OPEN ACCESS
Carbon nanotubes (CNT’s) has revolutionized the world of nanotechnology by their exceptional proprieties, which make them the core of many applications in several fields, many studies has been done to investigate their mechanical proprieties since their discovery. In this paper, the free vibration of a single walled carbon nanotube is studied in an elastic environment based on the theory of non-local elasticity and discretized by differential quadrature method (DQM); the effect of the surrounding medium on fundamental frequencies is discussed.
Free Vibration, Carbon Nanotubes, Natural Frequency, Non-local Elasticity, Differential Quadrature Method, Euler-Bernoulli.
[1] Iijima S. (1991). Helical microtubules of graphitic carbon, Nature, Vol. 345, pp. 56-58. DOI: 10.1038/354056a0
[2] Cha S.N., Jang J.E., Choi Y., Amaratunga G.A.J., et al. (2005). Fabrication of a nanoelectromechanical switch using a suspended carbon nanotube, Applied Physics Letters, Vol. 86, 083105. DOI: 10.1063/1.1868064
[3] Lu J.P. (1997). Elastic properties of carbon nanotubes and nanoropes, Physical Review Letters, Vol. 79, pp. 1297–1300. DOI: 10.1103/PhysRevLett.79.1297
[4] Chong K.P. (2008). Nano science and engineering in solid mechanics, Acta Mechanica. Solida Sinica, Vol. 21, No. 2, pp 95–103. DOI: 10.1007/s10338-008-0812-7
[5] Eringen A.C. (1972). Nonlocal polar elastic continua, International Journal of Engineering Science, Vol. 10, No. 1, pp. 1–16. DOI: 10.1016/0020-7225(72)90070-5
[6] Murmu T., Pradhan S.C. (2009). Buck ling analysis of a single-walled carbon nanotube embedded in an elastic medium based on nonlocal elasticity and Timoshenko beam theory and using DQM, Physica E 2, Vol. 41, No. 7, pp. 1232-1239. DOI: https://doi.org/10.1016/j.physe.2009.02.004
[7] Heireche H., Tounsi A., Benzair A., Maachou M., Adda Bedia E.A. (2008a). Sound wave propagation insingle-walled carbon nanotubes using nonlocal elasticity, Physica E, Vol. 40, pp. 2791-2799. DOI: 10.1016/j.physe.2007.12.021
[8] Semmah A., Tounsi A., Zidour M., Heireche H., Naceri M. (2014). Effect of chirality on critical buckling temperature of a zigzag single-walled carbon nanotubes using nonlocal continuum theory, Fullerenes, Nanotubes. And Carbon Nanostructures, Vol. 23, pp. 518-522. DOI: 10.1080/1536383X.2012.749457
[9] Houmat A. (2015). Nonlinear free vibration of non-prismatic single-walled carbon nanotubes by a non-local shear deformable beam p-element, Acta Mechanicca, Vol. 227l, No. 4, pp. 1051–1065. DOI: 10.1007/s00707-015-1507-z
[10] Belhadj A., Boukhalfa A., Belalia S.A. (2017). Carbon nanotube structure vibration based on non-local elasticity, Journal of Modern Materials, Vol. 3, No. 1, pp. 9-13. DOI: 10.21467/jmm.3.1.9-13
[11] Gupta S.S., Bosco F.G., Batra R.C. (2010). Wall thickness and elastic moduli of single-walled carbon nanotubes from frequencies of axial, torsional and
inextensional modes of vibration, Computational Materials Science, Vol. 47, No. 4, pp. 1049-1059. DOI: 10.1016/j.commatsci.2009.12.007
[12] Pirmohammadi A.A. et al. (2014). Modeling and active vibration suppression of a single-walled carbon nanotube subjected to a moving harmonic load based on a nonlocal elasticity theory, Applied Physics A, Vol. 117, No. 3, pp. 1547- 1555. DOI: 10.1007/s00339-014-8592-z
[13] Soltani P., Kassaei A., Taherian M.M. et al. ( 2012). Vibration of wavy single-walled carbon nanotubes based on nonlocal Euler Bernoulli and Timoshenko models, International Journal of Advanced Structural Engineering, Vol. 4, No. 3, pp. 1-10. DOI: 10.1186/2008-6695-4-3
[14] Lee H., Chang W. (2009). Vibration analysis of a viscous-fluid-conveying single-walled carbon nanotube embedded in an elastic medium, Physica. E, Vol. 41, pp. 529–532. DOI: 10.1016/j.physe.2008.10.002
[15] Lee H., Chang W. (2009). Vibration analysis of a viscous-fluid-conveying single-walled carbon nanotube embedded in an elastic medium, Physica E, Vol. 41, pp. 529–532. DOI: 10.1016/j.physe.2008.10.002
[16] Wang L., Ni Q. (2009). A reappraisal of the computational modelling of carbon nanotubes conveying viscous fluid, Mechanics Research Communications, Vol. 36, pp. 833–837. DOI: 10.1016/j.mechrescom.2009.05.003
[17] Arda M., Aydogdu M. (2015). Analysis of free torsional vibration in carbon nanotubes embedded in a viscoelastic medium, Advances in Science and Technology Research Journal, Vol. 9, No. 26, pp. 28–3. DOI: 10.12913/22998624/2361
[18] Bock J.O., LengvarskýP. (2014). Vibration of single-walled carbon nanotubes by using nonlocal theory, American Journal of Mechanical Engineering, Vol. 2, No. 7, pp. 195-198. DOI: 10.12691/ajme-2-7-5
[19] Bellman R., Kashef B.G., Casti J. (1972). Differential quadrature: a technique for the rapid solution of nonlinear partial differential equations, Journal of Computational Physics, Vol. 10, pp. 40-52. DOI: 10.1016/0021-9991(72)90089-7
[20] Bert C.W., Malik M. (1996). Differential quadrature method in computational mechanics: a review, Applied Mechanics Reviews, Vol. 49, pp. 1-27. DOI: 10.1115/1.3101882