Free vibrational analysis of composite beams reinforced with randomly aligned and oriented carbon nanotubes, resting on an elastic foundation
Abstract
The main interest of this paperwork is to examinate the dynamic behavior (free vibrational response) of carbon nanotubes (CNT) composite beams standing on an elastic foundation of Winkler-Pasternak’s. The affected beam consists of a polymer matrix reinforced with single-wall carbon nanotubes (SWCNT’s), in which, a large number of CNT’s reinforcement of infinite length are distributed in a linear elastic polymer matrix. In this study the CNT’s are considered either aligned or randomly oriented on the matrix.
A refined high-order beam theory (RBT) is adopted in the present analysis using a new shape function. The refined beam theory which is summarized by differentiating the displacement along the beam transverse section into shear and bending components, initially the material properties of the composite beam (CNTRC) are estimated using the Mori-Tanaka’s method. The beam is considered simply supported on the edge-lines. NAVIER’s solutions are proposed to solve the boundary conditions problems. Since there are no results to compare with in the literature; the results in this study are compared with a free vibrational analysis of an isotropic beam. Several aspects such as the length/thickness ratio, volume fraction of nanotubes, and vibrational modes are carried out in the parametric study.
References
Esawi, A. M., & Farag, M. M. (2007). Carbon nanotube reinforced composites: potential and current challenges. Materials & design, 28(9), 2394-2401.
Fidelus, J. D., Wiesel, E., Gojny, F. H., Schulte, K., & Wagner, H. D. (2005). Thermo-mechanical properties of randomly oriented carbon/epoxy nanocomposites. Composites Part A: Applied Science and Manufacturing, 36(11), 1555-1561.
Hill, R. (1965). A self-consistent mechanics of composite materials. Journal of the Mechanics and Physics of Solids, 13(4), 213-222.
Hu, N., Fukunaga, H., Lu, C., Kameyama, M., & Yan, B. (2005). Prediction of elastic properties of carbon nanotube reinforced composites. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 461(2058), 1685-1710.
Kargarnovin, M. H., & Arghavani, J. (2007). Limit analysis of FGM circular plates subjected to arbitrary rotational symmetric loads. International Journal of Mechanical and Mechatronics Engineering, 1(12), 719-724.S.H. Shen, Compos. Struct. 91 (2009) 9–19.
Ke, L. L., Yang, J., & Kitipornchai, S. (2010). Nonlinear free vibration of functionally graded carbon nanotube-reinforced composite beams. Composite Structures, 92(3), 676-683.
Popov, V. N., Van Doren, V. E., & Balkanski, M. J. S. S. C. (2000). Elastic properties of crystals of single-walled carbon nanotubes. Solid state communications, 114(7), 395-399.
Shi, D. L., Feng, X. Q., Huang, Y. Y., Hwang, K. C., & Gao, H. (2004). The effect of nanotube waviness and agglomeration on the elastic property of carbon nanotube-reinforced composites. J. Eng. Mater. Technol., 126(3), 250-257.
Shimpi, R. P., & Patel, H. G. (2006). Free vibrations of plate using two variable refined plate theory. Journal of Sound and Vibration, 296(4-5), 979-999.
Suresh, S. (1998). Fatigue of materials. Cambridge university press.
Tagrara, S. H., Benachour, A., Bouiadjra, M. B., & Tounsi, A. (2015). On bending, buckling and vibration responses of functionally graded carbon nanotube-reinforced composite beams. Steel and Composite Structures, 19(5), 1259-1277.
Thostenson, E. T., Ren, Z., & Chou, T. W. (2001). Advances in the science and technology of carbon nanotubes and their composites: a review. Composites science and technology, 61(13), 1899-1912.
Wattanasakulpong, N., & Ungbhakorn, V. (2013). Analytical solutions for bending, buckling and vibration responses of carbon nanotube-reinforced composite beams resting on elastic foundation. Computational Materials Science, 71, 201-208.
Yas, M. H., & Heshmati, M. (2012). Dynamic analysis of functionally graded nanocomposite beams reinforced by randomly oriented carbon nanotube under the action of moving load. Applied Mathematical Modelling, 36(4), 1371-1394.
Yas, M. H., & Samadi, N. (2012). Free vibrations and buckling analysis of carbon nanotube-reinforced composite Timoshenko beams on elastic foundation. International Journal of Pressure Vessels and Piping, 98, 119-128.
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