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Forced vibration analysis of functionally graded sandwich deep beams

  • Akbas, Seref D. (Department of Civil Engineering, Bursa Technical University, Yildirim Campus)
  • 투고 : 2019.03.05
  • 심사 : 2019.03.30
  • Published : 2019.06.25

Abstract

This paper presents forced vibration analysis of sandwich deep beams made of functionally graded material (FGM) in face layers and a porous material in core layer. The FGM sandwich deep beam is subjected to a harmonic dynamic load. The FGM in the face layer is graded though the layer thickness. In order to get more realistic result for the deep beam problem, the plane solid continua is used in the modeling of The FGM sandwich deep beam. The equations of the problem are derived based the Hamilton procedure and solved by using the finite element method. The novelty in this paper is to investigate the dynamic responses of sandwich deep beams made of FGM and porous material by using the plane solid continua. In the numerical results, the effects of different material distributions, porosity coefficient, geometric and dynamic parameters on the dynamic responses of the FGM sandwich deep beam are investigated and discussed.

Keywords

References

  1. Abdelaziz, H.H., Meziane, M.A.A., Bousahla, A.A., Tounsi, A., Mahmoud, S.R. and Alwabli, A.S. (2017), "An efficient hyperbolic shear deformation theory for bending, buckling and free vibration of FGM sandwich plates with various boundary conditions", Steel Compos. Struct., 25(6), 693-704. https://doi.org/10.12989/scs.2017.25.6.693.
  2. Akbas, S.D. (2013), "Geometrically nonlinear static analysis of edge cracked Timoshenko beams composed of functionally graded material", Math. Prob. Eng., http://dx.doi.org/10.1155/2013/871815.
  3. Akbas, S.D. (2015a), "Post-buckling analysis of axially functionally graded three-dimensional beams", Int. J. Appl. Mech., 7(03), 1550047. https://doi.org/10.1142/S1758825115500477.
  4. Akbas, S.D. (2015b), "On post-buckling behavior of edge cracked functionally graded beams under axial loads", Int. J. Struct. Stability Dyn., 15(04), 1450065. https://doi.org/10.1142/S0219455414500655.
  5. Akbas, S.D. (2015c), "Wave propagation of a functionally graded beam in thermal environments", Steel Compos. Struct., 19(6), 1421-1447. https://doi.org/10.12989/scs.2015.19.6.1421.
  6. Akbas, S.D. (2016a), "Post-buckling analysis of edge cracked columns under axial compression loads", Int. J. Appl. Mech., 8(8), 1650086. https://doi.org/10.1142/S1758825116500861.
  7. Akbas, S.D. (2016b), "Forced vibration analysis of viscoelastic nanobeams embedded in an elastic medium", Smart Struct. Syst., 18(6), 1125-1143. https://doi.org/10.12989/sss.2016.18.6.1125.
  8. Akbas, S.D. (2017a), "Nonlinear static analysis of functionally graded porous beams under thermal effect", Coupled Syst. Mech., 6(4), 399-415. https://doi.org/10.12989/csm.2017.6.4.399.
  9. Akbas, S.D. (2017b), "Post-buckling responses of functionally graded beams with porosities", Steel Compos. Struct., 24(5), 579-589. https://doi.org/10.12989/scs.2017.24.5.579.
  10. Akbas, S.D. (2017c), "Vibration and static analysis of functionally graded porous plates", J. Appl. Comput. Mech., 3(3), 199-207. https://dx.doi.org/10.22055/jacm.2017.21540.1107.
  11. Akbas, S.D. (2017d), "Thermal effects on the vibration of functionally graded deep beams with porosity", Int. J. Appl. Mech., 9(05), 1750076. https://doi.org/10.1142/S1758825117500764.
