Abstract
The present article deals with the viscoelastic modeling and dynamic responses of the carbon nanotubes (CNTs)-based carbon fiber-reinforced polymer (CNTs-CFRP) composite spherical shell panels where CNTs are reinforced in the polymer matrix phase. The Mori–Tanaka micromechanics in conjunction with weak interface theory has been developed for the mathematical formulations of the viscoelastic modeling of CNTs-based polymer matrix phase. Further, the strength of material method has been employed to formulate the viscoelastic material behavior of the homogenized hybrid CNTs-CFRP composite materials. An eight-noded shell element with five degrees of freedom per node has been formulated to study the vibration damping characteristics of spherical shell structures made by CNTs-CFRP composite materials. Frequency- and temperature-dependent material properties of such hybrid composite materials have been obtained and analyzed. Impulse and frequency responses of such structures have been performed to study the effects of various important parameters on the material properties and such dynamic responses. Obtained results demonstrate that quick vibration mitigation may be possible using such CNTs-based proposed composite materials.
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References
Iijima, S.: Helical microtubules of graphitic carbon. Nature. 354, 56–58 (1991). https://doi.org/10.1038/354056a0
Qu, J.: The effect of slightly weakened interfaces on the overall elastic properties of composite materials. Mech. Mater. 14, 269–281 (1993). https://doi.org/10.1016/0167-6636(93)90082-3
Li, J., Weng, G.J.: Effect of a viscoelastic interphase on the creep and stress/strain behavior of fiber-reinforced polymer matrix composites. Compos. Part B Eng. 27, 589–598 (1996). https://doi.org/10.1016/1359-8368(95)00040-2
Barai, P., Weng, G.J.: A theory of plasticity for carbon nanotube reinforced composites. Int. J. Plast. 27, 539–559 (2011). https://doi.org/10.1016/j.ijplas.2010.08.006
Koratkar, N., Wei, B.Q., Ajayan, P.M.: Carbon nanotube films for damping applications. Adv. Mater. 14, 997–1000 (2002). https://doi.org/10.1002/1521-4095(20020705)14:13/14%3c997::AID-ADMA997%3e3.0.CO;2-Y
Koratkar, N.A., Wei, B., Ajayan, P.M.: Multifunctional structural reinforcement featuring carbon nanotube films. Compos. Sci. Technol. 63, 1525–1531 (2003). https://doi.org/10.1016/S0266-3538(03)00065-4
Shi, D.-L., Feng, X.-Q., Huang, Y.Y., Hwang, K.-C., Gao, H.: The effect of nanotube waviness and agglomeration on the elastic property of carbon nanotube-reinforced composites. J. Eng. Mater. Technol. 126, 250 (2004). https://doi.org/10.1115/1.1751182
Zhou, X., Shin, E., Wang, K.W., Bakis, C.E.: Interfacial damping characteristics of carbon nanotube-based composites. Compos. Sci. Technol. 64, 2425–2437 (2004). https://doi.org/10.1016/j.compscitech.2004.06.001
Rajoria, H., Jalili, N.: Passive vibration damping enhancement using carbon nanotube-epoxy reinforced composites. Compos. Sci. Technol. 65, 2079–2093 (2005). https://doi.org/10.1016/j.compscitech.2005.05.015
Li, K., Gao, X.-L., Roy, A.K.: Micromechanical modeling of viscoelastic properties of carbon nanotube-reinforced polymer composites. Mech. Adv. Mater. Struct. 13, 317–328 (2006). https://doi.org/10.1080/15376490600583931
Putz, K., Krishnamoorti, R., Green, P.F.: The role of interfacial interactions in the dynamic mechanical response of functionalized SWNT-PS nanocomposites. Polymer (Guildf) 48, 3540–3545 (2007). https://doi.org/10.1016/j.polymer.2007.03.072
