Steel and Composite Structures

  • 제43권6호
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  • Pages.797-808
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  • 2022
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  • 1229-9367(pISSN)
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  • 1598-6233(eISSN)
테크노프레스 (Techno-Press)
권호 표지
DOI QR코드

DOI QR Code

Vibration characteristics of functionally graded carbon nanotube-reinforced composite double-beams in thermal environments

  • Zhao, Jing-Lei (College of Mechanical and vehicle Engineering, Chongqing University) ;
  • Chen, Xu (College of Mechanical and vehicle Engineering, Chongqing University) ;
  • She, Gui-Lin (College of Mechanical and vehicle Engineering, Chongqing University) ;
  • Jing, Yan (College of Mechanical and vehicle Engineering, Chongqing University) ;
  • Bai, Ru-Qing (College of Mechanical and vehicle Engineering, Chongqing University) ;
  • Yi, Jin (College of Mechanical and vehicle Engineering, Chongqing University) ;
  • Pu, Hua-Yan (College of Mechanical and vehicle Engineering, Chongqing University) ;
  • Luo, Jun (College of Mechanical and vehicle Engineering, Chongqing University)
  • 투고 : 2021.08.11
  • 심사 : 2022.05.24
  • 발행 : 2022.06.25
⟨ 이전 논문 다음 논문 ⟩

초록

This paper presents an investigation on the free vibration characteristics of functionally graded nanocomposite double-beams reinforced by single-walled carbon nanotubes (SWCNTs). The double-beams coupled by an interlayer spring, resting on the elastic foundation with a linear layer and shear layer, and is simply supported in thermal environments. The SWCNTs gradient distributed in the thickness direction of the beam forms different reinforcement patterns. The materials properties of the functionally graded carbon nanotube-reinforced composites (FG-CNTRC) are estimated by rule of mixture. The first order shear deformation theory and Euler-Lagrange variational principle are employed to derive the motion equations incorporating the thermal effects. The vibration characteristics under several patterns of reinforcement are presented and discussed. We conducted a series of studies aimed at revealing the effects of the spring stiffness, environment temperature, thickness ratios and carbon nanotube volume fraction on the nature frequency.

키워드

과제정보

This work was supported by the National Natural Science Foundation of China under Grants 51575329, 61773254, 61625304 and 61873157; in part by Shanghai Rising-Star Program under Grants 17QA1401500; in part by Science and Technology Commission of Shanghai under Grants 16441909400 and 17DZ1205000.

