.11, 2003, pp. 1533- 1542. doi:10.1016/S0266-3538(03)00058-7

[15] C. M. Wang, V. B. C. Tan and Y. Y. Zhang, “Timoshenko Beam Model for Vibra-tion Analysis of Multi-Walled Carbon Nanotubes,” Journal of Sound and Vibration, Vol. 294, No. 4-5, 2006, pp. 1060-1072.
doi:10.1016/j.jsv.2006.01.005

[16] S. C. Pradhan and T. Murmu, “Small-Scale Effect on Vibration Analysis of Sin-gle-Walled Carbon Nanotubes Embedded in an Elastic Me-dium Using Nonlocal Elasticity Theory,” Journal of Applied Physics, Vol. 105, No. 2, 2009, p. 114309.

[17] M. X. Shi and Q. M. Li, “Mode Bernoulli-Fourier in Single-Walled Carbon Nanotubes,” International Journal of Mechanical Sciences, Vol. 52, No. 5, 2010, pp. 663-671.
doi:10.1016/j.ijmecsci.2009.09.018

[18] R. B. Chen, C. H. Lee, C. P. Chang and M. F. Lin, “Electronic and Optical Properties of Finite Carbon Nanotubes in an Electric Field,” Nanotechnology, Vol. 18, No. 7, 2007, p. 075704. doi:10.1088/0957-4484/18/7/075704

[19] M. A. Moreles, S. Botello and R. Salinas, “A Root-Finding Technique to Compute Eigenfrequencies for Elastic Beams,” Journal of Sound and Vibration, Vol. 284, No. 3-5, 2005, pp. 1119-1129. doi:10.1016/j.jsv.2004.07.028

[20] J. Avsec and M. Oblak, “Thermal Vibrational Analysis for Simply Supported Beam and Clamped Beam,” Journal of Sound and Vibration, Vol. 308, No. 3-5, 2007, pp. 514-525. doi:10.1016/j.jsv.2007.04.002

[21] F. P. Beer and E. R. Johnston, “Mechanics of Materials,” McGraw-Hill, New York, 1981.