Advances in nano research

  • 제14권5호
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  • Pages.421-433
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  • 2023
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  • 2287-237X(pISSN)
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  • 2287-2388(eISSN)
테크노프레스 (Techno-Press)
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DOI QR코드

DOI QR Code

The influence of non-linear carbon nanotube reinforcement on the natural frequencies of composite beams

  • Mehmet Avcar (Department of Civil Engineering, Faculty of Engineering, Suleyman Demirel University) ;
  • Lazreg Hadji (Faculty of Civil Engineering, Ton Duc Thang University) ;
  • Omer Civalek (Department of Medical Research, China Medical University Hospital, China Medical University)
  • 투고 : 2022.04.21
  • 심사 : 2022.09.14
  • 발행 : 2023.05.25
⟨ 이전 논문 다음 논문 ⟩

초록

In the present paper, the influences of the variation of exponent of volume fraction of carbon nanotubes (CNTs) on the natural frequencies (NFs) of the carbon nanotube-reinforced composite (CNTRC) beams under four different boundary conditions (BCs) are investigated. The single-walled carbon nanotubes (SWCNTs) are assumed to be aligned and dispersed in a polymeric matrix with various reinforcing patterns, according to the variation of exponent of volume fraction of CNTs for functionally graded (FG) reinforcements. Besides, uniform distribution (UD) of reinforcement is also considered to analyze the influence of the non-linear (NL) variation of the reinforcement of CNTs. Using Hamilton's principle and third-order shear deformation theory (TSDT), the equations of motion of the CNTRC beam are derived. Under four different BCs, the resulting equations are solved analytically. To verify the present formulation, comparison investigations are conducted. To examine the impacts of several factors on the NFs of the CNTRC beams, numerical examples and some benchmark results are presented.

