Steel and Composite Structures

Techno-Press (테크노프레스)
권호 표지
DOI QR코드

DOI QR Code

Nonlinear forced vibrations of multi-scale epoxy/CNT/fiberglass truncated conical shells and annular plates via 3D Mori-Tanaka scheme

  • Received : 2020.03.07
  • Accepted : 2020.05.23
  • Published : 2020.06.25
⟨ Previous Next ⟩

Abstract

In the context of classic conical shell formulation, nonlinear forced vibration analysis of truncated conical shells and annular plates made of multi-scale epoxy/CNT/fiberglass composites has been presented. The composite material is reinforced by carbon nanotube (CNT) and also fiberglass for which the material properties are defined according to a 3D Mori-Tanaka micromechanical scheme. By utilizing the Jacobi elliptic functions, the frequency-deflection curves of truncated conical shells and annular plates related to their forced vibrations have been derived. The main focus is to study the influences of CNT amount, fiberglass volume, open angle, fiber angle, truncated distance and force magnitude on forced vibrational behaviors of multi-scale truncated conical shells and annular plates.

Keywords

Acknowledgement

The first and second authors would like to thank FPQ (Fidar project Qaem) for providing the fruitful and useful help.

References

  1. Abualnour, M., Chikh, A., Hebali, H., Kaci, A., Tounsi, A., Bousahla, A.A. and Tounsi, A. (2019), "Thermomechanical analysis of antisymmetric laminated reinforced composite plates using a new four variable trigonometric refined plate theory. Comput. Concrete, 24(6), 489-498. https://doi.org/10.12989/cac.2019.24.6.489.
  2. Addou, F.Y., Meradjah, M., Bousahla, A.A., Benachour, A., Bourada, F., Tounsi, A. and Mahmoud, S.R. (2019), "Influences of porosity on dynamic response of FG plates resting on Winkler/Pasternak/Kerr foundation using quasi 3D HSDT. Comput. Concrete, 24(4), 347-367. https://doi.org/10.12989/cac.2019.24.4.347.
  3. Ahmed, R.A., Fenjan, R.M. and Faleh, N.M. (2019), "Analyzing post-buckling behavior of continuously graded FG nanobeams with geometrical imperfections," Geomech. Eng., 17(2), 175-180. https://doi.org/10.12989/gae.2019.17.2.175.
  4. Azimi, M., Mirjavadi, S.S., Shafiei, N. and Hamouda, A.M.S. (2017), "Thermo-mechanical vibration of rotating axially functionally graded nonlocal Timoshenko beam", Appl. Phys. A, 123(1), 104.
  5. Azimi, M., Mirjavadi, S.S., Shafiei, N., Hamouda, A.M.S. and Davari, E. (2018), "Vibration of rotating functionally graded Timoshenko nano-beams with nonlinear thermal distribution", Mech. Adv. Mater. Struct, 25(6), 467-480. https://doi.org/10.1080/15376494.2017.1285455
  6. Barati, M.R. and Zenkour, A.M. (2017), "Post-buckling analysis of refined shear deformable graphene platelet reinforced beams with porosities and geometrical imperfection", Compos. Struct., 181, 194-202. https://doi.org/10.1016/j.compstruct.2017.08.082.
  7. Balubaid, M., Tounsi, A., Dakhel, B. and Mahmoud, S.R. (2019), "Free vibration investigation of FG nanoscale plate using nonlocal two variables integral refined plate theory", Comput. Concrete, 24(6), 579-586. https://doi.org/10.12989/cac.2019.24.6.579.
  8. Batou, B., Nebab, M., Bennai, R., Atmane, H.A., Tounsi, A. and Bouremana, M. (2019), "Wave dispersion properties in imperfect sigmoid plates using various HSDTs", Steel Compos. Struct., 33(5), 699-716. https://doi.org/10.12989/scs.2019.33.5.699.
  9. Bellal, M., Hebali, H., Heireche, H., Bousahla, A.A., Tounsi, A., Bourada, F. and Tounsi, A. (2020), "Buckling behavior of a single-layered graphene sheet resting on viscoelastic medium via nonlocal four-unknown integral model", Steel Compos. Struct., 34(5), 643-655. https://doi.org/10.12989/scs.2020.34.5.643.
