DOI QR코드

DOI QR Code

Wave propagation of FG-CNTRC plates in thermal environment using the high-order shear deformation plate theory

  • Hao-Xuan Ding (College of Mechanical and Vehicle Engineering, Chongqing University) ;
  • Hai-Bo Liu (College of Mechanical and Electric Engineering, Hunan University of Science and Technology) ;
  • Gui-Lin She (College of Mechanical and Vehicle Engineering, Chongqing University) ;
  • Fei Wu (College of Mechanical and Vehicle Engineering, Chongqing University)
  • Received : 2022.04.21
  • Accepted : 2023.05.08
  • Published : 2023.08.25

Abstract

This paper investigates wave propagation in functionally graded carbon nano-reinforced composite (FG-CNTRC) plates under the influence of temperature based on Reddy' plate model. The material properties of Carbon Nanotubes (CNTs) are size-dependent, and the volume fraction of CNTs varies only along the thickness direction of the plate for different CNTs reinforcement modes. In addition, the material properties of CNTs can vary for different temperature parameters. By solving the eigenvalue problem, analytical dispersion relations can be derived for CNTRC plates. The partial differential equations for the system are derived from Lagrange's principle and higher order shear deformation theory is used to obtain the wave equations for the CNTRC plate. Numerical analyses show that the wave propagation properties in the CNTRC plate are related to the volume fraction parameters of the CNTRC plate and the distribution pattern of the CNTs in the polymer matrix. The effects of different volume fractions of CNTs and the distribution pattern of carbon nanotubes along the cross section (UD-O-X plate) are discussed in detail.

Keywords

References

  1. Abdalla, A.W. (2021), "Nonlinear thermal vibration of pre/post-buckled two-dimensional FGM tapered microbeams based on a higher order shear deformation theory", Steel Compos. Struct., 41(6), 787-802. https://doi.org/10.12989/scs.2021.41.6.787.
  2. Abdelrahman, A.A., Esen, I., Daikh, A.A. and Eltaher, M.A. (2021), "Dynamic analysis of FG nanobeam reinforced by carbon nanotubes and resting on elastic foundation under moving load", Mech. Based Des. Struct., 2021, 1-24. https://doi.org/10.1080/15397734.2021.1999263.
  3. Alazwari, M.A., Daikh, A.A. and Eltaher, M.A. (2022), "Novel quasi 3D theory for mechanical responses of FG-CNTs reinforced composite nanoplates", Adv. Nano. Res., 12(2), 117-137. https://doi.org/10.12989/anr.2022.12.2.117.
  4. Alnujaie, A., Akba, E.D., Eltaher, M. and Assie, A. (2021), "Forced vibration of a functionally graded porous beam resting on viscoelastic foundation", Geomech. Eng., 24(1), http://doi.org/10.12989/gae.2021.24.1.091.
  5. Aminipour, H., Janghorban, M. and Civalek, O. (2020), "Analysis of functionally graded doubly-curved shells with different materials via higher order shear deformation theory", Compos. Struct., 251, 112645. http://doi.org/10.1016/j.compstruct.2020.112645.
  6. Asiri, S.A., Akba, E.D. and Eltaher, M. (2020). "Damped dynamic resonses of a layered functionally graded thick beam under a pulse load", Struct. Eng. Mech., 75(6), 713-722. http://doi.org/10.12989/sem.2020.75.6.713.
  7. Akgoz, B. and Civalek, O. (2017), "Effects of thermal and shear deformation on vibration response of functionally graded thick composite microbeams", Compos. Part B: Eng., 129, 77-87. http://doi.org/10.1016/j.compositesb.2017.07.024.
  8. Amar, L.H.H., Kaci, A., Yeghnem, R. and Tounsi, A. (2018), "A new four-unknown refined theory based on modified couple stress theory for size-dependent bending and vibration analysis of functionally graded micro-plate", Steel Compos. Struct., 26(1), 89-102. https://doi.org/10.12989/scs.2018.26.1.089.
  9. Attia, M.A. and Mohamed, S.A. (2020a), "Thermal vibration characteristics of pre/post-buckled bi-directional functionally graded tapered microbeams based on modified couple stress Reddy beam theory", Eng. Comput., 38(3), 2079-2105 https://doi.org/10.1007/s00366-020-01188-4.
  10. Attia, M.A. and Mohamed, S.A. (2020b), "Nonlinear thermal buckling and postbuckling analysis of bidirectional functionally graded tapered microbeams based on Reddy beam theory", Eng. Comput., 38(1), 525-554 https://doi.org/10.1007/s00366-020-01080-1.