키워드

참고문헌

  1. Afshin, S. and Yas, M.H. (2020), "Dynamic and buckling analysis of polymer hybrid composite beam with variable thickness", Appl. Math. Mech., 41, 785-804. https://doi.org/10.1007/S10483-020-2610-7
  2. Alibeigloo, A. and Emtehani, A. (2015), "Static and free vibration analyzes of carbon nanotube-reinforced composite plate using differential quadrature method", Meccanica, 50, 61-76. https://doi.org/10.1007/S11012-014-0050-7
  3. Ansari, R., Faghih Shojaei, M., Mohammadi, V., Gholami R. and Sadeghi, F. (2014), "Nonlinear forced vibration analysis of functionally graded carbon nanotube-reinforced composite Timoshenko beams", Compos. Struct.,113, 316-327. https://doi.org/10.1016/j.compstruct.2014.03.015
  4. Ansari, R., Torabi, J. and Hassani, R. (2019), "A comprehensive study on the free vibration of arbitrary shaped thick functionally graded CNT-reinforced composite plates", Eng. Struct., 181, 653-669. https://doi.org/10.1016/j.engstruct.2018.12.049
  5. Arani, A. G., Kolahchi, R. and Esmailpour, M. (2016), "Nonlinear vibration analysis of piezoelectric plates reinforced with carbon nanotubes using DQM", Smart Struct. Syst., Int. J., 18(4), 787-800. https://doi.org/10.12989/sss.2016.18.4.787
  6. Barretta R., Caporale A., Faghidian S.A., Luciano R., Marotti de Sciarra F. and Medaglia C. M. (2019), "A stress-driven local-nonlocal mixture model for Timoshenko nano-beams", Compos. Part B Eng., 164, 590-598. https://doi.org/10.1016/j.compositesb.2019.01.012
  7. Benachour, A., Tahar, H.D., Atmane, H.A., Tounsi, A. and Ahmed, M.S. (2011), "A four variable refined plate theory for free vibrations of functionally graded plates with arbitrary gradient", Compos. Part B Eng. 42, 1386-1394. https://doi.org/10.1016/j.compositesb.2011.05.032
  8. Bisheh, H., Wu, N. and Rabczuk, T. (2020), "Free vibration analysis of smart laminated carbon nanotube-reinforced composite cylindrical shells with various boundary conditions in hygrothermal environments", Thin Walled Struct., 149, 106500. https://doi.org/10.1016/J.TWS.2019.106500
  9. Borjalilou, V., Taati, E. and Ahmadian, M.T. (2019), "Bending, buckling and free vibration of nonlocal FG-carbon nanotube-reinforced composite nanobeams: exact solutions", SN Appl. Sci., 1, 1323. https://doi.org/10.1007/S42452-019-1359-6
  10. Bousahla, A.A., Bourada, F., Mahmoud, S.R., Tounsi, A., Algarni, A., Adda Bedia, E.A. and Tounsi, A. (2020), "Buckling and dynamic behavior of the simply supported CNT-RC beams using an integral-first shear deformation theory", Comput. Concr., 25, 155-166. https://doi.org/10.12989/cac.2020.25.2.155
  11. Chamran, S., Chen, C.-S., Fung, C.-P., Wang, H. and Chen, W.-R. (2022), "Dynamic response of functionally graded carbon nanotube-reinforced hybrid composite plates", J. Appl. Comput. Mech., 8, 182-195. https://doi.org/10.22055/JACM.2021.37884.3108
  12. Chiroiu, V., Munteanu, L. and Gliozzi, A.S. (2010), "Application of cosserat theory to the modelling of reinforced carbon nananotube beams", Comput. Mater. Contin., 19, 1-16. https://doi.org/10.3970/cmc.2010.019.001
  13. Civalek, O . and Avcar, M. (2020), "Free vibration and buckling analyzes of CNT reinforced laminated non-rectangular plates by discrete singular convolution method", Eng. Comput. 1, 1-33. https://doi.org/10.1007/s00366-020-01168-8
  14. Civalek, O . and Baltacioglu, A.K. (2018), "Vibration of carbon nanotube reinforced composite (CNTRC) annular sector plates by discrete singular convolution method", Compos. Struct., 203, 458-465. https://doi.org/10.1016/j.compstruct.2018.07.037
  15. Deepak, B.P., Ganguli, R. and Gopalakrishnan, S. (2012), "Dynamics of rotating composite beams: A comparative study between CNT reinforced polymer composite beams and laminated composite beams using spectral finite elements", Int. J. Mech. Sci., 64, 110-126. https://doi.org/10.1016/j.ijmecsci.2012.07.009
  16. Ehyaei, J. and Daman, M. (2017), "Free vibration analysis of double walled carbon nanotubes embedded in an elastic medium with initial imperfection", Adv. Nano Res., 5(2), 179. https://doi.org/10.12989/anr.2017.5.2.179
  17. El-Ashmawy, A.M. and Xu, Y. (2021), "Combined effect of carbon nanotubes distribution and orientation on functionally graded nano-composite beams using finite element analysis" Mater. Res. Express, 8. https://doi.org/10.1088/2053-1591/ABC773