  10. Berghouti, H., Adda Bedia, E.A., Benkhedda, A. and Tounsi, A. (2019), "Vibration analysis of nonlocal porous nanobeams made of functionally graded material", Adv. Nano Res., 7(5), 351-364. https://doi.org/10.12989/anr.2019.7.5.351.
  11. Bouamoud, A., Boucham, B., Bourada, F., Houari, M.S.A. and Tounsi, A. (2019), "Thermomechanical bending investigation of FGM sandwich plates using four shear deformation plate theory", Steel Compos. Struct., 32(5), 611-632. https://doi.org/10.12989/scs.2019.32.5.611.
  12. Bourada, F., Bousahla, A.A., Bourada, M., Azzaz, A., Zinata, A. and Tounsi, A. (2019), "Dynamic investigation of porous functionally graded beam using a sinusoidal shear deformation theory", Wind Struct., 28(1), 19-30. https://doi.org/10.12989/was.2019.28.1.019.
  13. Boussoula, A., Boucham, B., Bourada, M., Bourada, F., Tounsi, A., Bousahla, A.A. and Tounsi, A. (2020), "A simple nth-order shear deformation theory for thermomechanical bending analysis of different configurations of FG sandwich plates", Smart Struct. Syst., 25(2), 197-218. https://doi.org/10.12989/sss.2020.25.2.197.
  14. Boutaleb, S., Benrahou, K. H., Bakora, A., Algarni, A., Bousahla, A.A., Tounsi, A. and Mahmoud, S.R. (2019), "Dynamic analysis of nanosize FG rectangular plates based on simple nonlocal quasi 3D HSDT", Adv. Nano Res., 7(3), 191-208. https://doi.org/10.12989/anr.2019.7.3.191.
  15. Chaabane, L.A., Bourada, F., Sekkal, M., Zerouati, S., Zaoui, F.Z., Tounsi, A. and Tounsi, A. (2019), "Analytical study of bending and free vibration responses of functionally graded beams resting on elastic foundation", Struct. Eng. Mech., 71(2), 185-196. https://doi.org/10.12989/sem.2019.71.2.185.
  16. Draiche, K., Bousahla, A.A., Tounsi, A., Alwabli, A.S., Tounsi, A. and Mahmoud, S.R. (2019), "Static analysis of laminated reinforced composite plates using a simple first-order shear deformation theory", Comput. Concrete, 24(4), 369-378. https://doi.org/10.12989/cac.2019.24.4.369.
  17. Draoui, A., Zidour, M., Tounsi, A. and Adim, B. (2019), "Static and dynamic behavior of nanotubes-reinforced sandwich plates using (FSDT)", J. Nano Res., 57, 117-135. https://doi.org/10.4028/www.scientific.net/JNanoR.57.117.
  18. Dai, T., Yang, Y., Dai, H.L., Tang, H. and Lin, Z.Y. (2019), "Hygrothermal mechanical behaviors of a porous FG-CRC annular plate with variable thickness considering aggregation of CNTs", Compos. Struct., 215, 198-213. https://doi.org/10.1016/j.compstruct.2019.02.061.
  19. Dong, Y.H., Li, Y.H., Chen, D. and Yang, J. (2018), "Vibration characteristics of functionally graded graphene reinforced porous nanocomposite cylindrical shells with spinning motion", Compos. Part B: Eng., 145, 1-13. https://doi.org/10.1016/j.compositesb.2018.03.009
  20. Feng, C., Kitipornchai, S. and Yang, J. (2017), "Nonlinear bending of polymer nanocomposite beams reinforced with non-uniformly distributed graphene platelets (GPLs)", Compos. Part B: Eng., 110, 132-140. https://doi.org/10.1016/j.compositesb.2016.11.024
  21. Feng, Q. and Meng, F. (2017), "Traveling wave solutions for fractional partial differential equations arising in mathematical physics by an improved fractional Jacobi elliptic equation method", Math. Method. Appl. Sci., 40(10), 3676-3686. https://doi.org/10.1002/mma.4254.
  22. Hellal, H., Bourada, M., Hebali, H., Bourada, F., Tounsi, A., Bousahla, A.A. and Mahmoud, S.R. (2019), "Dynamic and stability analysis of functionally graded material sandwich plates in hygro-thermal environment using a simple higher shear deformation theory", J. Sandw. Struct. Mater., 1099636219845841.https://doi.org/10.1177%2F1099636219845841.