  11. Babaei, H. and Eslami, M.R. (2021), "Nonlinear analysis of thermal-mechanical coupling bending of FGP infinite length cylindrical panels based on PNS and NSGT", Appl. Math. Model., 91, 1061-1080. https://doi.org/10.1016/j.apm.2020.10.004.
  12. Babaei, H., Kiani, Y. and Eslami, M.R. (2019), "Large amplitude free vibrations of long FGM cylindrical panels on nonlinear elastic foundation based on physical neutral surface", Compos. Struct., 220, 888-898. https://doi.org/10.1016/j.compstruct.2019.03.064.
  13. Babaei, H. (2022a), "Free vibration and snap-through instability of FG-CNTRC shallow arches supported on nonlinear elastic foundation", Appl. Math Comput., 413, 126606. https://doi.org/10.1016/j.amc.2021.126606.
  14. Babaei, H. (2021a), "Large deflection analysis of FG-CNT reinforced composite pipes under thermal-mechanical coupling loading", Struct., 34, 886-900. https://doi.org/10.1016/j.istruc.2021.07.091.
  15. Babaei, H, (2022b), "Thermomechanical analysis of snap-buckling phenomenon in long FG-CNTRC cylindrical panels resting on nonlinear elastic foundation", Compos. Struct., 286, 115199. https://doi.org/10.1016/j.compstruct.2022.115199.
  16. Babaei, H. (2021b), "Thermoelastic buckling and post-buckling behavior of temperature-dependent nanocomposite pipes reinforced with CNTs", Eur. Phys. J. Plus, 136(10), 1093. https://doi.org/10.1140/epjp/s13360-021-01992-x.
  17. Barretta, R., Ali Faghidian, S., Marotti de Sciarra, F., Penna, R. and Pinnola F.P. (2020), "On torsion of nonlocal Lam strain gradient FG elastic beams", Compos. Struct., 233, 111550. https://doi.org/10.1016/j.compstruct.2019.111550.
  18. Bashiri, A.H., Akbas, S.D., Abdelrahman, A.A., Assie, A. Eltaher, M.A. and Mohamed, E.F. (2021), "Vibration of multilayered functionally graded deep beams under thermal load", Geomech. Eng., 24(6), 545-557. https://doi.org/10.12989/gae.2021.24.6.545.
  19. Bisheh, H. and Wu, N. (2019), "Wave propagation in smart laminated composite cylindrical shells reinforced with carbon nanotubes in hygrothermal environments", Compos. Part B: Eng., 162, 219-241. https://doi.org/10.1016/j.compositesb.2018.10.064.
  20. Chen, X., Zhao, J.L., She, G.L., Jing, Y., Luo, J. and Pu, H.Y. (2022a), "On wave propagation of functionally graded CNT strengthened fluid-conveying pipe in thermal environment", Eur. Phys. J. Plus., 137(10), 1158. https://doi.org/10.1140/epjp/s13360-022-03234-0.
  21. Chen, X., Zhao, J.L., She, G.L., Jing, Y., Pu, H.Y. and Luo, J. (2022b), "Nonlinear free vibration analysis of functionally graded carbon nanotube reinforced fluid-conveying pipe in thermal environment", Steel. Compos. Struct., 45(5), 641-652. https://doi.org/10.12989/scs.2022.45.5.641.
  22. Civalek, O., Akba, E.D., Akgz, B. and Dastjerdi, S. (2021), "Forced vibration analysis of composite beams reinforced by carbon nanotubes", Nanomater. Basel, 11(3), 571. https://doi.org/10.3390/nano11030571.
  23. 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-Basel, 11(7), 3250. https://doi.org/10.3390/app11073250.
  24. 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. https://doi.org/10.12989/sem.2021.80.1.063.
  25. Ding, H.X., She, G.L. and Zhang, Y.W. (2022a), "Nonlinear buckling and resonances of functionally graded fluid-conveying pipes with initial geometric imperfection", Eur. Phys. J. Plus, 137, 1329. https://doi.org/10.1140/epjp/s13360-022-03570-1.
  26. Ding, H.X., Zhang, Y.W. and She, G.L. (2022b), "On the resonance problems in FG-GPLRC beams with different boundary conditions resting on elastic foundations", Comput. Concrete, 30(6), 433-443. https://doi.org/10.12989/cac.2022.30.6.433.
  27. Ding, H.X. and She, G.L. (2023), "Nonlinear resonance of axially moving graphene platelet reinforced metal foam cylindrical shells with geometric imperfection", Arch. Civil Mech. Eng., 23, 97. http://doi.org/10.1007/s43452-023-00634-6.