  18. Esawi, A.M.K. and Farag, M.M. (2007), "Carbon nanotube reinforced composites: potential and current challenges", Mater. Des., 28, 2394-2401. https://doi.org/10.1016/j.matdes.2006.09.022
  19. Feng, T., Liu, N., Wang, S., Qin, C., Shi, S., Zeng, X. and Liu, G. (2021), "Research on the dispersion of carbon nanotubes and their application in solution-processed polymeric matrix composites: A review", Adv. Nano Res., 10(6), 559-576. https://doi.org/10.12989/anr.2021.10.6.559
  20. Griebel, M. and Hamaekers, J. (2004), "Molecular dynamics simulations of the elastic moduli of polymer-carbon nanotube composites", Comput. Methods Appl. Mech. Eng., 193, 1773-1788. https://doi.org/10.1016/j.cma.2003.12.025
  21. Han, Y. and Elliott, J. (2007), "Molecular dynamics simulations of the elastic properties of polymer/carbon nanotube composites", Comput. Mater. Sci., 39, 315-323. https://doi.org/10.1016/j.commatsci.2006.06.011
  22. Hedayati, H. and Sobhani Aragh, B. (2012), "Influence of graded agglomerated CNTs on vibration of CNT-reinforced annular sectorial plates resting on Pasternak foundation", Appl. Math. Comput., 218, 8715-8735. https://doi.org/10.1016/J.AMC.2012.01.080
  23. Heshmati M. and Yas M. H. (2013), "Free vibration analysis of functionally graded CNT-reinforced nano-composite beam using Eshelby-Mori-Tanaka approach", J. Mech. Sci. Technol., 27, 3403-3408. https://doi.org/10.1007/S12206-013-0862-8
  24. Heshmati, M., Yas, M.H. and Daneshmand, F. (2015), "A comprehensive study on the vibrational behavior of CNT-reinforced composite beams", Compos. Struct., 125, 434-448. https://doi.org/10.1016/j.compstruct.2015.02.033
  25. Hussain, M., Naeem, M. N., Asghar, S., & Tounsi, A. (2020), "Theoretical impact of Kelvin's theory for vibration of double walled carbon nanotubes", Adv. Nano Res., 8(4), 307-322. https://doi.org/10.12989/anr.2020.8.4.307
  26. Iijima S. (1991), "Helical microtubules of graphitic carbon", Nature, 354, 56-58. https://doi.org/10.1038/354056a0
  27. Jalaei, M.H., Thai, H.T. and Civalek, O. (2022), "On viscoelastic transient response of magnetically imperfect functionally graded nanobeams", Int. J. Eng. Sci., 172, 103629. https://doi.org/10.1016/j.ijengsci.2022.103629
  28. Jam, J.E. and Kiani, Y. (2015), "Buckling of pressurized functionally graded carbon nanotube reinforced conical shells", Compos. Struct., 125, 586-595. https://doi.org/10.1016/j.compstruct.2015.02.052
  29. Kamarian, S., Salim, M., Dimitri, R. and Tornabene, F. (2016), "Free vibration analysis of conical shells reinforced with agglomerated Carbon Nanotubes", Int. J. Mech. Sci., 108-109, 157-165. https://doi.org/10.1016/j.ijmecsci.2016.02.006
  30. Kamarian, S., Shakeri, M., Karimi, B. and Pourasghar, A. (2016), "Free vibration analysis and design optimization of nanocomposite-laminated beams using various higher order beam theories and imperialist competitive algorithm", Polym. Compos., 37, 2442-2451. https://doi.org/10.1002/PC.23429
  31. Kaw, A. (2006), Mechanics Composite of Materials, CRC Press, Boca Raton.
  32. 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
  33. Khadimallah, M.A., Hussain, M., Taj, M., Ayed, H. and Tounsi, A. (2021), "Parametric vibration analysis of single-walled carbon nanotubes based on Sanders shell theory", Adv. Nano Res., 10(2), 165-174. https://doi.org/10.12989/anr.2021.10.2.165
  34. Khadir, A.I., Daikh, A.A. and Eltaher, M.A. (2021), "Novel four-unknowns quasi 3D theory for bending, buckling and free vibration of functionally graded carbon nanotubes reinforced composite laminated nanoplates", Adv. Nano Res., 11(6), 621-640. https://doi.org/10.12989/anr.2021.11.6.621
  35. Khilari, S., Kochar, S., Sanvordenker, R. and Thomas B. (2018), "Free vibration analysis of carbon nanotube reinforced composite Timoshenko beam", Prog. Ind. Ecol., 12, 78-92. https://doi.org/10.1504/PIE.2018.095873
  36. Kumar, P. and Srinivas, J. (2017), "Free vibration, bending and buckling of a FG-CNT reinforced composite beam Comparative analysis with hybrid laminated composite beam", Multidiscipl. Model. Mater. Struct., 13, 590-611. https://doi.org/10.1108/MMMS-05-2017-0032
  37. Lau, K.T., Gu, C., Gao, G.H., Ling, H.Y. and Reid, S.R. (2004), "Stretching process of single- and multi-walled carbon nanotubes for nano-composite applications", Carbon N. Y., 42, 426-428. https://doi.org/10.1016/j.carbon.2003.10.040
