Coupled systems mechanics

Techno-Press (테크노프레스)
권호 표지
DOI QR코드

DOI QR Code

Vibration analysis of porous FGM plate resting on elastic foundations: Effect of the distribution shape of porosity

  • Hadj, Bekki (Laboratory of Geomatics and sustainable development, University of Tiaret) ;
  • Rabia, Benferhat (Laboratory of Geomatics and sustainable development, University of Tiaret) ;
  • Daouadji, Tahar Hassaine (Laboratory of Geomatics and sustainable development, University of Tiaret)
  • Received : 2020.08.06
  • Accepted : 2021.01.17
  • Published : 2021.02.25
⟨ Previous Next ⟩

Abstract

The porosity of functionally graded materials (FGM) can affect the static and dynamic behavior of plates, which is important to take this aspect into account when analyzing such structures. The present work aims to study the effect of the distribution shape of porosity on the free vibration response of simply supported FG plate reposed on the Winkler-Pasternak foundation. A refined theory of shear deformation is expanded to study the influence of the distribution shape of porosity on the free vibration behavior of FG plates. The findings showed that the distribution shape of porosity significantly influences the free vibration behavior of thick rectangular FG plates for small values of Winkler-Pasternak elastic foundation parameters.

Keywords

References

  1. Abdederak, R., Hassaine Daouadji, T., Benferhat, R. and Adim, B. (2018), "Nonlinear analysis of damaged RC beams strengthened with glass fiber reinforced polymer plate under symmetric loads", Earthq. Struct., 15(2), 113-122. https://doi.org/10.12989/eas.2018.15.2.113.
  2. Abdelhak, Z., Hadji, L., Khelifa, Z., Hassaine Daouadji, T. and Adda Bedia, E.A. (2016), "Analysis of buckling response of functionally graded sandwich plates using a refined shear deformation theory", Wind Struct., 22(3), 291-305. https://doi.org/10.12989/was.2016.22.3.291.
  3. Abdelhak, Z., Hadji, L., Khelifa, Z., Hassaine Daouadji, T. and Adda Bedia, E.A. (2016), "Analysis of buckling response of functionally graded sandwich plates using a refined shear deformation theory", Wind Struct., 22(3), 291-305. https://doi.org/10.12989/was.2016.22.3.291.
  4. Abderezak, R., Daouadji, T.H. and Rabia, B. (2020), "Analysis of interfacial stresses of the reinforced concrete foundation beams repairing with composite materials plate", Coupl. Syst. Mech., 9(5), 473-498. http://dx.doi.org/10.12989/csm.2020.9.5.473.
  5. Ait Atmane, H., Mokhtar, N., Bennai, R., Tounsi, A. and Adda Bedia, E.A. (2019), "Vibration response and wave propagation in FG plates resting on elastic foundations using HSDT", Struct. Eng. Mech., 69(5), 511-525. https://doi.org/10.12989/sem.2019.69.5.511.
  6. Al-Furjan, M.S.H., Habibi, M., Chen, G., Safarpour, H., Safarpour, M. and Tounsi, A. (2020b), "Chaotic simulation of the multi-phase reinforced thermo-elastic disk using GDQM", Eng. Comput., 1-24. https://doi.org/10.1007/s00366-020-01144-2.
  7. Al-Furjan, M.S.H., Habibi, M., Ni, J., won Jung, D. and Tounsi, A. (2020), "Frequency simulation of viscoelastic multi-phase reinforced fully symmetric systems", Eng. Comput., 1-17. https://doi.org/10.1007/s00366-020-01200-x.
  8. Al-Furjan, M.S.H., Habibi, M., won Jung, D., Sadeghi, S., Safarpour, H., Tounsi, A. and Chen, G. (2020d), "A computational framework for propagated waves in a sandwich doubly curved nanocomposite panel", Eng. Comput., 1-18. https://doi.org/10.1007/s00366-020-01130-8.
  9. Al-Furjan, M.S.H., hatami, A., Habibi, M., Shan, L. and Tounsi, A. (2021), "On the vibrations of the imperfect sandwich higher-order disk with a lactic core using generalize differential quadrature method", Compos. Struct., 113150. https://doi.org/10.1016/j.compstruct.2020.113150.