참고문헌

  1. Abo-Bakr, H.M., Abo-Bakr, R.M., Mohamed, S.A. and Eltaher, M. A. (2020a), "Weight optimization of axially functionally graded microbeams under buckling and vibration behaviors", Mech. Based Des. Struct. Machines, 1-22. http://doi.org/10.1080/15397734.2020.1838298.
  2. Abo-bakr, H.M., Abo-bakr, R.M., Mohamed, S.A. and Eltaher, M. A. (2021), "Multi-objective shape optimization for axially functionally graded microbeams", Compos. Struct., 258. http://doi.org/10.1016/j.compstruct.2020.113370.
  3. Abo-Bakr, R.M., Eltaher, M.A. and Attia, M.A. (2020b), "Pull-in and freestanding instability of actuated functionally graded nanobeams including surface and stiffening effects", Eng. Comput., 38, 255-276. http://doi.org/10.1007/s00366-020-01146-0.
  4. Adhikari, B. and Singh, B.N. (2019), "Dynamic Response of FGCNT Composite Plate Resting on an Elastic Foundation Based on Higher-Order Shear Deformation Theory", JAerE 32. http://doi.org/10.1061/(asce)as.1943-5525.0001052.
  5. Akbas, S.D., Bashiri, A.H., Assie, A.E. and Eltaher, M.A. (2020), "Dynamic analysis of thick beams with functionally graded porous layers and viscoelastic support", J. Vib. Control, 27, 1644-1655. http://doi.org/10.1177/1077546320947302.
  6. Alazwari, M.A., Abdelrahman, A.A., Wagih, A., Eltaher, M.A. and Abd-El-Mottaleb, H.E. (2021), "Static analysis of cutout microstructures incorporating the microstructure and surface effects", Steel Compos. Struct., 38, 583-597. http://doi.org/10.12989/scs.2021.38.5.583.
  7. Alibeigloo, A. and Liew, K.M. (2013), "Thermoelastic analysis of functionally graded carbon nanotube-reinforced composite plate using theory of elasticity", Compos. Struct.,106, 873-881. http://doi.org/10.1016/j.compstruct.2013.07.002.
  8. Almitani, K.H., Abdelrahman, A.A. and Eltaher, M.A. (2020), "Stability of perforated nanobeams incorporating surface energy effects", Steel Compos. Struct., 35, 555-566. http://doi.org/10.12989/scs.2020.35.4.555.
  9. Ansari, M.I., Chaubey, A.K., Kumar, A., Chakrabarti, A. and Mishra, S.S. (2019), "Analysis of functionally graded carbon nanotube-reinforced laminates", Mater. Today: Proceedings 18, 628-637. http://doi.org/10.1016/j.matpr.2019.06.457.
  10. Arani, A.G., Kiani, F. and Afshari, H. (2021), "Free and forced vibration analysis of laminated functionally graded CNTreinforced composite cylindrical panels", J. Sandwich Struct. Mater., 23, 255-278. http://doi.org/10.1177/1099636219830787.
  11. Bendenia, N., Zidour, M., Bousahla, A.A., Bourada, F., Tounsi, A., Benrahou, K.H., Bedia, E.A.A., Mahmoud, S.R. and Tounsi, A. (2020), "Deflections, stresses and free vibration studies of FGCNT reinforced sandwich plates resting on Pasternak elastic foundation", Comput. Concrete, 26, 213-226. http://doi.org/10.12989/cac.2020.26.3.213.
  12. Cao, Y., Musharavati, F., Baharom, S., Talebizadehsardari, P., Sebaey, T.A., Eyvazian, A. and Zain, A.M. (2020), "Vibration response of FG-CNT-reinforced plates covered by magnetic layer utilizing numerical solution", Steel Compos. Struct., 37, 253-258. http://doi.org/10.12989/scs.2020.37.2.253.
  13. Chen, X., Alian, A.R. and Meguid, S.A. (2019), "Modeling of CNT-reinforced nanocomposite with complex morphologies using modified embedded finite element technique", Compos. Struct., 227. http://doi.org/10.1016/j.compstruct.2019.111329.
  14. Cheng, H., Li, C.F. and Jiang, Y. (2020), "Free vibration analysis of rotating pre-twisted ceramic matrix carbon nanotubes reinforced blades", Mech. Adv. Mater. Struct., 1-75. http://doi.org/10.1080/15376494.2020.1849881.
  15. Civalek, O. and Jalaei, M.H. (2020), "Shear buckling analysis of functionally graded (FG) carbon nanotube reinforced skew plates with different boundary conditions", Aeros. Sci. Technol. 99. http://doi.org/10.1016/j.ast.2020.105753.
  16. Craveiro, D.S. and Loja, M.A.R. (2020), "A study on the effect of carbon nanotubes' distribution and agglomeration in the free vibration of nanocomposite plates", C 6. http://doi.org/10.3390/c6040079.