  38. Lau, A.K.T. and Hui, D. (2002), "The revolutionary creation of new advanced materials - Carbon nanotube composites", Compos. Part B Eng., 33, 263-277. https://doi.org/10.1016/S1359-8368(02)00012-4
  39. Liew, K.M., Lei, Z.X. and Zhang, L.W. (2015), "Mechanical analysis of functionally graded carbon nanotube reinforced composites: A review", Compos. Struct. 120, 90-97. https://doi.org/10.1016/j.compstruct.2014.09.041
  40. Lin, F. and Xiang, Y. (2014a), "Numerical analysis on nonlinear free vibration of carbon nanotube reinforced composite beams", Int. J. Struct. Stab. Dyn. 14, 1350056. https://doi.org/10.1142/S0219455413500569
  41. Lin, F. and Xiang, Y. (2014b), "Vibration of carbon nanotube reinforced composite beams based on the first and third order beam theories", Appl. Math. Model., 38, 3741-3754. https://doi.org/10.1016/j.apm.2014.02.008
  42. Loos, M. R. (2014), "Carbon Nanotube Reinforced Composites: CNR Polymer Science and Technology", Carbon Nanotub. Reinf. Compos. CNR Polym. Sci. Technol., 1-289. https://doi.org/10.1016/C2012-0-06123-6
  43. Mahmoodi, S.N., Jalili N. and Khadem S.E. (2005), "Passive nonlinear vibrations of a directly excited nanotube-reinforced composite cantilever beam", Am. Soc. Mech. Eng. Dyn. Syst. Control Div. DSC 74 DSC, 1913-1920. https://doi.org/10.1115/IMECE2005-81608
  44. Mahmoodi, M.J., Maleki, M. and Hassanzadeh-Aghdam, M.K. (2018), "Static bending and free vibration analysis of hybrid fuzzy-fiber reinforced nano-composite beam-A multi-scale modeling", Int. J. Appl. Mech., 10. https://doi.org/10.1142/S1758825118500539
  45. Mayandi, K. and Jeyaraj, P. (2015), "Bending, buckling and free vibration characteristics of FG-CNT-reinforced polymer composite beam under non-uniform thermal load", Proc. Inst. Mech. Eng. Part L J. Mater. Des. Appl., 229, 13-28. https://doi.org/10.1177/1464420713493720
  46. Mohammadimehr, M. and Alimirzaei, S. (2017), "Buckling and free vibration analysis of tapered FG-CNTRC micro Reddy beam under longitudinal magnetic field using FEM", Smart Struct. Syst., 19, 309-322. https://doi.org/10.12989/SSS.2017.19.3.309
  47. Mohammadimehr, M., Mohammadi-Dehabadi, A.A., Alavi, S.M.A., Alambeigi, K., Bamdad, M., Yazdani, R. and Hanifehlou, S. (2018), "Bending, buckling, and free vibration analyzes of carbon nanotube reinforced composite beams and experimental tensile test to obtain the mechanical properties of nano-composite", Steel Compos. Struct., 29, 405-422. https://doi.org/10.12989/SCS.2018.29.3.405
  48. Mohammadimehr M., Monajemi A.A. and Afshari H. (2020), "Free and forced vibration analysis of viscoelastic damped FG-CNT reinforced micro composite beams", Microsyst. Technol., 26, 3085-3099. https://doi.org/10.1007/S00542-017-3682-4
  49. Mohseni, A. and Shakouri, M. (2019), "Vibration and stability analysis of functionally graded CNT-reinforced composite beams with variable thickness on elastic foundation", Proc. Inst. Mech. Eng. Part L J. Mater. Des. Appl., 233, 2478-2489. https://doi.org/10.1177/1464420719866222
  50. Moradi-Dastjerdi, R. and Payganeh, G. (2017), "Thermoelastic dynamic analysis of wavy carbon nanotube reinforced cylinders under thermal loads", Steel Compos. Struct., 25, 315-326. https://doi.org/10.12989/scs.2017.25.3.315
  51. Nejadi, M.M., Mohammadimehr, M. and Mehrabi, M. (2021), "Free vibration and buckling of functionally graded carbon nanotubes/graphene platelets Timoshenko sandwich beam resting on variable elastic foundation", Adv. Nano Res., 10(6), 539-548. https://doi.org/10.12989/anr.2021.10.6.539
  52. Nejati M., Eslampanah A. and Najafizadeh M. (2018), "Buckling and vibration analysis of functionally graded carbon nanotube-reinforced beam under axial load, Int. J. Appl. Mech., 8, 1650008. https://doi.org/10.1142/S1758825116500083
  53. Rashad, A.M. (2017), "Effect of carbon nanotubes (CNTs) on the properties of traditional cementitious materials", Constr. Build. Mater., 153, 81-101. https://doi.org/10.1016/j.conbuildmat.2017.07.089
  54. Ramezani, M., Kim, Y.H. and Sun, Z. (2021), "Elastic modulus formulation of cementitious materials incorporating carbon nanotubes: Probabilistic approach" Constr. Build. Mater., 275, 122092. https://doi.org/10.1016/j.conbuildmat.2020.122092
  55. Ramezani, M., Dehghani, A. and Sherif, M. M. (2022), "Carbon nanotube reinforced cementitious composites: A comprehensive review", Constr. Build. Mater., 315, 125100. https://doi.org/10.1016/j.conbuildmat.2021.125100
