Geomechanics and Engineering

Techno-Press (테크노프레스)
권호 표지
DOI QR코드

DOI QR Code

Wave propagation of FGM plate via new integral inverse cotangential shear model with temperature-dependent material properties

  • Mokhtar Ellali (Smart Structures Laboratory, University of Ain Temouchent-Belhadj) ;
  • Mokhtar Bouazza (Department of Civil Engineering, University Tahri Mohamed of Bechar) ;
  • Ashraf M. Zenkour (Department of Mathematics, Faculty of Science, King Abdulaziz University)
  • Received : 2022.07.25
  • Accepted : 2023.03.07
  • Published : 2023.06.10
⟨ Previous Next ⟩

Abstract

The objective of this work is to study the wave propagation of an FGM plate via a new integral inverse shear model with temperature-dependent material properties. In this contribution, a new model based on a high-order theory field of displacement is included by introducing indeterminate integral variables and inverse co-tangential functions for the presentation of shear stress. The temperature-dependent properties of the FGM plate are assumed mixture of metal and ceramic, and its properties change by the power functions of the thickness of the plate. By applying Hamilton's principle, general formulas of wave propagation were obtained to plot the phase velocity curves and wave modes of the FGM plate with simply supported edges. The effects of the temperature and volume fraction by distributions on wave propagation of the FGM plate are investigated in detail. The results of the dispersion and the phase velocity curves of the propagation wave in the functionally graded plate are compared with previous research.