  17. Daikh, A.A., Drai, A., Houari, M.S.A. and Eltaher, M.A. (2020), "Static analysis of multilayer nonlocal strain gradient nanobeam reinforced by carbon nanotubes", Steel Compos. Struct., 36, 643-656. http://doi.org/10.12989/scs.2020.36.6.643.
  18. Daikh, A.A., Houari, M.S.A., Karami, B., Eltaher, M.A., Dimitri, R. and Tornabene, F. (2021), "Buckling analysis of CNTRC curved sandwich nanobeams in thermal environment", Appl. Sci., 11. http://doi.org/10.3390/app11073250.
  19. Ding, H.X. and She, G.L. (2021), "A higher-order beam model for the snap-buckling analysis of FG pipes conveying fluid", Struct. Eng. Mech., 80(1), 63-72. http://dx.doi.org/10.12989/sem.2021.80.1.063.
  20. Duc, N.D., Cong, P.H., Tuan, N.D., Tran, P. and Thanh, N.V. (2017), "Thermal and mechanical stability of functionally graded carbon nanotubes (FG CNT)-reinforced composite truncated conical shells surrounded by the elastic foundations", Thin-Wall. Struct., 115, 300-310. http://doi.org/10.1016/j.tws.2017.02.016.
  21. Duc, N.D. and Minh, P.P. (2021), "Free vibration analysis of cracked FG CNTRC plates using phase field theory", Aeros. Sci. Technol., 112. http://doi.org/10.1016/j.ast.2021.106654.
  22. Ebrahimi, F. and Farazmandnia, N. (2016), "Thermo-mechanical vibration analysis of sandwich beams with functionally graded carbon nanotube-reinforced composite face sheets based on a higher-order shear deformation beam theory". Mech. Adv. Mater. Struct., 24, 820-829. http://doi.org/10.1080/15376494.2016.1196786.
  23. Eltaher, M.A. and Abdelrahman, A.A. (2020), "Bending behavior of squared cutout nanobeams incorporating surface stress effects", Steel Compos. Struct., 36, 143-161. http://doi.org/10.12989/scs.2020.36.2.143.
  24. Esawi, A.M.K. and Farag, M.M. (2007), "Carbon nanotube reinforced composites: Potential and current challenges", Mater. Des., 28, 2394-2401. http://doi.org/10.1016/j.matdes.2006.09.022.
  25. Esen, I., Abdelrhmaan, A.A. and Eltaher, M.A. (2021a), "Free vibration and buckling stability of FG nanobeams exposed to magnetic and thermal fields", Eng. Comput., http://doi.org/10.1007/s00366-021-01389-5.
  26. Esen, I., Daikh, A.A. and Eltaher, M.A. (2021b), "Dynamic response of nonlocal strain gradient FG nanobeam reinforced by carbon nanotubes under moving point load", Europ. Phys. J. Plus, 136. http://doi.org/10.1140/epjp/s13360-021-01419-7.
  27. Esen, I., Ozarpa, C. and Eltaher, M.A. (2021c), "Free vibration of a cracked FG microbeam embedded in an elastic matrix and exposed to magnetic field in a thermal environment", Compos. Struct., 261. http://doi.org/10.1016/j.compstruct.2021.113552.
  28. Fu, T., Chen, Z., Yu, H., Hao, Q. and Zhao, Y. (2020), "Vibratory response and acoustic radiation behavior of laminated functionally graded composite plates in thermal environments", J. Sandw. Struct. Mater., 22, 1681-1706. http://doi.org/10.1177/1099636219856556.
  29. Han, F., Dan, D. and Cheng, W. (2018), "An exact solution for dynamic analysis of a complex double-beam system", Compos. Struct., 193, 295-305. http://doi.org/10.1016/j.compstruct.2018.03.088.
  30. Han, F., Dan, D. and Cheng, W. (2019), "Exact dynamic characteristic analysis of a double-beam system interconnected by a viscoelastic layer", Compos. Part B: Eng., 163, 272-281. http://doi.org/10.1016/j.compositesb.2018.11.043.
  31. Han, Y. and Elliott, J. (2007), "Molecular dynamics simulations of the elastic properties of polymer/carbon nanotube composites", Comput. Mater. Sci., 39, 315-323. http://doi.org/10.1016/j.commatsci.2006.06.011.
  32. Heidari, M. and Arvin, H. (2019), "Nonlinear free vibration analysis of functionally graded rotating composite Timoshenko beams reinforced by carbon nanotubes", J. Vib. Control, 25, 2063-2078. http://doi.org/10.1177/1077546319847836.
  33. Heshmati, M. and Yas, M.H. (2013), "Dynamic analysis of functionally graded multi-walled carbon nanotube-polystyrene nanocomposite beams subjected to multi-moving loads". Materials & Design 49, 894-904. http://doi.org/10.1016/j.matdes.2013.01.073
  34. Iijima, S. (1991), "Helical Microtubles of Graphtic Carbon", Natur, 354, 56-58. http://doi.org/10.1038/354056a0.