  23. Hussain, M., Naeem, M.N., Tounsi, A. and Taj, M. (2019), "Nonlocal effect on the vibration of armchair and zigzag SWCNTs with bending rigidity", Adv. Nano Res., 7(6), 431-442. https://doi.org/10.12989/anr.2019.7.6.431.
  24. Houari, T., Bessaim, A., Houari, M.S.A., Benguediab, M. and Tounsi, A. (2018), "Bending analysis of advanced composite plates using a new quasi 3D plate theory", Steel Compos. Struct., 26(5), 557-572. https://doi.org/10.12989/scs.2018.26.5.557.
  25. Kaddari, M., Kaci, A., Bousahla, A.A., Tounsi, A., Bourada, F., Bedia, E.A. and Al-Osta, M.A. (2020), "A study on the structural behaviour of functionally graded porous plates on elastic foundation using a new quasi-3D model: bending and free vibration analysis", Comput. Concrete, 25(1), 37. https://doi.org/10.12989/cac.2020.25.1.037.
  26. Khiloun, M., Bousahla, A.A., Kaci, A., Bessaim, A., Tounsi, A. and Mahmoud, S.R. (2019), "Analytical modeling of bending and vibration of thick advanced composite plates using a four-variable quasi 3D HSDT", Eng. with Comput., 1-15. https://doi.org/10.1007/s00366-019-00732-1.
  27. Kazakov, I.A., Krasnovskii, A.N. and Kishuk, P.S. (2019), "The influence of randomly oriented CNTs on the elastic properties of unidirectionally aligned composites", Mech. Mater., 134, 54-60. https://doi.org/10.1016/j.mechmat.2019.04.002.
  28. Keleshteri, M.M., Asadi, H. and Aghdam, M.M. (2019), "Nonlinear bending analysis of FG-CNTRC annular plates with variable thickness on elastic foundation", Thin-Wall. Struct., 135, 453-462. https://doi.org/10.1016/j.tws.2018.11.020.
  29. Liu, D., Li, Z., Kitipornchai, S. and Yang, J. (2019), "Three-dimensional free vibration and bending analyses of functionally graded graphene nanoplatelets-reinforced nanocomposite annular plates", Compos. Struct., 229, 111453. https://doi.org/10.1016/j.compstruct.2019.111453.
  30. Medani, M., Benahmed, A., Zidour, M., Heireche, H., Tounsi, A., Bousahla, A.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.
  31. Meksi, R., Benyoucef, S., Mahmoudi, A., Tounsi, A., Adda Bedia, E.A. and Mahmoud, S.R. (2019), "An analytical solution for bending, buckling and vibration responses of FGM sandwich plates", J. Sandw. Struct. Mater., 21(2), 727-757. https://doi.org/10.1177%2F1099636217698443. https://doi.org/10.1177/1099636217698443
  32. Marynowski, K. (2017), Free vibration analysis of an axially moving multiscale composite plate including thermal effect", Int. J. Mech. Sci., 120, 62-69. https://doi.org/10.1016/j.ijmecsci.2016.11.013.
  33. Mirjavadi, S.S., Rabby, S., Shafiei, N., Afshari, B.M. and Kazemi, M. (2017), "On size-dependent free vibration and thermal buckling of axially functionally graded nanobeams in thermal environment", Appl. Phys. A, 123(5), 315. https://doi.org/10.1007/s00339-017-0918-1
  34. Mirjavadi, S.S., Afshari, B.M., Shafiei, N., Hamouda, A.M.S. and Kazemi, M. (2017), "Thermal vibration of two-dimensional functionally graded (2D-FG) porous Timoshenko nanobeams. Steel Compos. Struct., 25(4), 415-426. https://doi.org/10.12989/scs.2017.25.4.415.
  35. Mirjavadi, S.S., Afshari, B.M., Barati, M.R. and Hamouda, A.M.S. (2018), "Strain gradient based dynamic response analysis of heterogeneous cylindrical microshells with porosities under a moving load", Mater. Res. Express, 6(3), 035029. https://doi.org/10.1088/2053-1591/aaf5a2
  36. Mirjavadi, S.S., Afshari, B.M., Khezel, M., Shafiei, N., Rabby, S. and Kordnejad, M. (2018), "Nonlinear vibration and buckling of functionally graded porous nanoscaled beams", J. Brazilian Soc. Mech. Sci. Eng., 40(7), 352. https://doi.org/10.1007/s40430-018-1272-8