Keywords

References

  1. 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.
  2. Aminipoura, H., Janghorbana, M. and Li, L. (2018), "A new model for wave propagation in functionally graded anisotropic doubly-curved shells". Compos. Struct. 190, 91-111. https://doi.org/10.1016/j.compstruct.2018.02.003
  3. Ashour, A.S. (2003), "Buckling and vibration of symmetric laminated composite plates with edges elastically restrained", Steel Compos. Struct., 3(6), 439-450. https://doi.org/10.12989/scs.2003.3.6.439.
  4. Assie, A.E., Eltaher, M.A. and Mahmoud, F.F. (2011), "Behavior of a viscoelastic composite plate under transient load", J. Mech. Sci. Tech., 25, 1129-1140. https://doi.org/10.1007/s12206-011-0302-6.
  5. Basha, M., Daikh, A.A., Melaibari, A., Wagih, A., Othman, R., Almitani, K.H. and Eltaher, M.A. (2022), "Nonlocal strain gradient theory for buckling and bending of FG-GRNC laminated sandwich plates", Steel Compos. Struct., 43, 639-660. https://doi.org/10.12989/scs.2022.43.5.639.
  6. Becheri, T., Amara, K., Bouazza, M. and Benseddiq, N. (2016), "Buckling of symmetrically laminated plates using nth-order shear deformation theory with curvature effects", Steel Compos. Struct., 21(6) 1347-1368. https://doi.org/10.12989/scs.2016.21.6.1347.
  7. Bensattalah, T., Zidour, M., Daouadji, T.H. and Bouakaz, K. (2019), "Theoretical analysis of chirality and scale effects on critical buckling load of zigzag triple walled carbon nanotubes under axial compression embedded in polymeric matrix", Struct. Eng. Mech., 70(3), 269-277. https://doi.org/10.12989/sem.2019.70.3.269.
  8. Bouazza, M., Antar, K., Amara, K., Benyoucef, S. and Bedia, E. (2019), "Influence of temperature on the beams behavior strengthened by bonded composite plates", Geomech. Eng., 18(5), 555-566. https://doi.org/10.12989gae.2019.18.5.555. https://doi.org/10.12989gae.2019.18.5.555
  9. Bouazza, M., Becheri, T., Boucheta, A. and Benseddiq, N. (2019), "Bending behavior of laminated composite plates using the refined four-variable theory and the finite element method", Earthq. Struct., 17(3), 257-270. https://doi.org/10.12989/eas.2019.17.3.257.
  10. Bouazza, M. and Benseddiq, N. (2015), "Analytical modeling for the thermoelastic buckling behavior of functionally graded rectangular plates using hyperbolic shear deformation theory under thermal loadings". Multidiscip. Model.Mater. Struct., 11(4), 558-578. https://doi 10.1108/MMMS-02-2015-0008.
  11. Bouazza, M. and Zenkour, A.M. (2020), "Hygro-thermomechanical buckling of laminated beam using hyperbolic refined shear deformation theory", Compos. Struct., 252, 112689. https://doi.org/10.1016/j.compstruct.2020.112689.
  12. Bouderba, B., Houari, M.S.A. and Tounsi, A. (2013), "Thermomechanical bending response of FGM thick plates resting on Winkler-Pasternak elastic foundations", Steel Compos. Struct., 14(1), 85-104. https://doi.org/10.12989/scs.2013.14.1.085.
  13. Bui, T.Q., Do T.V., Ton, L.H.T., Doan, D.H., Tanaka, S., Pham, D.T., Nguyen-Van T.-A., Yu, T. and Hiros, S. (2016), "On the high-temperature mechanical behaviours analysis of heated functionally graded plates using FEM and a new third-order shear deformation plate theory", Compos. B Eng., 92, 218-241, https://doi.org/ 10.1016/j.compositesb.2016.02.048.
  14. Bounouara, F., Benrahou, K.H., Belkorissat, I. and Tounsi, A. (2016), "A nonlocal zeroth-order shear deformation theory for free vibration of functionally graded nanoscale plates resting on elastic foundation", Steel Compos. Struct., 20(2), 227-249. https://doi.org/10.12989/scs.2016.20.2.227.
  15. Chen, J., Xu, R., Huang, X. and Ding, H. (2006), "Exact solutions of axisymmetric free vibration of transversely isotropic magnetoelectroelastic laminated circular plates", Struct. Eng. Mech, 23(2), 115-127. https://doi.org/10.12989/sem.2006.23.2.115.
  16. Choudhary, J., Patle, B.K., Ramteke, P.M., Hirwani, C.K., Panda, S.K. and Katariya, P.V. (2022), "Static and dynamic deflection characteristics of cracked porous FG panels", Int. J. Appl. Mech., 14(7), 2250076. https://doi.org/10.1142/S1758825122500764.
  17. Daikh, A.A., Sid Ahmed Houari M. and Eltaher, M.A. (2021), "A novel nonlocal strain gradient quasi-3D bending analysis of sigmoid functionally graded sandwich nanoplates", Compos. Struct., 262, 113347. https://doi.org/10.1016/j.compstruct.2020.113347.