  35. Janghorban, M. and Nami, M.R. (2016), "Wave propagation in functionally graded nanocomposites reinforced with carbon nanotubes based on second-order shear deformation theory", Mech. Adv. Mater. Struct., 24, 458-468. http://doi.org/10.1080/15376494.2016.1142028.
  36. Janghorban, M. and Zare, A. (2011), "Free vibration analysis of functionally graded carbon nanotubes with variable thickness by differential quadrature method", Physica E: Low-dimen. Syst. Nanostruct., 43, 1602-1604. http://doi.org/10.1016/j.physe.2011.05.002.
  37. Jun, L. and Hongxing, H. (2008), "Dynamic stiffness vibration analysis of an elastically connected three-beam system", ApAc 69, 591-600. http://doi.org/10.1016/j.apacoust.2007.02.005.
  38. Kanagaraj, S., Varanda, F.R., Zhil'tsova, T.V., Oliveira, M.S.A. and Simoes, J.A.O. (2007), "Mechanical properties of high density polyethylene/carbon nanotube composites", Compos. Sci. Technol., 67, 3071-3077. http://doi.org/10.1016/j.compscitech.2007.04.024.
  39. Khosravi, F., Simyari, M., Hosseini, S.A. and Tounsi, A. (2020), "Size dependent axial free and forced vibration of carbon nanotube via different rod models", Adv. Nano Res., 9, 157-172. http://doi.org/10.12989/anr.2020.9.3.157.
  40. Liu, S. and Yang, B. (2019), "A closed-form analytical solution method for vibration analysis of elastically connected doublebeam systems", Compos. Struct., 212, 598-608. http://doi.org/10.1016/j.compstruct.2019.01.038.
  41. Lu, L., She, G.L. and Guo, X. (2021a), "Size-dependent postbuckling analysis of graphene reinforced composite microtubes with geometrical imperfection", Int. J. Mech. Sci., 199. http://doi.org/10.1016/j.ijmecsci.2021.106428
  42. Lu, L., Wang, S., Li, M. and Guo, X. (2021b), "Free vibration and dynamic stability of functionally graded composite microtubes reinforced with graphene platelets", Compos. Struct., 272. http://doi.org/10.1016/j.compstruct.2021.114231.
  43. Mallek, H., Jrad, H., Wali, M., Kessentini, A., Gamaoun, F. and Dammak, F. (2020), "Dynamic analysis of functionally graded carbon nanotube-reinforced shell structures with piezoelectric layers under dynamic loads", J. Vib. Control, 26, 1157-1172. http://doi.org/10.1177/1077546319892753.
  44. Nie, X., Zhao, L., Deng, S. and Chen, X. (2020), "How interlayer twist angles affect thermal conduction of double-walled nanotubes: A non-equilibrium molecular dynamics study", Int. J. Heat Mass Transfer, 160. http://doi.org/10.1016/j.ijheatmasstransfer.2020.120234.
  45. Odom, T.W., Huang, J.L., Kim, P. and Lieber, C.M. (1998), "Atomic structure and electronic properties of single-walled carbon nanotubes", Nature, 391, 62-64. http://doi.org/10.1038/34145.
  46. Ranjbar, M. and Feli, S. (2018), "Temperature-dependent analysis of axially functionally graded CNT reinforced micro-cantilever beams subjected to low velocity impact", Mech. Adv. Mater. Struct., 26, 1154-1168. http://doi.org/10.1080/15376494.2018.1432788.
  47. Rezaiee-Pajand, M., Sobhani, E. and Masoodi, A.R. (2020), "Free vibration analysis of functionally graded hybrid matrix/fiber nanocomposite conical shells using multiscale method", Aeros. Sci. Technol., 105. http://doi.org/10.1016/j.ast.2020.105998.
  48. She, G.L., Liu, H.B. and Karami, B. (2021), "Resonance analysis of composite curved microbeams reinforced with graphene nanoplatelets", Thin-Wall. Struct., 160, http://doi.org/10.1016/j.tws.2020.107407.
  49. She, G.L., Ding, H.X. and Zhang, Y.W. (2022), "Wave propagation in a FG circular plate via the physical neutral surface concept", Struct. Eng. Mech., 82(2), 225-232.
  50. She, G.L. (2021), "Guided wave propagation of porous functionally graded plates: The effect of thermal loadings", J. Thermal Stresses, 44(10), 1289-1305. https://doi.org/10.1080/01495739.2021.1974323.
  51. Shen, H.S. (2009), "Nonlinear bending of functionally graded carbon nanotube-reinforced composite plates in thermal environments", Compos. Struct., 91, 9-19. http://doi.org/10.1016/j.compstruct.2009.04.026.