Suhr, J., Koratkar, N.A.: Energy dissipation in carbon nanotube composites: a review. J. Mater. Sci. 43, 4370–4382 (2008)
Man, Y., Li, Z., Zhang, Z.: Interfacial friction damping characteristics in MWNT-filled polycarbonate composites. Front. Mater. Sci. China 3, 266–272 (2009). https://doi.org/10.1007/s11706-009-0040-1
Huang, Y., Tangpong, X.W.: A distributed friction model for energy dissipation in carbon nanotube-based composites. Commun. Nonlinear Sci. Numer. Simul. 15, 4171–4180 (2010). https://doi.org/10.1016/j.cnsns.2010.01.017
Huang, Y., Tangpong, X.W.: A new friction model for evaluating energy dissipation in carbon nanotube-based composites. In: Luo, ACJ. (eds.) Dynamical Systems, pp. 95–104. Springer, New York (2010)
Khan, S.U., Li, C.Y., Siddiqui, N.A., Kim, J.-K.: Vibration damping characteristics of carbon fiber-reinforced composites containing multi-walled carbon nanotubes. Compos. Sci. Technol. 71, 1486–1494 (2011). https://doi.org/10.1016/j.compscitech.2011.03.022
Li, R., Sun, L.: A micromechanics-based viscoelastic model for nanocomposites with imperfect interface. Int. J. Damage Mech. 22, 967–981 (2013). https://doi.org/10.1177/1056789512469890
Tahan Latibari, S., Mehrali, M., Mottahedin, L., Fereidoon, A., Metselaar, H.S.C.: Investigation of interfacial damping nanotube-based composite. Compos. B Eng. 50, 354–361 (2013). https://doi.org/10.1016/j.compositesb.2013.02.022
Spitas, V., Spitas, C., Michelis, P.: Modeling of the elastic damping response of a carbon nanotube-polymer nanocomposite in the stress–strain domain using an elastic energy release approach based on stick-slip. Mech. Adv. Mater. Struct. 20, 791–800 (2013). https://doi.org/10.1080/15376494.2012.677100
Kim, H.C., Kim, E.H., Lee, I., Byun, J.H., Kim, B.S., Ahn, S.M.: Fabrication of carbon nanotubes dispersed woven carbon fiber/epoxy composites and their damping characteristics. J. Compos. Mater. 47, 1045–1054 (2013). https://doi.org/10.1177/0021998312445513
Alva, A., Raja, S.: Damping characteristics of epoxy-reinforced composite with multiwall carbon nanotubes. Mech. Adv. Mater. Struct. 21, 197–206 (2014). https://doi.org/10.1080/15376494.2013.834091
Bhattacharya, S., Alva, A., Raja, S.: Modeling and characterization of multiwall carbon nanotube reinforced polymer composites for damping applications. Int. J. Comput. Methods Eng. Sci. Mech. 15, 258–264 (2014). https://doi.org/10.1080/15502287.2014.882442
Gardea, F., Glaz, B., Riddick, J., Lagoudas, D.C., Naraghi, M.: Energy dissipation due to interfacial slip in nanocomposites reinforced with aligned carbon nanotubes. ACS Appl. Mater. Interfaces 7, 9725–9735 (2015). https://doi.org/10.1021/acsami.5b01459
Wang, T.-Y., Liu, S.-C., Tsai, J.-L.: Micromechanical stick-slip model for characterizing damping responses of single-walled carbon nanotube nanocomposites. J. Compos. Mater. 50, 57–73 (2016). https://doi.org/10.1177/0021998315570371
Shokrieh, M.M., Ghajar, R., Shajari, A.R.: The effect of time-dependent slightly weakened interface on the viscoelastic properties of CNT/polymer nanocomposites. Compos. Struct. 146, 122–131 (2016). https://doi.org/10.1016/j.compstruct.2016.03.022
Jarali, C.S., Madhusudan, M., Vidyashankar, S., Lu, Y.C.: Modelling of the interfacial damping due to nanotube agglomerations in nanocomposites. Smart Struct. Syst. 19, 57–66 (2017). https://doi.org/10.12989/sss.2017.19.1.057
Swain, A., Roy, T., Nanda, B.K.: Vibration damping characteristics of carbon nanotubes-based thin hybrid composite spherical shell structures. Mech. Adv. Mater. Struct. 24, 95–113 (2017). https://doi.org/10.1080/15376494.2015.1107669