  28. Draoui, A., Zidour, M., Tounsi, A. and Adim, B. (2019), "Static and dynamic behavior of nanotubes-reinforced sandwich plates using (FSDT)", J. Nano. Res-Sw., 57, 117-135. https://doi.org/10.4028/www.scientific.net/JNanoR.57.117.
  29. Ebrahimi, F. and Farazmandnia, N. (2018), "Vibration analysis of functionally graded carbon nanotube-reinforced composite sandwich beams in thermal environment", Adv. Aircr. Spacecr. Sci., 5(1), 107-128. http://doi.org/10.12989/aas.2018.5.1.107.
  30. Ebrahimi, F., Habibi, M. and Safarpour, H. (2019), "On modeling of wave propagation in a thermally affected GNP-reinforced imperfect nanocomposite shell", Eng. Comput., 35(4), 1375-1389. http://doi.org/10.1007/s00366-018-0669-4.
  31. Esen, I., Abdelrhmaan, A.A. and Eltaher, M.A. (2022), "Free vibration and buckling stability of FG nanobeams exposed to magnetic and thermal fields", Eng. Comput., 38(4), 3463-3482. https://doi.org/10.1007/s00366-021-01389-5.
  32. 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", Eur. Phys. J. Plus, 136(4), 458. https://doi.org/10.1140/epjp/s13360-021-01419-7.
  33. Esen, I., Ozarpa, C. and Eltaher, M.A. (2021a), "Free vibration of a cracked FG microbeam embedded in an elastic matrix and exposed to magnetic field in a thermal environment", Compos. Struct., 261, 113552. https://doi.org/10.1016/j.compstruct.2021.113552.
  34. Faghidian, S.A. (2016), "Unified formulation of the stress field of saint-Venant's flexure problem for symmetric cross-sections", Int. J. Mech. Sci., 111, 65-72. https://doi.org/10.1016/j.ijmecsci.2016.04.003.
  35. Farzad, E. and Pooya, R, (2018), "Wave propagation analysis of carbon nanotube reinforced composite beams", Eur. Phys. J. Plus, 133(7), 285. https://doi.org/10.1140/epjp/i2018-12069-y.
  36. Gan, L.L. and She, G.L. (2023), "Nonlinear snap-buckling and resonance of FG-GPLRC curved beams with different boundary conditions", Geomech. Eng., 32(5), 541-551. https://doi.org/10.12989/gae.2023.32.5.541.
  37. Gan, L.L., Xu, J.Q. and She, G.L. (2023), "Wave propagation of graphene platelets reinforced metal foams circular plates", Struct. Eng. Mech., 85(5), 645-654. https://doi.org/10.12989/sem.2023.85.5.645.
  38. Golmakani, M.E., Malikan, M. and Pour, S.G. (2021), "Bending analysis of functionally graded nanoplates based on a higher-order shear deformation theory using dynamic relaxation method", Continuum Mech. Therm., https://doi.org/10.1007/s00161-021-00995-4.
  39. Hadji, L., Meziane, M. and Safa, A. (2018), "A new quasi-3D higher shear deformation theory for vibration of functionally graded carbon nanotube-reinforced composite beams resting on elastic foundation", Struct. Eng. Mech., 66(6), 771-781. https://doi.org/10.12989/sem.2018.66.6.771.
  40. Heydari, A. (2018), "Exact vibration and buckling analyses ofarbitrary gradation of nano-higher order rectangular beam", Steel Compos. Struct., 28(5), 589-606. http://doi.org/10.12989/scs.2018.28.5.589.
  41. Karami, B., Shahsavari, D. and Janghorban, M. (2018), "A comprehensive analytical study on functionally graded carbon nanotube-reinforced composite plates", Aerosp. Sci. Technol., 82, 499-512. http://doi.org/10.1016/j.ast.2018.10.001.
  42. Khelifa, Z., Hadji, L., Daouadji, T.H. and Bourada, M. (2018), "Buckling response with stretching effect of carbon nanotube-reinforced composite beams resting on elastic foundation", Struct. Eng. Mech., 67(2), 125-130. http://dx.doi.org/10.12989/sem.2018.67.2.125.
  43. Khosravi, S., Arvin, H. and Kiani, Y. (2019a), "Interactive thermal and inertial buckling of rotating temperature-dependent FG-CNT reinforced composite beams", Compos. Part B-Eng., 175, 107178. https://doi.org/10.1016/j.compositesb.2019.107178.