  37. Mirjavadi, S.S., Forsat, M., Hamouda, A.M.S. and Barati, M.R. (2019), "Dynamic response of functionally graded graphene nanoplatelet reinforced shells with porosity distributions under transverse dynamic loads", Mater. Res. Express, 6(7), 075045. https://doi.org/10.1088/2053-1591/ab1552
  38. Mirjavadi, S.S., Forsat, M., Nikookar, M., Barati, M.R. and Hamouda, A.M.S. (2019), "Nonlinear forced vibrations of sandwich smart nanobeams with two-phase piezo-magnetic face sheets", The European Phys. J. Plus, 134(10), 508. https://doi.org/10.1140/epjp/i2019-12806-8
  39. Mirjavadi, S.S., Afshari, B.M., Barati, M.R. and Hamouda, A.M.S. (2019), "Transient response of porous FG nanoplates subjected to various pulse loads based on nonlocal stress-strain gradient theory", Eur. J. Mech.-A/Solids, 74, 210-220. https://doi.org/10.1016/j.euromechsol.2018.11.004
  40. Mirjavadi, S.S., Afshari, B.M., Barati, M.R. and Hamouda, A.M.S. (2019), "Nonlinear free and forced vibrations of graphene nanoplatelet reinforced microbeams with geometrical imperfection", Microsyst. Technologies, 25, 3137-3150. https://doi.org/10.1007/s00542-018-4277-4
  41. Mirjavadi, S.S., Forsat, M., Barati, M.R., Abdella, G.M., Hamouda, A.M.S., Afshari, B.M. and Rabby, S. (2019), "Post-buckling analysis of piezo-magnetic nanobeams with geometrical imperfection and different piezoelectric contents", Microsyst. Technologies, 25(9), 3477-3488. https://doi.org/10.1007/s00542-018-4241-3
  42. Mirjavadi, S.S., Forsat, M., Barati, M.R., Abdella, G.M., Afshari, B.M., Hamouda, A.M.S. and Rabby, S. (2019), "Dynamic response of metal foam FG porous cylindrical micro-shells due to moving loads with strain gradient size-dependency," The European Phys. J. Plus, 134(5), 214. https://doi.org/10.1140/epjp/i2019-12540-3
  43. Mori, T. and Tanaka, K. (1973), "Average stress in matrix and average elastic energy of materials with misfitting inclusions", Acta metallurgica, 21(5), 571-574. https://doi.org/10.1016/0001-6160(73)90064-3.
  44. Rahmani, M.C., Kaci, A., Bousahla, A.A., Bourada, F., Tounsi, A., Bedia, E.A. and Tounsi, A. (2020), "Influence of boundary conditions on the bending and free vibration behavior of FGM sandwich plates using a four-unknown refined integral plate theory", Comput. Concrete, 25(3), 225-244. https://doi.org/10.12989/cac.2020.25.3.225.
  45. Refrafi, S., Bousahla, A.A., Bouhadra, A., Menasria, A., Bourada, F., Tounsi, A. and Tounsi, A. (2020), "Effects of hygro-thermo-mechanical conditions on the buckling of FG sandwich plates resting on elastic foundations", Comput. Concrete, 25(4), 311-325. DOI: https://doi.org/10.12989/cac.2020.25.4.311.
  46. Safaei, B., Moradi-Dastjerdi, R., Qin, Z. and Chu, F. (2019). Frequency-dependent forced vibration analysis of nanocomposite sandwich plate under thermo-mechanical loads", Compos. Part B: Eng., 161, 44-54. ] https://doi.org/10.1016/j.compositesb.2018.10.049
  47. Safarpour, M., Ghabussi, A., Ebrahimi, F., Habibi, M. and Safarpour, H. (2020), "Frequency characteristics of FG-GPLRC viscoelastic thick annular plate with the aid of GDQM", Thin-Wall. Struct., 150, 106683. https://doi.org/10.1016/j.tws.2020.106683.
  48. Sahla, M., Saidi, H., Draiche, K., Bousahla, A.A., Bourada, F. and Tounsi, A. (2019), "Free vibration analysis of angle-ply laminated composite and soft core sandwich plates", Steel Compos. Struct., 33(5), 663-679. https://doi.org/10.12989/scs.2019.33.5.663.
  49. Semmah, A., Heireche, H., Bousahla, A.A. and Tounsi, A. (2019), "Thermal buckling analysis of SWBNNT on Winkler foundation by non local FSDT", Adv. Nano Res., 7(2), 89-98. https://doi.org/10.12989/anr.2019.7.2.089.
  50. Soltani, K., Bessaim, A., Houari, M.S.A., Kaci, A., Benguediab, M., Tounsi, A. and Alhodaly, M.S. (2019), "A novel hyperbolic shear deformation theory for the mechanical buckling analysis of advanced composite plates resting on elastic foundations", Steel Compos. Struct., 30(1), 13-29. https://doi.org/10.12989/scs.2019.30.1.013.