  10. Al-Furjan, M.S.H., Safarpour, H., Habibi, M., Safarpour, M. and Tounsi, A. (2020c), "A comprehensive computational approach for nonlinear thermal instability of the electrically FG-GPLRC disk based on GDQ method", Eng. Comput., 1-18. https://doi.org/10.1007/s00366-020-01088-7.
  11. Alimirzaei, S., Mohammadimehr, M. and Tounsi, A. (2019), "Nonlinear analysis of viscoelastic micro-composite beam with geometrical imperfection using FEM: MSGT electro-magneto-elastic bending, buckling and vibration solutions", Struct. Eng. Mech., 71(5), 485-502. https://doi.org/10.12989/sem.2019.71.5.485.
  12. 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.
  13. 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.
  14. Belbachir, N., Bourada, M., Draiche, K., Tounsi, A., Bourada, F., Bousahla, A.A. and Mahmoud, S.R. (2020) "Thermal flexural analysis of anti-symmetric cross-ply laminated plates using a four variable refined theory" Smart Struct. Syst., 25(4), 409-422. http://dx.doi.org/10.12989/sss.2020.25.4.409.
  15. Belbachir, N., Draich, K., Bousahla, A.A., Bourada, M., Tounsi, A. and Mohammadimehr, M. (2019), "Bending analysis of anti-symmetric cross-ply laminated plates under nonlinear thermal and mechanical loadings", Steel Compos. Struct., 33(1), 81-92. https://doi.org/10.12989/scs.2019.33.1.081.
  16. Belkacem, A. and Hassaine Daouadji, T. (2016), "Effects of thickness stretching in FGM plates using a quasi-3D higher order shear deformation theory", Adv. Mater. Res., 5(4), 223-244. https://doi.org/10.12989/amr.2016.5.4.223.
  17. Belkacem, A., Tahar, H.D., Abderrezak, R., Amine, B.M., Mohamed, Z. and Boussad, A. (2018), "Mechanical buckling analysis of hybrid laminated composite plates under different boundary conditions", Struct. Eng. Mech., 66(6), 761-769. https://doi.org/10.12989/sem.2018.66.6.761.
  18. Bellal, M., Hebali, H., Heireche, H., Bousahla, A.A., Tounsi, A., Bourada, F., ... & 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.
  19. Benferhat, R., Daouadji, T.H., Mansour, M.S. and Hadji, L. (2016), "Effect of porosity on the bending and free vibration response of functionally graded plates resting on Winkler-Pasternak foundations", Earthq. Struct., 10(5), 1429-1449. https://doi.org/10.12989/eas.2016.10.5.1033.
  20. Benferhat, R., Hassaine Daouadji, T., Hadji, L. and Said Mansour, M. (2016), "Static analysis of the FGM plate with porosities", Steel Compos. Struct, 21(1), 123-136. https://doi.org/10.12989/scs.2016.21.1.123.
  21. Benhenni, M.A., Adim, B., Daouadji, T.H., Abbes, B., Abbes, F., Li, Y. and Bouzidane, A. (2019), "A comparison of closed form and finite element solutions for the free vibration of hybrid cross ply laminated plates", Mech. Compos. Mater., 55(2), 181-194. https://doi.org/10.1007/s11029-019-09803-2.
  22. Benhenni, M.A., Daouadji, T.H., Abbes, B., Abbes, F., Li, Y. and Adim, B. (2019), "Numerical analysis for free vibration of hybrid laminated composite plates for different boundary conditions", Struct. Eng. Mech., 70(5), 535-549. https://doi.org/10.12989/sem.2019.70.5.535.
  23. Benhenni, M.A., Daouadji, T.H., Abbes, B., Adim, B., Li, Y. and Abbes, F. (2018), "Dynamic analysis for anti-symmetric cross-ply and angle-ply laminates for simply supported thick hybrid rectangular plates", Adv. Mater. Res., 7(2), 83-103. https://doi.org/10.12989/amr.2018.7.2.119.
  24. Bensattalah, T., Daouadji, T.H., Zidour, M., Tounsi, A. and Bedia, E.A. (2016), "Investigation of thermal and chirality effects on vibration of single walled carbon nanotubes embedded in a polymeric matrix using nonlocal elasticity theories", Mech. Compos. Mater., 52(4), 555-568. https://doi.org/10.1007/s11029-016-9606-Z.
  25. Bensattalah, T., Zidour, M. and Daouadji, T.H. (2018), "Analytical analysis for the forced vibration of CNT surrounding elastic medium including thermal effect using nonlocal Euler-Bernoulli theory", Adv. Mater. Res., 7(3), 163-174. https://doi.org/10.12989/amr.2018.7.3.163.