  44. Khosravi, S., Arvin, H. and Kiani, Y. (2019b), "Vibration analysis of rotating composite beams reinforced with carbon nanotubes in thermal environment", Int. J. Mech. Sci., 164, 105187. https://doi.org/10.1016/j.ijmecsci.2019.105187.
  45. Kiani, Y. (2017), "Free vibration of carbon nanotube reinforced composite plate on point supports using lagrangian multipliers", Meccanica, 52(6), 1353-1367. https://doi.org/10.1007/s11012-016-0466-3.
  46. Kiani, Y. (2016), "Thermal post-buckling of temperature-dependent sandwich beams with carbon nanotube-reinforced face sheets", J. Therm. Stress., 39(9), 1098-1110. https://doi.org/10.1080/01495739.2016.1192856.
  47. Kiani, Y. (2018), "Thermal post-buckling of temperature dependent sandwich plates with FG-CNTRC face sheets", J. Therm. Stress., 41(7), 866-882. https://doi.org/10.1080/01495739.2018.1425645.
  48. Li, Y.P., She, G.L., Gan, L.L. and Liu, H.B. (2023), "Nonlinear thermal post-buckling analysis of graphene platelets reinforced metal foams plates with initial geometrical imperfection", Steel. Compos. Struct., 46(5) 649-658. https://doi.org/10.12989/scs.2023.46.5.649.
  49. Lu, L., She, G.L. and Guo, X. (2021), "Size-dependent postbuckling analysis of graphene reinforced composite microtubes with geometrical imperfection", Int. J. Mech. Sci., 199, 106428. https://doi.org/10.1016/j.ijmecsci.2021.106428.
  50. Sun, D. and Luo, S.N. (2012), "Wave propagation and transient response of a functionally graded material plate under a point impact load in thermal environments", Appl. Math. Model., 36(1), 444-462. https://doi.org/10.1016/j.apm.2011.07.023.
  51. Malikan, M. and Eremeyev, V.A. (2021), "Effect of surface on the flexomagnetic response of ferroic composite nanostructures; nonlinear bending analysis", Compos. Struct., 271, 114179. https://doi.org/10.1016/j.compstruct.2021.114179.
  52. Medani, M., Benahmed, A., Zidour, M., Heireche, H., Tounsi, A., Bousahla, A.A., Tounsi, A. and Mahmoud, S.R. (2019), "Static and dynamic behavior of (FG-CNT) reinforced porous sandwich plate using energy principle", Steel Compos. Struct., 32(5), 595-610. https://doi.org/10.12989/scs.2019.32.5.595.
  53. Melaibari, A., Daikh, A.A., Basha, M., Abdalla, A.W., Othman, R., Almitani, K.H., Hamed, M.A., Abdelrahman, A. and Eltaher, M.A. (2022a), "Free vibration of FG-CNTRCs nano-plates/shells with temperature-dependent properties", Math. Basel, 10(4), 583. https://doi.org/10.3390/math10040583,2022.
  54. Melaibari, A., Daikh, A.A., Basha, M., Wagih, A., Othman, R., Almitani, K.H., Hamed, M.A., Abdelrahman, A. and Eltaher, M.A. (2022b), "A dynamic analysis of randomly oriented functionally graded carbon nanotubes/fiber-reinforced composite laminated shells with different geometries", Math. Basel, 10(3), 408. https://doi.org/10.3390/math10030408.
  55. Reddy, J.N. (1999), "A simple higher order-theory for laminated composite plates", J. Appl. Mech-T Asme., 51, 745-752. https://doi.org/10.1115/1.3167719.
  56. She, G.L. (2021a), "Guided wave propagation of porous functionally graded plates: The effect of thermal loadings", J. Therm. Stress., 44(10), 1289-1305. https://doi.org/10.1080/01495739.2021.1974323.
  57. She, G.L., Liu, H.B. and Karami, B. (2021b), "Resonance analysis of composite curved microbeams reinforced with graphene nanoplatelets", Thin Wall. Struct., 160, 107407. https://doi.org/10.1016/j.tws.2020.107407.
  58. She, G.L. and Ding, H.X. (2023), "Nonlinear primary resonance analysis of initially stressed graphene platelet reinforced metal foams doubly curved shells with geometric imperfection", Acta Mech. Sin., 39, 522392. https://doi.org/10.1007/s10409-022-22392-x.
  59. 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. https://doi.org/10.12989/sem.2022.82.2.225.
  60. She, G.L. and Li, Y.P. (2022), "Wave propagation in an FG circular plate in thermal environment", Geomech. Eng., 31(6), 615-622. https://doi.org/10.12989/gae.2022.31.6.615.