Kundalwal, S.I., Suresh, R.S., Ray, M.C.: Smart damping of laminated fuzzy fiber reinforced composite shells using 1–3 piezoelectric composites. Smart Mater. Struct. 22, 105001 (2013). https://doi.org/10.1088/0964-1726/22/10/105001
Kundalwal, S.I., Meguid, S.A.: Effect of carbon nanotube waviness on active damping of laminated hybrid composite shells. Acta Mech. 226, 2035–2052 (2015). https://doi.org/10.1007/s00707-014-1297-8
Kundalwal, S.I., Ray, M.C.: Smart damping of fuzzy fiber reinforced composite plates using 1–3 piezoelectric composites. J. Vib. Control 22, 1526–1546 (2016). https://doi.org/10.1177/1077546314543726
Suresh, R.S., Kundalwal, S.I., Ray, M.C.: Control of large amplitude vibrations of doubly curved sandwich shells composed of fuzzy fiber reinforced composite facings. Aerosp. Sci. Technol. 70, 10–28 (2017). https://doi.org/10.1016/j.ast.2017.07.027
Eshelby, J.D.: The determination of the elastic field of an ellipsoidal inclusion, and related problems. Proc. R. Soc. Lond. A Math. Phys. Eng. Sci. 241, 376–396 (1957)
Mori, T., Tanaka, K.: Average stress in matrix and average elastic energy of materials with misfitting inclusions. Acta Metall. 21, 571–574 (1973). https://doi.org/10.1016/0001-6160(73)90064-3
Tanaka, K., Wakashima, K., Mori, T.: Plastic deformation anisotropy and work-hardening of composite materials. J. Mech. Phys. Solids 21, 207–214 (1973). https://doi.org/10.1016/0022-5096(73)90020-3
Weng, G.J.: Some elastic properties of reinforced solids, with special reference to isotropic ones containing spherical inclusions. Int. J. Eng. Sci. 22, 845–856 (1984). https://doi.org/10.1016/0020-7225(84)90033-8
Benveniste, Y.: A new approach to the application of Mori–Tanaka’s theory in composite materials. Mech. Mater. 6, 147–157 (1987). https://doi.org/10.1016/0167-6636(87)90005-6
Qiu, Y.P., Weng, G.J.: On the application of Mori–Tanaka’s theory involving transversely isotropic spheroidal inclusions. Int. J. Eng. Sci. 28, 1121–1137 (1990). https://doi.org/10.1016/0020-7225(90)90112-V
Esteva, M., Spanos, P.: Effective elastic properties of nanotube reinforced composites with slightly weakened interfaces. J. Mech. Mater. Struct. 4, 887–900 (2009). https://doi.org/10.2140/jomms.2009.4.887
Swain, A., Baad, S., Roy, T.: Modeling and analyses of thermo-elastic properties of radially grown carbon nanotubes-based woven fabric hybrid composite materials. Mech. Adv. Mater. Struct. (2016). https://doi.org/10.1080/15376494.2016.1227498
Kundalwal, S.I., Ray, M.C.: Micromechanical analysis of fuzzy fiber reinforced composites. Int. J. Mech. Mater. Des. 7, 149–166 (2011). https://doi.org/10.1007/s10999-011-9156-4
Ray, M.C., Kundalwal, S.I.: Effect of carbon nanotube waviness on the load transfer characteristics of short fuzzy fiber-reinforced composite. J. Nanomech. Micromech. 4, A4013010 (2014). https://doi.org/10.1061/(ASCE)NM.2153-5477.0000082
Kundalwal, S.I., Ray, M.C.: Effect of carbon nanotube waviness on the elastic properties of the fuzzy fiber reinforced composites. J. Appl. Mech. 80, 21010 (2013). https://doi.org/10.1115/1.4007722
Smith, W.A., Auld, B.A.: Modeling 1–3 composite piezoelectrics: thickness-mode oscillations. IEEE Trans. Ultrason. Ferroelectr. Freq. Control 38, 40–47 (1991). https://doi.org/10.1109/58.67833
Koiter, W.T.: A consistent first approximation of the general theory of thin elastic shell. In: Proceedings of First IUTAM Symposium, pp. 12 – 33, North Holland, Amsterdam (1960)