  12. Akbas, S.D. (2017e), "Forced vibration analysis of functionally graded nanobeams", Int. J. Appl. Mech., 9(07), 1750100. https://doi.org/10.1142/S1758825117501009.
  13. Akbas, S.D. (2017f), "Free vibration of edge cracked functionally graded microscale beams based on the modified couple stress theory", Int. J. Struct. Stability Dyn., 17(03), 1750033. https://doi.org/10.1142/S021945541750033X.
  14. Akbas, S.D. (2018a), "Forced vibration analysis of functionally graded porous deep beams", Compos. Struct., 186, 293-302. https://doi.org/10.1016/j.compstruct.2017.12.013.
  15. Akbas, S.D. (2018b), "Forced vibration analysis of cracked functionally graded microbeams", Adv. Nano Res., 6(1), 39-55. https://doi.org/10.12989/anr.2018.6.1.39.
  16. Akbas, S.D. (2018c), "Geometrically nonlinear analysis of functionally graded porous beams", Wind Struct., 27(1), 59-70. https://doi.org/10.12989/was.2018.27.1.59.
  17. Akbas, S.D. (2018d), "Investigation on free and forced vibration of a bi-material composite beam", J. Polytechnic-Politeknik Dergisi, 21(1), 65-73.
  18. Avcar, M. (2015), "Effects of rotary inertia shear deformation and non-homogeneity on frequencies of beam", Struct. Eng. Mech., 55(4), 871-884. https://doi.org/10.12989/sem.2015.55.4.871.
  19. Avcar, M. and Alwan, H.H.A. (2017), "Free vibration of functionally graded Rayleigh beam", Int. J. Eng. Appl. Sci., 9(2), 127-137. http://dx.doi.org/10.24107/ijeas.322884.
  20. Avcar, M. and Mohammed, W.K.M. (2018), "Free vibration of functionally graded beams resting on Winkler-Pasternak foundation", Arab. J. Geosci., 11(10), 232. https://doi.org/10.1007/s12517-018-3579-2.
  21. Barka, M., Benrahou, K. H., Bakora, A. and Tounsi, A. (2016), "Thermal post-buckling behavior of imperfect temperature-dependent sandwich FGM plates resting on Pasternak elastic foundation", Steel Compos. Struct., 22(1), 91-112. https://doi.org/10.12989/scs.2016.22.1.91.
  22. Benbakhti, A., Bouiadjra, M. B., Retiel, N. and Tounsi, A. (2016), "A new five unknown quasi-3D type HSDT for thermomechanical bending analysis of FGM sandwich plates", Steel Compos. Struct., 22(5), 975-999. https://doi.org/10.12989/scs.2016.22.5.975.
  23. Bennai, R., Atmane, H.A. and Tounsi, A. (2015), "A new higher-order shear and normal deformation theory for functionally graded sandwich beams", Steel Compos. Struct., 19(3), 521-546. https://doi.org/10.12989/scs.2015.19.3.521.
  24. Bhangale, R.K. and Ganesan, N. (2006), "Thermoelastic buckling and vibration behavior of a functionally graded sandwich beam with constrained viscoelastic core", J. Sound Vib., 295(1-2), 294-316. https://doi.org/10.1016/j.jsv.2006.01.026.
  25. Bouakkaz, K., Hadji, L., Zouatnia, N. and Bedia E.A.A. (2015), "An analytical method for free vibration analysis of functionally graded sandwich beams", Wind Struct., 23(1), 59-73. https://doi.org/10.12989/was.2015.23.1.59.
  26. 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.2019.28.1.19.
  27. Chen, D., Kitipornchai, S. and Yang, J. (2016), "Nonlinear free vibration of shear deformable sandwich beam with a functionally graded porous core", Thin-Walled Struct., 107, 39-48. https://doi.org/10.1016/j.tws.2016.05.025.
  28. Civalek, O. and Baltacioglu, A.K. (2019), "Free vibration analysis of laminated and FGM composite annular sector plates", Compos. Part B Eng., 157, 182-194. https://doi.org/10.1016/j.compositesb.2018.08.101.