  18. Dehshahri, K., Nejad, M.Z., Ziaee, S., Niknejad, A. and Hadi, A. (2020), "Free vibrations analysis of arbitrary three-dimensionally FGM nanoplates", Adv. Nano Res., 8(2), 115-134. https://doi.org/10.12989/anr.2020.8.1.013.
  19. Ebrahimi, F., Ghazali, M. and Dabbagh, A. (2022a), "Hygro-thermo-viscoelastic wave propagation analysis of FGM nanoshells via nonlocal strain gradient fractional time-space theory", Waves Random Complex Media, In Press. https://doi.org/10.1080/17455030.2022.2105978.
  20. Ebrahimi, F., Seyfi, A., Dabbag, H.A. and Tornabene, F. (2019a), "Wave dispersion characteristics of porous graphene platelet-reinforced composite shells", Struct. Eng. Mech., 71(1), 99-107. https://doi.org/10.12989/sem.2019.71.1.099.
  21. Ellali, M., Amara, K., Bouazza, M. and Bourada, F. (2018), "The buckling of piezoelectric plates on Pasternak elastic foundation using higher-order shear deformation plate theories", Smart Struct. Syst., 21(1), 113-122. https://doi.org/10.12989/sss.2018.21.1.113.
  22. Ebrahimi, F., Ghazali, M. and Dabbagh, A. (2022b), "Hygro-thermo-viscoelastic wave propagation analysis of FGM nanoshells via nonlocal strain gradient fractional time-space theory", Waves Random Complex Media, https://doi.org/10.1080/17455030.2022.2105978.
  23. Ebrahimi, F., Khosravi, K. and Dabbagh, A. (2021a), "A novel spatial-temporal nonlocal strain gradient theorem for wave dispersion characteristics of FGM nanoplates", Waves Random Complex Media, In press. https://doi.org/10.1080/17455030.2021.1979272.
  24. Ebrahimi, F., Khosravi, K. and Dabbagh, A. (2021b) "Wave dispersion in viscoelastic FG nanobeams via a novel spatial-temporal nonlocal strain gradient framework", Waves Random Complex Media, In press. https://doi.org/10.1080/17455030.2021.1970282.
  25. Ebrahimi, F. and Dabbagh, A. (2018), "Effect of humid-thermal environment on wave dispersion characteristics of single-layered graphene sheets", Appl. Phys. A 124, 301. https://doi.org/10.1007/s00339-018-1734-y
  26. Ebrahimi, F., Nouraei, M., Dabbagh, A. and Rabczuk, T. (2019b), "Thermal buckling analysis of embedded graphene-oxide powder-reinforced nanocomposite plates", Adv. Nano Res., 7(5), 293-310. https://doi.org/10.12989/anr.2019.7.5.293.
  27. Ebrahimi, F., Dabbagh, A. and Taheri, M. (2021c), "Vibration analysis of porous metal foam plates rested on viscoelastic substrate", Eng. Comput., 37, 3727-3739. https://doi.org/10.1007/s00366-020-01031-w.
  28. Ebrahimi, F., Nopour, R. and Dabbagh, A. (2022c), "Effect of viscoelastic properties of polymer and wavy shape of the CNTs on the vibrational behaviors of CNT/glass fiber/polymer plates", Eng. Comput., 38(5), 4113-4126. https://doi.org/10.1007/s00366-021-01387-7.
  29. Ellali, M., Bouazza, M. and Zenkour. A.M. (2022), "Impact of micromechanical approaches on wave propagation of FG plates via indeterminate integral variables with a hyperbolic secant shear model", Int. J. Comput. Meth. 19(9), 2250019. https://doi.org/10.1142/S0219876222500190.
  30. Garg, A., Mukhopadhyay, T., Belarbi, M.O., Chalak, H.D., Singh, A. and Zenkour, A.M. (2023), "On accurately capturing the through-thickness variation of transverse shear and normal stresses for composite beams using FSDT coupled with GPR", Compos. Struct., 305, 116551. https://doi.org/10.1016/j.compstruct.2022.116551.
  31. Grover, N., Singh, B.N. and Maiti, D.K. (2013), "New nonpolynomial shear-deformation theories for structural behavior of laminated-composite and sandwich plates", AIAA J., 51(8), 1861-1871. https://doi.org/10.2514/1.J052399.
  32. Hissaria, P., Ramteke, P.M., Hirwani, C.K., Mahmoud, S.R., Kumar, E.K. and Panda, S.K. (2022), "Numerical investigation of eigenvalue characteristics (vibration and buckling) of damaged porous bidirectional FG panels", J. Vib. Eng. Tech., In press. https://doi.org/10.1007/s42417-022-00677-8
  33. Kahya, V., Karaca, S. and Vo, T.P. (2019), "Shear-deformable finite element for free vibrations of laminated composite beams with arbitrary lay-up", Steel Compos. Struct., 33(4), 473-487. https://doi.org/10.12989/scs.2019.33.4.473.
  34. Kar, V.R., Mahapatra, T.R., Panda. S.K. (2015), "Nonlinear flexural analysis of laminated composite flat panel under hygro-thermo-mechanical loading", Steel Compos. Struct., 19(4), 1011-1033. https://doi.org/10.12989/scs.2015.19.4.1011.
  35. Kar, V.R. and Panda, S.K. (2016), "Nonlinear thermomechanical deformation behaviour of P-FGM shallow spherical shell panel", Chinese J. Aeronautics, 29(1), 173-183. https://doi.org/10.1016/j.cja.2015.12.007.