  52. Shen, H.S. (2014), "Torsional postbuckling of nanotube-reinforced composite cylindrical shells in thermal environments", Compos. Struct., 116, 477-488. http://doi.org/10.1016/j.compstruct.2014.05.039.
  53. Shen, H.S. and Xiang, Y. (2013), "Nonlinear analysis of nanotubereinforced composite beams resting on elastic foundations in thermal environments", Eng. Struct., 56, 698-708. http://doi.org/10.1016/j.engstruct.2013.06.002.
  54. Shen, H.S. and Zhang, C.L. (2010), "Thermal buckling and postbuckling behavior of functionally graded carbon nanotubereinforced composite plates", Mater. Des., 31, 3403-3411. http://doi.org/10.1016/j.matdes.2010.01.048.
  55. Shirvanimoghaddam, K., Polisetti, B., Dasari, A., Yang, J., Ramakrishna, S. and Naebe, M. (2018), "Thermomechanical performance of cheetah skin carbon nanotube embedded composite: Isothermal and non-isothermal investigation", Polymer, 145, 294-309. http://doi.org/10.1016/j.polymer.2018.04.079.
  56. Sofiyev, A.H., Tornabene, F., Dimitri, R. and Kuruoglu, N. (2020), "Buckling behavior of FG-CNT reinforced composite conical shells subjected to a combined loading", Nanomaterials (Basel) 10. http://doi.org/10.3390/nano10030419.
  57. Subramani, M. and Ramamoorthy, M. (2021), "Vibration analysis of the multi-walled carbon nanotube reinforced doubly curved laminated composite shallow shell panels: An experimental and numerical study", J. Sandw. Struct. Mater., 23, 1594-1634. http://doi.org/10.1177/1099636219900484.
  58. Tans, S.J., Devoret, M.H., Dai, H.J., Thess, A., Smalley, R.E., Geerligs, L.J. and Dekker, C. (1997), "Individual single-wall carbon nanotubes as quantum wires". Nature 386, 474-477. http://doi.org/10.1038/386474a0.
  59. Vinyas, M. and Harursampath, D. (2020), "Nonlinear vibrations of magneto-electro-elastic doubly curved shells reinforced with carbon nanotubes", Compos. Struct., 253. http://doi.org/10.1016/j.compstruct.2020.112749.
  60. Wattanasakulpong, N. and Ungbhakorn, V. (2013), "Analytical solutions for bending, buckling and vibration responses of carbon nanotube-reinforced composite beams resting on elastic foundation", Comput. Mater. Sci., 71, 201-208. http://doi.org/10.1016/j.commatsci.2013.01.028.
  61. Yang, J., Huang, X.H. and Shen, H.S. (2020), "Nonlinear Vibration of Temperature-Dependent FG-CNTRC Laminated Beams with Negative Poisson's Ratio", Int. J. Struct. Stabil. Dyn., 20. http://doi.org/10.1142/s0219455420500431.
  62. Yang, J., Ke, L.L. and Feng, C. (2015), "Dynamic buckling of thermo-electro-mechanically loaded FG-CNTRC beams", Int. J. Struct. Stabil. Dyn., 15. http://doi.org/10.1142/s0219455415400179.
  63. Yas, M.H. and Heshmati, M. (2012), "Dynamic analysis of functionally graded nanocomposite beams reinforced by randomly oriented carbon nanotube under the action of moving load", Appl. Mathem. Modelling, 36, 1371-1394. http://doi.org/10.1016/j.apm.2011.08.037.
  64. Zghal, S., Frikha, A. and Dammak, F. (2018), "Free vibration analysis of carbon nanotube-reinforced functionally graded composite shell structures", Appl. Mathem. Modelling, 53, 132- 155. http://doi.org/10.1016/j.apm.2017.08.021.
  65. Zhang, C.L. and Shen, H.S. (2006), "Temperature-dependent elastic properties of single-walled carbon nanotubes: Prediction from molecular dynamics simulation", Appl. Phys. Lett., 89. http://doi.org/10.1063/1.2336622.
  66. Zhang, Y.Y., Wang, Y.X., Zhang, X., Shen, H.M. and She, G.L. (2021), "On snap-buckling of FG-CNTR curved nanobeams considering surface effects", Steel Compos. Struct., 38, 293-304. http://doi.org/10.12989/scs.2021.38.3.293.
  67. Zhang, Y.W. and She, G.L. (2022), "Wave propagation and vibration of FG pipes conveying hot fluid", Steel Compos. Struct., 42(3), 397-405. http://doi.org/10.12989/scs.2022.42.3.397.
  68. Zhu, P., Lei, Z. X. and Liew, K.M. (2012), "Static and free vibration analyses of carbon nanotube-reinforced composite plates using finite element method with first order shear deformation plate theory", Compos. Struct., 94, 1450-1460. http://doi.org/10.1016/j.compstruct.2011.11.010.