Skip to content
BY-NC-ND 4.0 license Open Access Published by De Gruyter Open Access February 24, 2017

Free vibrations of non-uniform CNT/fiber/polymer nanocomposite beams

  • J. Seidi and S. Kamarian EMAIL logo

Abstract

In this paper, free vibrations of non-uniform multi-scale nanocomposite beams reinforced by carbon nanotubes (CNTs) are studied. Mori-Tanaka (MT) technique is employed to estimate the effective mechanical properties of three-phase CNT/fiber/polymer composite (CNTFPC) beam. In order to obtain the natural frequencies of structure, the governing equation is solved by means of Generalized Differential Quadrature (GDQ) approach. The accuracy and efficiency of the applied methods are studied and compared with some experimental data reported in previous published works. The influences of volume fraction and agglomeration of nanotubes, volume fraction of long fibers, and different laminate lay-ups on the natural frequency response of structure are examined.

References

[1] F. Tornabene, N. Fantuzzi, M. Bacciocchi, E. Viola, “Effect of agglomeration on the natural frequencies of functionally graded carbon nanotube-reinforced laminated composite doubly-curved shellsOriginal’, Composites Part B: Engineering, 2016, 89: 187-21810.1016/j.compositesb.2015.11.016Search in Google Scholar

[2] K. Mehar, S. Panda, “Geometrical nonlinear free vibration analysis of FG-CNT reinforced composite flat panel under uniform thermal field”, Composite Structures, 2016, 143: 336-346.10.1016/j.compstruct.2016.02.038Search in Google Scholar

[3] Z.X. Lei, L.W. Zhang, K.M. Liew, “Vibration of FG-CNT reinforced composite thick quadrilateral plates resting on Pasternak foundations”, Engineering Analysis with Boundary Elements, 2016, 64: 1-11.10.1016/j.enganabound.2015.11.014Search in Google Scholar

[4] S. Kamarian, M. Salim, R. Dimitri, F. Tornabene, “Free Vibration Analysis of Conical Shells Reinforced with Agglomerated Carbon Nanotubes” International Journal of Mechanical Sciences, 2016, 108 (1), 157-165.10.1016/j.ijmecsci.2016.02.006Search in Google Scholar

[5] Z.X. Lei, K.M. Liew, J.L. Yu, “Buckling analysis of functionally graded carbon nanotube-reinforced composite plates using the element-free kp-Ritz method”, Composite Structures, 2013, 98: 160-16810.1016/j.compstruct.2012.11.006Search in Google Scholar

[6] L.W. Zhang, K.M. Liew, “Postbuckling analysis of axially compressed CNT reinforced functionally graded composite plates resting on Pasternak foundations using an element-free approach”, Composite Structures, 2016, 138: 40-51.10.1016/j.compstruct.2015.11.031Search in Google Scholar

[7] L.W. Zhang, K.M. Liew, J.N. Reddy, “Postbuckling of carbon nanotube reinforced functionally graded plates with edges elastically restrained against translation and rotation under axial compression”, Comput. Methods Appl. Mech. Engrg., 2016, 298: 1-28.10.1016/j.cma.2015.09.016Search in Google Scholar

[8] M. Mohammadimehr, M. Salemi, B. Rousta Navi, “Bending, buckling, and free vibration analysis of MSGT microcomposite Reddy plate reinforced by FG-SWCNTs with temperaturedependentmaterial properties under hydro-thermo-mechanical loadings using DQM”, Composite Structures, 2016, 138: 361-380.10.1016/j.compstruct.2015.11.055Search in Google Scholar

[9] K. Mayandi, P. Jeyaraj, “Bending, buckling and free vibration characteristics of FG-CNT-reinforced polymer composite beam under non-uniform thermal load”, Journal of Materials: Design and Applications, 2015, 229(1): 13-28.Search in Google Scholar

[10] F. Tornabene, N. Fantuzzi, M. Bacciocchi “Linear static response of nanocomposite plates and shells reinforced by agglomerated carbon nanotubes” Composites Part B: Engineering, 20016, Available online.Search in Google Scholar

[11] H. Dai, “Carbon nanotubes: opportunities and challenges”, Surface Science, 2002, 500: 218-241.10.1016/S0039-6028(01)01558-8Search in Google Scholar

[12] T. Lau, C. Gu, D. Hui, “A critical review on nanotube and nanotube/ nanoclay related polymer composite materials”, Composites Part B, 2006, 37: 425-436.10.1016/j.compositesb.2006.02.020Search in Google Scholar

[13] I. Kang, Y. Heung, J. Kim, J. Lee, R. Gollapudi, S. Subramaniam, S. Narasimhadevara, D. Hurd, G. Kirkera, V. Shanov, M. Schulz, D. Shi, J. Boerio, S.Mall, D. Ruggles-Wren, “Introduction to carbon nanotube and nanofiber smart materials”, Composites Part B, 2006, 37: 382-394.10.1016/j.compositesb.2006.02.011Search in Google Scholar