  36. Kar, V.R. and Panda, S.K. (2017), Postbuckling analysis of shear deformable FG shallow spherical shell panel under nonuniform thermal environment, J. Therm. Stresses, 40(1), 25-39. https://doi.org/10.1080/01495739.2016.1207118.
  37. Mellouli, H., Jrad, H., Wali, M. and Dammak, F. (2019), "Geometrically nonlinear meshfree analysis of 3D-shell structures based on the double directors shell theory with finite rotations", Steel Compos. Struct., 31(4), 397-408. https://doi.org/10.12989/scs.2019.31.4.397.
  38. Nami, M.R. and Janghorban, M. (2014), "Wave propagation in rectangular nanoplates based on strain gradient theory with one gradient parameter with considering initial stress", Mod. Phys. Lett. B, 28(3), 1450021. https://doi.org/10.1142/S0217984914500213.
  39. Nazira, M., Eltaher, M.A., Mohamed, S.A. and Seddek, L.F. (2019), "Energy equivalent model in analysis of postbuckling of imperfect carbon nanotubes resting on nonlinear elastic foundation", Struct. Eng. Mech., 70(6), 737-750. https://doi.org/10.12989/sem.2019.70.6.737.
  40. Pham, Q.H., Tran, T.T., Tran, V.K., Nguyen, P.C., Nguyen-Thoi, T. and Zenkour, A.M. (2022), "Bending and hygro-thermomechanical vibration analysis of a functionally graded porous sandwich nanoshell resting on elastic foundation", Mech. Adv. Mater. Struct., 29(27), 5885-5905. https://doi.org/10.1080/15376494.2021.1968549.
  41. Ramteke, P.M., Kumar, V., Sharma, N. and Panda, S.K. (2022), "Geometrical nonlinear numerical frequency prediction of porous functionally graded shell panel under thermal environment", Int. J. Nonlinear Mech., 143, 104041. https://doi.org/10.1016/j.ijnonlinmec.2022.104041.
  42. Ramteke, P.M., Panda, S.K. and Sharma, N. (2022), Nonlinear vibration analysis of multidirectional porous functionally graded panel under thermal environment", AIAA J., In press. https://doi.org/10.2514/1.J061635
  43. Sahoo, B., Sharma, N., Sahoo, B., Ramteke, P.M., Panda, S.K. and Mahmoud, S.R. (2022), "Nonlinear vibration analysis of FGM sandwich structure under thermal loadings", Structures, 44, 1392-1402. https://doi.org/10.1016/j.istruc.2022.08.081.
  44. Shen, H.S. (2009), Functionally Graded Materials: Nonlinear Analysis of Plates and Shell, CRC Press, https://doi.org/10.1201/ 9781420092578.
  45. Sun, D. and Lou, S.N. (2011), "Wave propagation of functionally graded material plates in thermal environment". Ultrasonics, 51(8), 940-952. https://doi.org/10.1016/j.ultras.2011.05.009.
  46. Tho, N.C., Thom, D.V., Cong, P.H., Zenkour, A.M., Doan, D.H. and Minh, P.V. (2023), "Finite element modeling of the bending and vibration behavior of three-layer composite plates with a crack in the core layer", Compos. Struct., 305, 116529. https://doi.org/10.1016/j.compstruct.2022.116529.
  47. Yang, Y. and Liu, Y.J. (2020), "A new boundary element method for modeling wave propagation in functionally graded materials", Europ. J. Mech. - A Solids, 80, 103987. https://doi.org/10.1016/j.euromechsol.2019.103897.
  48. Yang, Y., Lam, C.C., Kou, K.P. and Iu, V.P. (2014) "Free vibration analysis of the functionally graded sandwich beams by a meshfree boundary-domain integral equation method", Compos. Struct., 117, 32-39. https://doi.org/10.1016/j.compstruct.2014.06.016
  49. Yang, Y., Kou, K.P., Iu, V.P., Lam, C.C. and Zhang, C.Z. (2014), "Free vibration analysis of two-dimensional functionally graded structures by a meshfree boundary-domain integral equation method", Compos. Struct., 110, 342-353. https://doi.org/10.1016/j.compstruct.2013.11.028.
  50. Yang, Y., Kou, K.P., Lam, C.C. and Iu, V.P. (2015) "Free vibration analysis of two-dimensional functionally graded coated and undercoated substrate structures", Eng. Anal. Bound. Elem., 60, 10-17. https://doi.org/10.1016/j.enganabound.2015.04.009
  51. Zheng, B.J., Yang, Y., Gao, X.W. and Zeng, C.H. (2018), Dynamic fracture analysis of functionally graded materials under thermal shock loading by using the radial integration boundary element method", Compos. Struct., 201, 468-476. https://doi.org/10.1016/j.compstruct.2018.06.050.
  52. Zenkour, A.M. and El-Shahrany, H.D. (2022), "Hygrothermal vibration of a cross-ply composite plate with magnetostrictive layers, viscoelastic faces, and a homogeneous core", Eng. Comput., 38, 4437-4456. https://doi.org/10.1007/s00366-021-01482-9.