  26. 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.
  27. Bouakaz, K., Daouadji, T.H., Meftah, S.A., Ameur, M., Tounsi, A. and Bedia, E.A. (2014), "A numerical analysis of steel beams strengthened with composite materials", Mech. Compos. Mater., 50(4), 685-696. https://doi.org/10.1007/s11029-014-9435-x.
  28. Boulefrakh, L., Hebali, H., Chikh, A., Bousahla, A.A., Tounsi, A. and Mahmoud, S.R. (2019), "The effect of parameters of visco-Pasternak foundation on the bending and vibration properties of a thick FG plate", Geomech. Eng., 18(2), 161-178. https://doi.org/10.12989/gae.2019.18.2.161.
  29. Bourada, F., Bousahla, A.A., Tounsi, A., Bedia, E.A., Mahmoud, S.R., Benrahou, K.H. and Tounsi, A. (2020), "Stability and dynamic analyses of SW-CNT reinforced concrete beam resting on elastic-foundation", Comput. Concrete, 25(6), 485-495. https://doi.org/10.12989/cac.2020.25.6.485.
  30. Bourada, F., Bousahla, A.A., Tounsi, A., Bedia, E.A., Mahmoud, S.R., Benrahou, K.H. and Tounsi, A. (2020), "Stability and dynamic analyses of SW-CNT reinforced concrete beam resting on elastic-foundation", Comput. Concrete, 25(6), 485-495. https://doi.org/10.12989/cac.2020.25.6.485.
  31. 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.
  32. Chaabane, L.A., Bourada, F., Sekkal, M., Zerouati, S., Zaoui, F.Z., Tounsi, A., ... & 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.
  33. Chedad, A., Daouadji, T.H., Abderezak, R., Adim, B., Abbes, B., Rabia, B. and Abbes, F. (2018), "A high-order closed-form solution for interfacial stresses in externally sandwich FGM plated RC beams", Adv. Mater. Res., 6(4), 317-328. https://doi.org/10.12989/amr.2017.6.4.317.
  34. Chergui, S., Daouadji, T.H., Hamrat, M., Boulekbache, B., Bougara, A., Abbes, B. and Amziane, S. (2019), "Interfacial stresses in damaged RC beams strengthened by externally bonded prestressed GFRP laminate plate: Analytical and numerical study", Adv. Mater. Res., 8(3), 197-217. https://doi.org/10.12989/amr.2019.8.3.197.
  35. Chikr, S.C., Kaci, A., Bousahla, A.A., Bourada, F., Tounsi, A., Bedia, E.A., ... & Tounsi, A. (2020), "A novel four-unknown integral model for buckling response of FG sandwichplates resting on elastic foundations under various boundary conditions using Galerkin's approach", Geomech. Eng., 21(5), 471-487. https://doi.org/10.12989/gae.2020.21.5.471.
  36. Daouadji, H.T. (2013), "Analytical analysis of the interfacial stress in damaged reinforced concrete beams strengthened by bonded composite plates", Strength Mater., 45(5), 587-597. htttps://doi.org/10.1007/s11223-013-9496-4.
  37. Daouadji, H.T. (2017), "Analytical and numerical modeling of interfacial stresses in beams bonded with a thin plate", Adv. Comput. Des., 2(1) 57-69. https://doi.org/10.12989/acd.2017.2.1.057.
  38. Daouadji, T. H., & Benferhat, R. (2016), "Bending analysis of an imperfect FGM plates under hygro-thermo-mechanical loading with analytical validation", Adv. Mater. Res., 5(1), 35-53. https://doi.org/10.12989/amr.2016.5.1.035.
  39. Daouadji, T.H. (2016b), "Theoretical analysis of composite beams under uniformly distributed load", Adv. Mater. Res., 5(1), 1-9. https://doi.org/10.12989/amr.2016.5.1.001.
  40. Daouadji, T.H. and Adim, B. (2016a), "An analytical approach for buckling of functionally graded plates", Adv. Mater. Res., 5(3), 141-169. https://doi.org/10.12989/amr.2016.5.3.141.
  41. Daouadji, T.H., Benferhat, R. and Adim, B. (2016), "Bending analysis of an imperfect advanced composite plates resting on the elastic foundations", Coupl. Syst. Mech., 5(3), 269-285. http://dx.doi.org/10.12989/csm.2017.5.3.269.