[14] M. Shokrieh, R. Rafiee, “Prediction of mechanical properties of an embedded carbon nanotube in polymer matrix based on developing an equivalent long fiber”. Mechanics Research Communications, 2010, 37: 235-240.10.1016/j.mechrescom.2009.12.002Search in Google Scholar

[15] A. Montazeri, J. Javadpour, A. Khavandi, A. Mohajeri, A. Tcharkhtch, “Mechanical properties ofmulti-walled carbon nanotube/ epoxy composites”, Materials & Design, 2010, 31(9): 4202-4208.Search in Google Scholar

[16] Q.S. Yang, X.Q. He, X. Liu, F.F. Leng, Y.W.Ma, “The effective properties and local agglomeration effect of CNT/SMP composites”, Composites Part B, 2012, 43(1): 33-38.Search in Google Scholar

[17] P. Barai, G.J. Weng, “A theory of plasticity for carbon nanotube reinforced composites”, International Journal of Plasticity, 2011, 27(4): 539-559.Search in Google Scholar

[18] S. Kamarian, A. Pourasghar, M. H. Yas, “Eshelby-Mori-Tanaka approach for vibrational behavior of functionally graded carbon nanotube-reinforced plate resting on elastic foundation” Journal of Mechanical Science and Technology, 2013, 27 (11), 3395-3401.10.1007/s12206-013-0861-9Search in Google Scholar

[19] M. Heshmati, M. H. Yas, “Free vibration analysis of functionally graded CNT-reinforced nanocomposite beamusing Eshelby- Mori-Tanaka approach”, Journal of Mechanical Science and Technology, 2013, 27 (11): 3403-3408.Search in Google Scholar

[20] A. Pourasghar, M.H. Yas, S. Kamarian, “Local agglomeration effect of CNT on the vibrational behavior of four-parameter continuous graded nanotube-reinforced cylindrical panels”, Polymer Composites, 2013, 34(5): 707-721.Search in Google Scholar

[21] E. Bekyarova, E.T. Thostenson, A. Yu, H. Kim, J. Gao, J. Tang, H.T. Hahn, T.W. Chou, M.E. Itkis, R.C. Haddon, “Multiscale carbon nanotube-carbon fiber reinforcement for advanced epoxy composites”, Langmuir, 2007, 23: 3970-3974.10.1021/la062743pSearch in Google Scholar PubMed

[22] M.S. Kim, Y.B. Park, O.I. Okoli, C.H. Zhang, “Processing, characterization, and modeling of carbon nanotube-reinforced multiscale composites”, Composites Science and Technology, 2009, 69: 335-342.10.1016/j.compscitech.2008.10.019Search in Google Scholar

[23] E.T. Thostenson,W.Z. Li, D.Z.Wang, Z.F. Ren, T.W. Chou, “Carbon nanotube/carbon fiber hybrid multiscale composites”, Journal of Applied Physics, 2002, 91: 6034-6037.10.1063/1.1466880Search in Google Scholar

[24] A. Godara, L. Mezzo, F. Luizi, F. Warrier, S.V. Lomov, A.W.V. Vuure, L. Gorbatikh, P. Moldenaers, I. Verpoest, “Influence of carbon nanotube reinforcement on the processing and the mechanical behaviour of carbon fiber/epoxy composites”, Carbon, 2009, 47: 2914-2923.10.1016/j.carbon.2009.06.039Search in Google Scholar

[25] K.J. Green, R.D. Derrick, K.V. Uday, N. Elijah, “Multiscale fiber reinforced composites based on a carbon nanofiber/epoxy nanophased polymermatrix synthesis, mechanical, and hermomechanical behavior” Composites Part A: Applied Science and Manufacturing, 2009, 40, 1470-1475.10.1016/j.compositesa.2009.05.010Search in Google Scholar

[26] M. Rafiee, X.F. Liu, X.Q. He, S. Kitipornchai, “Geometrically nonlinear free vibration of shear deformable piezoelectric carbon nanotube/fiber/polymer multi-scale laminated composite plates”, Journal of Sound and Vibration, 2014, 333 (14): 3236-3251.Search in Google Scholar

[27] S. Kamarian, M. Shakeri, M. H. Yas, “Natural frequency analysis and optimal design of CNT/fiber/polymer hybrid composites plates using Mori-Tanaka approach, GDQ technique and Firefly algorithm”, Polymer Composites, 2016, Available online.10.1002/pc.24083Search in Google Scholar