  29. Ebrahimi, F. and Farazmandnia, N. (2017), "Thermo-mechanical analysis of carbon nanotube-reinforced composite sandwich beams", Coupled Syst. Mech., 6(2), 207-227. https://doi.org/10.12989/csm.2017.6.2.207.
  30. Ebrahimi, F. and Farazmandnia, N. (2018), "Thermal buckling analysis of functionally graded carbon nanotube-reinforced composite sandwich beams", Steel Compos. Struct., 27(2), 149-159. https://doi.org/10.12989/scs.2018.27.2.149.
  31. Gholami, R. and Ansari, R. (2018), "Nonlinear harmonically excited vibration of third-order shear deformable functionally graded graphene platelet-reinforced composite rectangular plates", Eng. Struct., 156, 197-209. https://doi.org/10.1016/j.engstruct.2017.11.019.
  32. Hadji, L., and Adda Bedia, E.A. (2015), "Influence of the porosities on the free vibration of FGM beams", Wind Struct., 21(3), 273-287. https://doi.org/10.12989/was.2015.21.3.273.
  33. Hadji, L., Zouatnia, N. and Bernard, F. (2019), "An analytical solution for bending and free vibration responses of functionally graded beams with porosities: Effect of the micromechanical models", Struct. Eng. Mech., 69(2), 231-241. https://doi.org/10.12989/sem.2019.69.2.231.
  34. Hadji, L., Zouatnia, N. and Kassoul, A. (2017), "Wave propagation in functionally graded beams using various higher-order shear deformation beams theories", Struct. Eng. Mech., 62(2), 143-149. https://doi.org/10.12989/sem.2017.62.2.143.
  35. Nguyen, T.K. and Nguyen, B.D. (2015), "A new higher-order shear deformation theory for static, buckling and free vibration analysis of functionally graded sandwich beams", J. Sandw. Struct. Mater., 17(6), 613-631. https://doi.org/10.1177%2F1099636215589237. https://doi.org/10.1177/1099636215589237
  36. Tounsi, A., Houari, M.S.A. and Bessaim, A. (2016), "A new 3-unknowns non-polynomial plate theory for buckling and vibration of functionally graded sandwich plate", Struct. Eng. Mech., 60(4), 547-565. https://doi.org/10.12989/sem.2016.60.4.547.
  37. Van Tung, H. (2017), "Nonlinear thermomechanical response of pressure-loaded doubly curved functionally graded material sandwich panels in thermal environments including tangential edge constraints", J. Sandw. Struct. Mater., 20(8), 974-1008. https://doi.org/10.1177%2F1099636216684312. https://doi.org/10.1177/1099636216684312
  38. Vo, T.P., Thai, H.T., Nguyen, T.K., Inam, F. and Lee, J. (2015), "Static behaviour of functionally graded sandwich beams using a quasi-3D theory", Compos. Part B Eng., 68, 59-74. https://doi.org/10.1016/j.compositesb.2014.08.030.
  39. Wang, Z.X. and Shen, H.S. (2011), "Nonlinear analysis of sandwich plates with FGM face sheets resting on elastic foundations", Compos. Struct., 93(10), 2521-2532. https://doi.org/10.1016/j.compstruct.2011.04.014.
  40. Yahia, S.A., Atmane, H.A., Houari, M.S.A. and Tounsi, A. (2015), "Wave propagation in functionally graded plates with porosities using various higher-order shear deformation plate theories", Struct. Eng. Mech., 53(6), 1143-1165. https://doi.org/10.12989/sem.2015.53.6.1143.
  41. Zenkour, A.M., Allam, M.N.M. and Sobhy, M. (2010), "Bending analysis of FG viscoelastic sandwich beams with elastic cores resting on Pasternak's elastic foundations", Acta Mechanica, 212(3-4), 233-252. https://doi.org/10.1007/s00707-009-0252-6.
  42. Zouatnia, N., Hadji, L. and Kassoul, A. (2017), "An analytical solution for bending and vibration responses of functionally graded beams with porosities", Wind Struct., 25(4), 329-342. https://doi.org/10.12989/was.2017.25.4.329.

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