  42. Daouadji, T.H., Rabahi, A., Abbes, B. and Adim, B. (2016), "Theoretical and finite element studies of interfacial stresses in reinforced concrete beams strengthened by externally FRP laminates plate", J. Adhes. Sci. Technol., 30(12), 1253-1280. https://doi.org/10.1080/01694243.2016.1140703.
  43. 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.
  44. Hadj, B., Rabia, B. and Daouadji, T.H. (2019), "Influence of the distribution shape of porosity on the bending FGM new plate model resting on elastic foundations", Struct. Eng. Mech., 72(1), 823-832. https://doi.org/10.12989/sem.2019.72.1.061.
  45. Hamrat, M., Bouziadi, F., Boulekbache, B., Daouadji, T.H., Chergui, S., Labed, A. and Amziane, S. (2020), "Experimental and numerical investigation on the deflection behavior of pre-cracked and repaired reinforced concrete beams with fiber-reinforced polymer", Constr. Build. Mater., 249(20), 1-13. https://doi.org/10.1016/j.conbuildmat.2020.118745.
  46. Hosseini-Hashemi, S., Fadaee, M. and Atashipour, S.R. (2011), "Study on the free vibration of thick functionally graded rectangular plates according to a new exact closed-form procedure", Compos. Struct., 93(2), 722-735. https://doi.org/10.1016/j.compstruct.2010.08.007.
  47. Hussain, M., Naeem, M.N., Khan, M.S. and Tounsi, A. (2020), "Computer-aided approach for modelling of FG cylindrical shell sandwich with ring supports", Comput. Concrete, 25(5), 411-425. https://doi.org/10.12989/cac.2020.25.5.411.
  48. Kaddari, M., Kaci, A., Bousahla, A.A., Tounsi, A., Bourada, F., Tounsi, A., ... & 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), 37-57. https://doi.org/10.12989/cac.2020.25.1.037.
  49. Khadimallah, M.A., Hussain, M., Khedher, K.M., Naeem, M.N. and Tounsi, A. (2020), "Backward and forward rotating of FG ring support cylindrical shells", Steel Compos. Struct., 37(2), 137-150. http://dx.doi.org/10.12989/scs.2020.37.2.137.
  50. Khiloun, M., Bousahla, A.A., Kaci, A., Bessaim, A., Tounsi, A. and Mahmoud, S.R. (2020), "Analytical modeling of bending and vibration of thick advanced composite plates using a four-variable quasi 3D HSDT", Eng. Comput., 36(3), 807-821. https://doi.org/10.1007/s00366-019-00732-1.
  51. Mahmoudi, A., Benyoucef, S., Tounsi, A., Benachour, A., Adda Bedia, E.A. and Mahmoud, S.R. (2019), "A refined quasi-3D shear deformation theory for thermo-mechanical behavior of functionally graded sandwich plates on elastic foundations", J. Sandw. Struct. Mater., 21(6), 1906-1926. https://doi.org/10.1177/1099636217727577.
  52. Matouk, H., Bousahla, A.A., Heireche, H., Bourada, F., Bedia, E.A., Tounsi, A., ... & Benrahou, K.H. (2020), "Investigation on hygro-thermal vibration of P-FG and symmetric S-FG nanobeam using integral Timoshenko beam theory", Adv. Nano Res., 8(4), 293-305. https://doi.org/10.12989/anr.2020.8.4.293.
  53. Matsunaga, H. (2008), "Free vibration and stability of functionally graded plates according to a 2-D higher-order deformation theory", Compos. Struct., 82(4), 499-512. http://dx.doi.org/10.1016/j.compstruct.2007.01.030.
  54. Praveen, G.N. and Reddy, J.N. (1998), "Nonlinear transient thermoelastic analysis of functionally graded ceramic-metal plates", Int. J. Solid. Struct., 35(33), 4457-4476. https://doi.org/10.1016/S0020-7683(97)00253-9.
  55. Rabahi, A., Benferhat, R. and Daouadji, H.T. (2019), "Elastic analysis of interfacial stresses in prestressed PFGM-RC hybrid beams", Adv. Mater. Res., 7(2), 83-103. https://doi.org/10.12989/amr.2018.7.2.083.
  56. Rabahi, A., Daouadji, T.H., Abbes, B. and Adim, B. (2016), "Analytical and numerical solution of the interfacial stress in reinforced-concrete beams reinforced with bonded prestressed composite plate", J. Reinf. Plast. Compos., 35(3) 258-272. https://doi.org/10.1177/0731684415613633.