[28] S. Kamarian, M. Bodaghi, A. Pourasghar, S. Talebi, “Vibrational behavior of non-uniform piezoelectric sandwich beamsmade of CNT-reinforced polymer nanocomposite by considering the agglomeration effect of CNTs”, Polymer composites, 2016, Available online.10.1002/pc.23933Search in Google Scholar

[29] D. Garijo, “Free vibration analysis of non-uniform Euler- Bernoulli beams by means of Bernstein pseudospectral collocation”, Engineering with Computers, 2015, 31(4): 813-823.10.1007/s00366-015-0401-6Search in Google Scholar

[30] S. Khani, N. Tabandeh, M.M. Ghomshei, “Natural frequency analysis of non-uniform smart beams with piezoelectric layers, using differential quadrature method”, Composites Part B, 2014, 58: 303-311.10.1016/j.compositesb.2013.10.022Search in Google Scholar

[31] M. Ahmadi, A. Nikkho, “Utilization of characteristic polynomials in vibration analysis of non-uniform beams under a moving mass excitation”. Applied Mathematical Modelling, 2014, 38(7-8): 2130-2140.10.1016/j.apm.2013.10.011Search in Google Scholar

[32] K. Torabi, H. Afshari, F. Haji Aboutalebi, “A DQEM for transverse vibration analysis of multiple cracked non-uniform Timoshenko beams with general boundary conditions”, Computers & Mathematics with Applications, 2014, 67(3): 527-541.Search in Google Scholar

[33] Z. Zhang, F. Chen, Z. Zhang, H. Hua, “Vibration analysis of nonuniform Timoshenko beams coupled with flexible attachments and multiple discontinuities”, International Journal of Mechanical Sciences, 2014, 80: 131-143.10.1016/j.ijmecsci.2014.01.008Search in Google Scholar

[34] A.A. Mahmoud, R. Awadalla, M.M. Nassar, “Free vibration of non-uniform column using DQM”, Mechanics Research Communications, 2011, 38(6): 443-448.Search in Google Scholar

[35] S.W. Tsai, C.V. Hoa, D. Gay, “Composite Materials, Design and Applications”, CRC Press, 2003.Search in Google Scholar

[36] D.L. Shi, X.Q. Feng, Y.Y. Huang, K.C. Hwang, H. Gao, “The effect of nanotube waviness and agglomeration on the elasticproperty of carbon nanotube reinforced composites”, Journal of Engineering Materials and Technology, 2004, 126: 250-257.10.1115/1.1751182Search in Google Scholar

[37] C. Shu, B.E. Richards, “Application of generalized differential quadrature to solve two-dimensional incompressible Navier- Stockes equations”, International Journal for Numerical Methods in Fluids, 1992, 15: 791-798.10.1002/fld.1650150704Search in Google Scholar

[38] Bert CW., Malik M., Differential quadrature method in computational mechanics, a review. Appl. Mech. Rev. 1996, 49:1-28.10.1115/1.3101882Search in Google Scholar

[39] F. Tornabene, A. Liverani, G. Caligiana, “FGM and laminated doubly curved shells and panels of revolution with a free-form meridian: A 2-D GDQ solution for free vibrations”, International Journal of Mechanical Sciences, 2011, 53(6): 446-470.Search in Google Scholar

[40] F. Tornabene, N. Fantuzzi, F. Ubertini, E. Viola, “Strong Formulation Finite Element Method Based on Differential Quadrature: A Survey”, Applied Mechanics Reviews, 2015, 67..10.1115/1.4028859Search in Google Scholar

[41] F. Tornabene, N. Fantuzzi, M. Bacciocchi, “The strong formulation finite element method: stability and accuracy” Frattura ed Integrità Strutturale, 2014, 29: 251-265.10.3221/IGF-ESIS.29.22Search in Google Scholar

[42] G.M. Odegard, T.S.Gates, K.E.Wise, C. Park, E.J. Siochi, “Constitutive modeling of nanotube-reinforced polymer composites”, Composites Science and Technology, 2003, 63: 1671-1687.10.1016/S0266-3538(03)00063-0Search in Google Scholar

[43] L. Shen, J. Li, “Transversely isotropic elastic properties of single-walled carbon nanotubes”. Physical Review B, 2004, 69: 045414.10.1103/PhysRevB.69.045414Search in Google Scholar

[44] V. Tita, J. de Carvalho, J. Lirani, ‘Theoretical and Experimental Dynamic Analysis of Fiber Reinforced Composite Beams’, Journal of the Brazilian Society of Mechanical Sciences and Engineerin, 2003, 25(3): 306-310.Search in Google Scholar

Received: 2016-6-26
Accepted: 2016-9-28
Published Online: 2017-2-24
Published in Print: 2017-1-26

© 2017

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Downloaded on 28.3.2024 from https://www.degruyter.com/document/doi/10.1515/cls-2017-0003/html
Scroll to top button