Roy, T., Manikandan, P., Chakraborty, D.: Improved shell finite element for piezothermoelastic analysis of smart fiber reinforced composite structures. Finite Elem. Anal. Des. 46, 710–720 (2010). https://doi.org/10.1016/j.finel.2010.03.009
Sk, L., Sinha, P.K.: Improved finite element analysis of multilayered, doubly curved composite shells. J. Reinf. Plast. Compos. 24, 385–404 (2005). https://doi.org/10.1177/0731684405044899
Cura, F., Mura, A., Scarpa, F.: Modal strain energy based methods for the analysis of complex patterned free layer damped plates. J. Vib. Control 18, 1291–1302 (2012). https://doi.org/10.1177/1077546311417277
Madeira, J.F.A., Araújo, A.L., Soares, C.M.M., Soares, C.A.M., Ferreira, A.J.M.: Multiobjective design of viscoelastic laminated composite sandwich panels. Compos. B Eng. 77, 391–401 (2015). https://doi.org/10.1016/j.compositesb.2015.03.025
Rouleau, L., Deü, J.-F., Legay, A.: A comparison of model reduction techniques based on modal projection for structures with frequency-dependent damping. Mech. Syst. Signal Process. 90, 110–125 (2017). https://doi.org/10.1016/j.ymssp.2016.12.013
Barkanov, E.: Transient response analysis of structures made from viscoelastic materials. Int. J. Numer. Methods Eng. 44, 393–403 (1999). https://doi.org/10.1002/(SICI)1097-0207(19990130)44:3%3c393::AID-NME511%3e3.0.CO;2-P
Seidel, G.D., Lagoudas, D.C.: Micromechanical analysis of the effective elastic properties of carbon nanotube reinforced composites. Mech. Mater. 38, 884–907 (2006). https://doi.org/10.1016/j.mechmat.2005.06.029
Reddy, J.N.: Exact solutions of moderately thick laminated shells. J. Eng. Mech. 110, 794–809 (1984). https://doi.org/10.1061/(ASCE)0733-9399(1984)110:5(794)
Cytec CYCOM® 934 Epoxy Prepreg Neat Resin. http://www.matweb.com/search/datasheet.aspx?matguid=8606fed685624b248744e1e8141ca5d2
Tornabene, F., Fantuzzi, N., Bacciocchi, M., Viola, E.: Effect of agglomeration on the natural frequencies of functionally graded carbon nanotube-reinforced laminated composite doubly-curved shells. Compos. B Eng. 89, 187–218 (2016). https://doi.org/10.1016/j.compositesb.2015.11.016
Ashrafi, B., Hubert, P., Vengallatore, S.: Carbon nanotube-reinforced composites as structural materials for microactuators in microelectromechanical systems. Nanotechnology 17, 4895–4903 (2006). https://doi.org/10.1088/0957-4484/17/19/019
Shen, L., Li, J.: Transversely isotropic elastic properties of single-walled carbon nanotubes. Phys. Rev. B. 69, 45414 (2004). https://doi.org/10.1103/PhysRevB.69.045414
Shen, L., Li, J.: Erratum: Transversely isotropic elastic properties of single-walled carbon nanotubes [Phys. Rev. B 69, 045414 (2004)]. Phys. Rev. B. 81, 119902 (2010). https://doi.org/10.1103/PhysRevB.81.119902
Lee, S.-K., Byun, J.-H., Hong, S.H.: Effect of fiber geometry on the elastic constants of the plain woven fabric reinforced aluminum matrix composites. Mater. Sci. Eng. A 347, 346–358 (2003). https://doi.org/10.1016/S0921-5093(02)00614-7
Torayca: T300 Data Sheet. www.toraycfa.com/pdfs/T300DataSheet.pdf
Mura, T.: Anisotropic inclusions. In: Mura, T. (eds.) Micromechanics of Defects in Solids, pp. 129–176. Springer, Dordrecht (1987)
Li, J.Y., Dunn, M.L.: Anisotropic coupled-field inclusion and inhomogeneity problems. Philos. Mag. A. 77, 1341–1350 (1998). https://doi.org/10.1080/01418619808214256
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Swain, A., Roy, T. Viscoelastic modeling and vibration damping characteristics of hybrid CNTs-CFRP composite shell structures. Acta Mech 229, 1321–1352 (2018). https://doi.org/10.1007/s00707-017-2051-9
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DOI: https://doi.org/10.1007/s00707-017-2051-9