  57. Rabhi, M., Benrahou, K.H., Kaci, A., Houari, M.S.A., Bourada, F., Bousahla, A.A., ... & Tounsi, A. (2020), "A new innovative 3-unknowns HSDT for buckling and free vibration of exponentially graded sandwich plates resting on elastic foundations under various boundary conditions", Geomech. Eng., 22(2), 119-132. https://doi.org/10.12989/gae.2020.22.2.119.
  58. Rabia, B., Abderezak, R., Daouadji, T.H., Abbes, B., Belkacem, A. and Abbes, F. (2018), "Analytical analysis of the interfacial shear stress in RC beams strengthened with prestressed exponentially-varying properties plate", Adv. Mater. Res., 7(1), 29-44. https://doi.org/10.12989/amr.2018.7.1.029.
  59. Rabia, B., Daouadji, T.H. and Abderezak, R. (2019), "Effect of distribution shape of the porosity on the interfacial stresses of the FGM beam strengthened with FRP plate", Earthq. Struct., 16(5), 601-609. https://doi.org/10.12989/eas.2019.16.5.601.
  60. Rahmani, M.C., Kaci, A., Bousahla, A.A., Bourada, F., Tounsi, A., Bedia, E.A., ... & 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.
  61. Refrafi, S., Bousahla, A.A., Bouhadra, A., Menasria, A., Bourada, F., Tounsi, A., Adda Bedia, E.A., Mahmoud, S.R., Benrahou, K.H. 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. https://doi.org/10.12989/cac.2020.25.4.311.
  62. Tahar, H.D., Abderezak, R. and Rabia, B (2020), "Flexural performance of wooden beams strengthened by composite plate", Struct. Monit. Mainten, 7(3), 233-259. http://dx.doi.org/10.12989/smm.2020.7.3.233.
  63. Tahar, H.D., Boussad, A., Abderezak, R., Rabia, B., Fazilay, A. and Belkacem, A. (2019), "Flexural behaviour of steel beams reinforced by carbon fibre reinforced polymer: Experimental and numerical study", Struct. Eng. Mech., 72(4), 409-419. https://doi.org/10.12989/sem.2019.72.4.409.
  64. Tayeb, B. and Daouadji, T.J. (2020), "Improved analytical solution for slip and interfacial stress in composite steel-concrete beam bonded with an adhesive", Adv. Mater. Res., 9(2), 133-153. https://doi.org/10.12989/amr.2020.9.2.133.
  65. Thai, H.T. and Kim, S.E. (2013), "Closed-form solution for buckling analysis of thick functionally graded plates on elastic foundation", Int. J. Mech. Sci., 75, 34-44. http://dx.doi.org/10.1016/j.ijmecsci.2013.06.007.
  66. 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.
  67. Tounsi, A., Daouadji, T.H. and Benyoucef, S. (2008), "Interfacial stresses in FRP-plated RC beams: Effect of adherend shear deformations", Int. J. Adhes. Adhesiv., 29, 313-351. https://doi.org/10.1016/j.ijadhadh.2008.06.008.
  68. Wattanasakulponga, N. and Ungbhakornb, V. (2014), "Linear and nonlinear vibration analysis of elastically restrained ends FGM beams with porosities", Aerosp. Sci. Technol., 32(1), 111-120. https://doi.org/10.1016/j.ast.2013.12.002.
  69. Zhao, X., Lee, Y.Y. and Liew, K.M. (2009), "Free vibration analysis of functionally graded plates using the element-free kp-Ritz method", J. Sound Vib., 319, 918-939. https://doi.org/10.1016/j.jsv.2008.06.025.
  70. Zine, A., Bousahla, A.A., Bourada, F., Benrahou, K.H., Tounsi, A., Adda Bedia, E.A., ... & Tounsi, A. (2020), "Bending analysis of functionally graded porous plates via a refined shear deformation theory", Comput. Concrete, 26(1), 63-74. http://dx.doi.org/10.12989/cac.2020.26.1.063.

Cited by

  1. A nonlocal quasi-3D theory for thermal free vibration analysis of functionally graded material nanoplates resting on elastic foundation vol.26, 2021, https://doi.org/10.1016/j.csite.2021.101170
  2. A new model for adhesive shear stress in damaged RC cantilever beam strengthened by composite plate taking into account the effect of creep and shrinkage vol.79, pp.5, 2021, https://doi.org/10.12989/sem.2021.79.5.531
  3. New solution for damaged porous RC cantilever beams strengthening by composite plate vol.10, pp.3, 2021, https://doi.org/10.12989/amr.2021.10.3.169