  51. Thanh, C.L., Tran, L.V., Vu-Huu, T. and Abdel-Wahab, M. (2019), "The size-dependent thermal bending and buckling analyses of composite laminate microplate based on new modified couple stress theory and isogeometric analysis", Comput. Method. Appl. M., 350, 337-361. https://doi.org/10.1016/j.cma.2019.02.028.
  52. Tlidji, Y., Zidour, M., Draiche, K., Safa, A., Bourada, M., Tounsi, A. and Mahmoud, S.R. (2019), "Vibration analysis of different material distributions of functionally graded microbeam", Struct. Eng. Mech., 69(6), 637-649. https://doi.org/10.12989/sem.2019.69.6.637.
  53. Tounsi, A., Al-Dulaijan, S.U., Al-Osta, M.A., Chikh, A., Al-Zahrani, M.M., Sharif, A. and Tounsi, A. (2020), "A four variable trigonometric integral plate theory for hygro-thermo-mechanical bending analysis of AFG ceramic-metal plates resting on a two-parameter elastic foundation", Steel Compos. Struct., 34(4), 511-524. https://doi.org/10.12989/scs.2020.34.4.511.
  54. Vo, T.P., Thai, H.T., Nguyen, T.K., Lanc, D. and Karamanli, A. (2017), "Flexural analysis of laminated composite and sandwich beams using a four-unknown shear and normal deformation theory", Compos. Struct., 176, 388-397. https://doi.org/10.1016/j.compstruct.2017.05.041
  55. Wang, Y., Zeng, R. and Safarpour, M. (2020), "Vibration analysis of FG-GPLRC annular plate in a thermal environment", Mech. Based Des. Struct. Mach., 1-19. https://doi.org/10.1080/15397734.2020.1719508.
  56. Wattanasakulpong, N. and Chaikittiratana, A. (2015), "Exact solutions for static and dynamic analyses of carbon nanotube-reinforced composite plates with Pasternak elastic foundation", Appl. Math. Model., 39(18), 5459-5472. https://doi.org/10.1016/j.apm.2014.12.058.
  57. Wu, H., Kitipornchai, S. and Yang, J. (2017), "Thermal buckling and postbuckling of functionally graded graphene nanocomposite plates", Mater. Design, 132, 430-441. https://doi.org/10.1016/j.matdes.2017.07.025.
  58. Zarga, D., Tounsi, A., Bousahla, A.A., Bourada, F. and Mahmoud, S.R. (2019), "Thermomechanical bending study for functionally graded sandwich plates using a simple quasi-3D shear deformation theory", Steel Compos. Struct., 32(3), 389-410. https://doi.org/10.12989/scs.2019.32.3.389.
  59. Zaoui, F.Z., Ouinas, D. and Tounsi, A. (2019), "New 2D and quasi-3D shear deformation theories for free vibration of functionally graded plates on elastic foundations", Compos. Part B: Eng., 159, 231-247. https://doi.org/10.1016/j.compositesb.2018.09.051.
  60. Zhang, L.W., Zhang, Y. and Liew, K.M. (2017), "Vibration analysis of quadrilateral graphene sheets subjected to an in-plane magnetic field based on nonlocal elasticity theory", Compos. Part B: Eng., 118, 96-103. https://doi.org/10.1016/j.compositesb.2017.03.017
  61. Zhao, Z., Feng, C., Wang, Y. and Yang, J. (2017), "Bending and vibration analysis of functionally graded trapezoidal nanocomposite plates reinforced with graphene nanoplatelets (GPLs)", Compos. Struct., 180, 799-808. https://doi.org/10.1016/j.compstruct.2017.08.044.

Cited by

  1. Post-buckling analysis of imperfect nonlocal piezoelectric beams under magnetic field and thermal loading vol.78, pp.1, 2020, https://doi.org/10.12989/sem.2021.78.1.015
  2. Investigating dynamic response of nonlocal functionally graded porous piezoelectric plates in thermal environment vol.40, pp.2, 2021, https://doi.org/10.12989/scs.2021.40.2.243
  3. Vibration characteristics of microplates with GNPs-reinforced epoxy core bonded to piezoelectric-reinforced CNTs patches vol.11, pp.2, 2020, https://doi.org/10.12989/anr.2021.11.2.115