  61. Shen, H.S. and Zhang, C.L. (2010), "Thermal buckling and postbuckling behavior of functionally graded carbon nanotube-reinforced composite plates", Mater. Des., 31(7), 3403-3411. https://doi.org/10.1016/j.matdes.2010.01.048.
  62. Song, J.P. and She, G.L. (2023), "Nonlinear resonance of axially moving GPLRMF plates with different boundary conditions", Struct. Eng. Sci., 86(3), 361-371. https://doi.org/10.12989/sem.2023.86.3.361.
  63. Xu, J.Q. and She, G.L. (2022), "Thermal post-buckling analysis of porous functionally graded pipes with initial geometric imperfection", Geomech. Eng., 31(3), 329-337. https://doi.org/10.12989/gae.2022.31.3.329.
  64. Zenkour, A.M. (2018), "A quasi-3D refined theory for functionallygraded single-layered and sandwich plates with porosities", Compos. Struct., 201, 38-48. https://doi.org/10.1016/j.compstruct.2018.05.147.
  65. Zenkour, A.M. and Radwan, A.F. (2019), "Bending response of FG plates resting on elastic foundations in hygro thermal environment with porosities", Compos. Struct., 213, 133-143. https://doi.org/10.1016/j.compstruct.2019.01.065.
  66. Zhang, Y.W., Ding, H.X. and She, G.L. (2022), "Snap-buckling and resonance of functionally graded graphene reinforced composites curved beams resting on elastic foundations in thermal environment", J. Therm. Stress., 45(12), 1029-1042.https://doi.org/10.1080/01495739.2022.2125137.
  67. Zhang, Y.W., Ding, H.X. and She, G.L. (2023a), "Wave propagation in spherical and cylindrical panels reinforced with carbon nanotubes", Steel Compos. Struct., 46(1), 133-141. https://doi.org/10.12989/scs.2023.46.1.133.
  68. Zhang, Y.W., She, G.L., and Ding, H.X. (2023b), "Nonlinear resonance of graphene platelets reinforced metal foams plates under axial motion with geometric imperfections", Eur. J. Mech. A-Solid., 98, 104887. https://doi.org/10.1016/j.euromechsol.2022.104887.
  69. 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. https://doi.org/10.12989/scs.2022.42.3.397.
  70. Zhang, Y.W. and She, G.L. (2023a), "Nonlinear low-velocity impact response of graphene platelet-reinforced metal foam cylindrical shells under axial motion with geometrical imperfection", Nonlinear Dyn., 111(7), 6317-6334. https://doi.org/10.1007/s11071-022-08186-9.
  71. Zhang, Y.W. and She, G.L. (2023b), "Nonlinear primary resonance of axially moving functionally graded cylindrical shells in thermal environment", Mech. Adv. Mater. Struct., 2023, 1-13. https://doi.org/10.1080/15376494.2023.2180556.
  72. Zhang, Y.W., She, G.L., Gan, L.L. and Li, Y.P. (2023c), "Thermal post-buckling behavior of GPLRMF cylindrical shells with initial geometrical imperfection", Geomech. Eng., 32(6), 615-625. https://doi.org/10.12989/gae.2023.32.6.615.
  73. Zhang, Y.Y., Wang, X.Y., Zhang, X., Shen, H.M. and She, G.L. (2021), "On snap-buckling of FG-CNTRC curved nanobeams considering surface effects", Steel Compos. Struct., 38(3), 293-304. https://doi.org/10.12989/scs.2021.38.3.293.
  74. Zhao, J.L., Chen, X., She, G.L., Jing, Y., Bai, R.Q., Yi, J., Pu, H.Y., and Luo, J. (2022a), "Vibration characteristics of functionally graded carbon nanotube-reinforced composite double-beams in thermal environments", Steel. Compos. Struct., 43(6), 797-808. https://doi.org/10.12989/scs.2022.43.6.797.
  75. Zhao, J.L., She, G.L., Wu, F., Yuan, S.J., Bai, R.Q., Pu, H.Y., Wang, S.L. and Luo, J. (2022b), "Guided waves of porous FG nanoplates with four edges clamped", Adv. Nano. Res., 13(5), 465-474. https://doi.org/10.12989/anr.2022.13.5.465.
  76. Zouatnia, N., Hadji, L. and Kassoul, A. (2017), "A refined hyperbolic shear deformation theory for bending of functionally graded beams based on neutral surface position", Struct. Eng. Mech., 63(5), 683-689. http://doi.org/10.12989/sem.2017.63.5.683.