  56. Rezaiee-Pajand, M., Masoodi, A.R. and Rajabzadeh-Safaei, N. (2019), "Nonlinear vibration analysis of carbon nanotube reinforced composite plane structures", Steel Compos. Struct., 30, 493-516. https://doi.org/10.12989/scs.2019.30.6.493
  57. Reddy, J.N. (2003a), Mechanics of Laminated Composite Plates and Shells, CRC Press, Boca Raton. https://doi.org/10.1201/b12409
  58. Reddy, J.N. (2003b), Theory And Analysis Of Elastic Plates And Shells, CRC Press, Boca Raton.
  59. Saifuddin, N., Raziah, A.Z., Junizah, A.R. (2013), "Carbon nanotubes: A review on structure and their interaction with proteins", J. Chem., 676815. https://doi.org/10.1155/2013/676815
  60. Seidi, J. and Kamarian, S. (2017), "Free vibrations of non-uniform CNT/fiber/polymer nano-composite beams", Curved Layer. Struct., 4, 21-30. https://doi.org/10.1515/CLS-2017-0003
  61. Shen, H.S. (2009), "Nonlinear bending of functionally graded carbon nanotube-reinforced composite plates in thermal environments", Compos. Struct., 91, 9-19. https://doi.org/10.1016/j.compstruct.2009.04.026
  62. Shen, H.S. (2012), "Thermal buckling and postbuckling behavior of functionally graded carbon nanotube-reinforced composite cylindrical shells", Compos. Part B Eng. 43, 1030-1038. https://doi.org/10.1016/j.compositesb.2011.10.004
  63. Shen, H.S. and Xiang, Y. (2012), "Nonlinear vibration of nanotube-reinforced composite cylindrical shells in thermal environments" Comput. Methods Appl. Mech. Eng., 213-216, 196-205. https://doi.org/10.1016/J.CMA.2011.11.025
  64. Shen, H.S. and Xiang, Y. (2013), "Nonlinear analysis of nanotube-reinforced composite beams resting on elastic foundations in thermal environments", Eng. Struct., 56, 698-708. https://doi.org/10.1016/j.engstruct.2013.06.002
  65. Shi, Z., Yao, X., Pang, F. and Wang, Q. (2017), "An exact solution for the free-vibration analysis of functionally graded carbon-nanotube-reinforced composite beams with arbitrary boundary conditions", Sci. Rep., 7, 1-18. https://doi.org/10.1038/s41598-017-12596-w
  66. Thomas B. and Suresh T.P. (2017), "Vibration and buckling analysis of functionally graded carbon nanotube reinforced composite beams", Int. J. Civ. Eng. Technol., 8, 74-84.
  67. Tounsi, A., Benguediab, S., Semmah, A. and Zidour, M. (2013), "Nonlocal effects on thermal buckling properties of double-walled carbon nanotubes", Adv. Nano Res., 1(1), 1-11. https://doi.org/10.12989/anr.2013.1.1.001
  68. Vinson, J.R. and Sierakowski R.L. (2008), The Behavior of Structures Composed of Composite Materials (Solid Mechanics and its Applications), Kluwer Academic Publishers.
  69. Vo-Duy, T., Ho-Huu, V. and Nguyen-Thoi, T. (2019), "Free vibration analysis of laminated FG-CNT reinforced composite beams using finite element method", Front. Struct. Civil Eng., 13, 324-336. https://doi.org/10.1007/S11709-018-0466-6
  70. Wang, Z.X. and Shen, H.S. (2011), "Nonlinear vibration of nanotube-reinforced composite plates in thermal environments", Comput. Mater. Sci., 50, 2319-2330. https://doi.org/10.1016/j.commatsci.2011.03.005
  71. Xu, J., Yang, Z., Yang, J. and Li, Y. (2021), "Free vibration analysis of rotating FG-CNT reinforced composite beams in thermal environments with general boundary conditions", Aerosp. Sci. Technol., 118. https://doi.org/10.1016/J.AST.2021.107030
  72. Yang, J., Huang, X.H. and Shen, H.S. (2020), "Nonlinear flexural behavior of temperature-dependent FG-CNTRC laminated beams with negative Poisson's ratio resting on the Pasternak foundation", Eng. Struct. 207, 110250. https://doi.org/10.1016/j.engstruct.2020.110250
  73. Yas, M.H. and Samadi N. (2012), "Free vibrations and buckling analysis of carbon nanotube-reinforced composite Timoshenko beams on elastic foundation" Int. J. Press. Vessel. Pip., 98, 119-128. https://doi.org/10.1016/j.ijpvp.2012.07.012
  74. Zerrouki, Rachid;Karas, Abdelkader;Zidour M. (2020), "Critical buckling analyzes of nonlinear FG-CNT reinforced nano-composite beam", Adv. Nano Res., 9(3), 211-220. https://doi.org/10.12989/anr.2020.9.3.211
  75. Zerrouki, R., Karas, A., Zidour, M., Bousahla, A.A., Tounsi, A., Bourada, F., Tounsi, A., Benrahou, K.H. and Mahmoud S.R. (2021), "Effect of nonlinear FG-CNT distribution on mechanical properties of functionally graded nano-composite beam", Struct. Eng. Mech., 78, 117-124. https://doi.org/10.12989/sem.2021.78.2.117