Advances in nano research

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On the vibration of aligned carbon nanotube reinforced composite beams

  • Aydogdu, Metin (Department of Mechanical Engineering, Trakya University)
  • Received : 2014.03.23
  • Accepted : 2015.01.21
  • Published : 2014.12.25
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Abstract

Carbon nanotubes have exceptional mechanical, thermal and electrical properties, and are considered for high performance structural and multifunctional composites. In the present study, the natural frequencies of aligned single walled carbon nanotube (CNT) reinforced composite beams are obtained using shear deformable composite beam theories. The Ritz method with algebraic polynomial displacement functions is used to solve the free vibration problem of composite beams. The Mori-Tanaka method is applied to find the composite beam mechanical properties. The continuity conditions are satisfied among the layers by modifying the displacement field. Results are found for different CNT diameters, length to thickness ratio of the composite beam and different boundary conditions. It is found that the use of smaller CNT diameter in the reinforcement element gives higher fundamental frequency for the composite beam.

Keywords

References

  1. Aydogdu, M. (2005), "Vibration analysis of cross-ply laminated beams with general boundary conditions by Ritz method", Int. J. Mech. Sci., 11, 1740-1755.
  2. Aydogdu, M. (2006a), "Buckling analysis of cross-ply laminated beams with general boundary conditions by Ritz method", Compos. Sci. Technol., 66, 1248-1255. https://doi.org/10.1016/j.compscitech.2005.10.029
  3. Aydogdu, M. (2006b), "Free vibration analysis of angle-ply laminated beams with general boundary conditions", J. Reinf. Plast. Compos., 25, 1571-1583. https://doi.org/10.1177/0731684406066752
  4. Aydogdu, M. (2009), "A new shear deformation theory for laminated composite plates", Compos. Struct., 89, 94-101. https://doi.org/10.1016/j.compstruct.2008.07.008
  5. Baharlou, B. and Leissa, A.W. (1987), "Vibration and buckling of generally laminated composite plates with arbitrary boundary conditions", Int. J. Mech. Sci., 29, 545-555. https://doi.org/10.1016/0020-7403(87)90026-9
  6. Chandrashekhara, K., Krishnamurty, K. and Roy, S., (1990), "Free vibration of comkposite beams including rotary inertia and shear deformation", Compos. Struct., 14, 269-279. https://doi.org/10.1016/0263-8223(90)90010-C
  7. Chen, W.Q., Lv, C.F. and Bian, Z.G., (2003), "Elasticity solution for free vibration of laminated beams" Compos. Struct., 62, 75-82. https://doi.org/10.1016/S0263-8223(03)00086-2
  8. Goze, C., Vaccarini, L., Henrard, L., Bernier, P., Hernandez, E. and Rubio, A. (1999), "Elastic and mechanical properties of carbon nanotubes", Synth. Metal., 58, 14013-14019.
  9. Herakovich, C.T. (1998), Mechanics of Fibrous Composites, John Wiley and Sons, New York, NY, USA.
  10. Hill, R. (1965), "A self-consistent mechanics of composite materials", J. Mech. Phy. Solid., 13, 213-222. https://doi.org/10.1016/0022-5096(65)90010-4
  11. Kantrovich, L.V. and Krylov, V.I. (1964), Approximate Methods in Higher Analysis, Groningen, Noordhoff.
  12. Ke, L.L., Yang, J. and Kitipornchai, S. (2010), "Nonlinear free vibration of functionally graded carbon nanotube-reinforced composite beams", Compos. Struct., 92, 676-683. https://doi.org/10.1016/j.compstruct.2009.09.024
  13. Khdeir, A.A. and Reddy, J.N. (1994), "Free vibration of cross-ply laminated beams with arbitrary boundary conditions" Int. J. Eng. Sci., 32, 1971-1980. https://doi.org/10.1016/0020-7225(94)90093-0
  14. Leissa, A.W. and Narita, Y. (1989), "Vibration studies for simply supported symmetrically laminated rectangular plates", Compos. Struct., 12,113-132. https://doi.org/10.1016/0263-8223(89)90085-8
  15. Lei, Z.X., Liew, K.M. and Yu, J.L. (2013), "Free vibration analysis of functionally graded carbon nanotubereinforced composite plates using the element-free kp-Ritz method in thermal environment", Compos. Struct., 106, 128-138. https://doi.org/10.1016/j.compstruct.2013.06.003
  16. Maghamikia, Sh. and Jam, J.E. (2011), "Buckling analysis of circular and annular composite plates reinforced with carbon nanotubes using FEM", J. Mech. Scie. Technol., 25, 2805-2810. https://doi.org/10.1007/s12206-011-0738-8
  17. Mindlin, R.D. (1951), "Influence of rotary inertia and shear on flexural motions of isotropic elastic plates", J. Appl. Mech., 18, A31-A38.
  18. Narita, Y. (2000), "Combinations for free vibration behaviors of anisotropic rectangular plates under general edge boundary conditions", J. Appl. Mech. T, ASME, 67, 568-573. https://doi.org/10.1115/1.1311959
  19. Odegard, G.M., Gates, T.S., Nicholson, L.M. and Wise, K.E. (2002). "Equivalent continuum modelling of nano-structured materials", Compos. Sci. Technol., 62, 1869-1880. https://doi.org/10.1016/S0266-3538(02)00113-6
  20. Popov, V.N., Doren, V.E. and Balkanski, M. (2000), "Elastic properties of cyristals of single-walled carbon nanotubes", Solid. State. Commun., 114, 395-399. https://doi.org/10.1016/S0038-1098(00)00070-3
  21. Reddy, J.N. (1984), "A simple higher-order theory for laminated composite plates", J. Appl. Mech., 51, 745-752. https://doi.org/10.1115/1.3167719
  22. Shen, H.S. (2009), "Nonlinear bending of functionally graded carbon nanotubereinforced composite plates in thermal environments", Compos. Struct., 91, 9-19. https://doi.org/10.1016/j.compstruct.2009.04.026
  23. Shi, D.L., Feng, X.Q., Huang, Y.Y., Hwang, K.C. and Gao, H. (2004), "The effect of nanotube waviness and agglomeration on the elastic property of carbon nanotube-reinforced composites", Tran. ASME, 126, 250-257. https://doi.org/10.1115/1.1677409
  24. Treacy, M.M.J., Ebbesen, T.W. and Gibson, J.M. (1996), "Exceptional high Young‟s modulus observed for individual carbon nanotubes", Nature, 381, 678-680. https://doi.org/10.1038/381678a0
  25. 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, 899-1912.
  26. Wuite, J. and Adali, S. (2005), "Deflection and stress behaviour of nanocomposite reinforced beams using a multiscale analysis", Compos. Struct., 71, 388-396. https://doi.org/10.1016/j.compstruct.2005.09.011
  27. Zhu, P., Lei, Z.X. and Liew, K.M. (2012), "Static and free vibration analyses of carbon nanotubereinforced composite plates using finite element method with first order shear deformation plate theory", Compos. Struct., 94, 1450-60. https://doi.org/10.1016/j.compstruct.2011.11.010

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