Earthquakes and Structures

  • 제17권1호
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  • Pages.31-37
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  • 2019
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  • 2092-7614(pISSN)
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  • 2092-7622(eISSN)
테크노프레스 (Techno-Press)
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DOI QR코드

DOI QR Code

Numerical analysis for free vibration of functionally graded beams using an original HSDBT

  • Sahouane, Abdelkader (Department of Civil Engineering, Ibn Khaldoun University) ;
  • Hadji, Lazreg (Department of Mechanical Engineering, Ibn Khaldoun University) ;
  • Bourada, Mohamed (Material and Hydrology Laboratory, Faculty of Technology, Civil Engineering Department, University of Sidi Bel Abbes)
  • 투고 : 2019.03.23
  • 심사 : 2019.04.10
  • 발행 : 2019.07.25
⟨ 이전 논문 다음 논문 ⟩

초록

This work presents a free vibration analysis of functionally graded beams by employing an original high order shear deformation theory (HSDBT). This theory use only three unknowns, but it satisfies the stress free boundary conditions on the top and bottom surfaces of the beam without requiring any shear correction factors. The mechanical properties of the beam are assumed to vary continuously in the thickness direction by a simple power-law distribution in terms of the volume fractions of the constituents. In order to investigate the free vibration response, the equations of motion for the dynamic analysis are determined via the Hamilton's principle. The Navier solution technique is adopted to derive analytical solutions for simply supported beams. The accuracy and effectiveness of proposed model are verified by comparison with previous research.

키워드

참고문헌

  1. Abdelaziz, H.H., Ait Amar Meziane, M., 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. (2015), "Wave propagation of a functionally graded beam in thermal environments", Steel Compos. Struct., 19(6), 1421-1447. http://dx.doi.org/10.12989/scs.2015.19.6.1421.
  3. Akbas, S.D. (2017a), "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.
  4. Akbas, S.D. (2017b), "Free vibration of edge cracked functionally graded microscale beams based on the modified couple stress theory", Int. J. Struct. Stab. Dyn., 17(03), 1750033. https://doi.org/10.1142/S021945541750033X.
  5. Akbas, S.D. (2018a), "Forced vibration analysis of cracked functionally graded microbeams", Adv. Nano Res., 6(1), 39-55. https://doi.org/10.12989/anr.2018.6.1.039.
  6. Akbas, S.D. (2018b), "Forced vibration analysis of functionally graded porous deep beams", Compos. Struct., 186, 293-302. https://doi.org/10.1016/j.compstruct.2017.12.013.
  7. Ansaria, R., Gholami, R., Shojaeia, M.F., Mohammadia, V. and Sahmania, S. (2013), "Size-dependent bending, buckling and free vibration of functionally graded Timoshenko microbeams based on the most general strain gradient theory", Compos. Struct., 100, 385-397. https://doi.org/10.1016/j.compstruct.2012.12.048.
  8. Attia, A., Bousahla, A.A., Tounsi, A., Mahmoud, S.R. and Afaf, A.S. (2018), "A refined four variable plate theory for thermoelastic analysis of FGM plates resting on variable elastic foundations", Struct. Eng. Mech., 65(4), 453-464. https://doi.org/10.12989/sem.2018.65.4.453.
  9. Bellifa, H., Bakora, A., Tounsi, A., Bousahla, A.A. and Mahmoud, S.R. (2017), "An efficient and simple four variable refined plate theory for buckling analysis of functionally graded plates", Steel Compos. Struct., 25(3), 257-270. https://doi.org/10.12989/scs.2017.25.3.257.
  10. Bennai, R., Ait Atmane, H. and Tounsi, A. (2015), "A new higherorder 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.
  11. Bouhadra, A., Tounsi, A., Bousahla, A.A., Benyoucef, S. and Mahmoud, S.R. (2018), "Improved HSDT accounting for effect of thickness stretching in advanced composite plates", Struct. Eng. Mech., 66(1), 61-73. https://doi.org/10.12989/sem.2018.66.1.061.
  12. 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.
  13. Bourada, M., Amara, K., Bousahla, A.A. Tounsi, A. and Mahmoud, S.R. (2018), "A novel refined plate theory for stability analysis of hybrid and symmetric S-FGM plates", Struct. Eng. Mech., 68(6), 661-675. https://doi.org/10.12989/sem.2018.68.6.661.
  14. Bourada, M., Kaci, A., Houari, M.S.A. and Tounsi, A. (2015), "A new simple shear and normal deformations theory for functionally graded beams", Steel Compos. Struct., 18(2), 409-423. https://doi.org/10.12989/scs.2015.18.2.409.
  15. Chikh, A., Tounsi, A., Hebali, H. and Mahmoud, S.R. (2017), "Thermal buckling analysis of cross-ply laminated plates using a simplified HSDT", Smart Struct. Syst., 19(3), 289-297. https://doi.org/10.12989/sss.2017.19.3.289.
  16. El-Haina, F., Bakora, A., Bousahla, A.A., Tounsi, A. and Mahmoud, S.R. (2017), "A simple analytical approach for thermal buckling of thick functionally graded sandwich plates", Struct. Eng. Mech., 63(5), 585-595. https://doi.org/10.12989/sem.2017.63.5.585.
  17. Fourn, H., Ait Atmane, H., Bourada, M., Bousahla, A.A., Tounsi, A. and Mahmoud, S.R. (2018), "A novel four variable refined plate theory for wave propagation in functionally graded material plates", Steel Compos. Struct., 27(1), 109-122. https://doi.org/10.12989/scs.2018.27.1.109.
  18. Ghumare, S.M. and Sayyad, A.S. (2017), "A new fifth-order shear and normal deformation theory for static bending and elastic buckling of P-FGM beams", Lat. Am. J. Solid. Struct., 14, 1-19. http://dx.doi.org/10.1590/1679-78253972.
  19. 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.
  20. Kahya, V. and Turan, M. (2017), "Finite element model for vibration and buckling of functionally graded beams based on the first order shear deformation theory", Compos. Part B Eng., 109, 108-115. https://doi.org/10.1016/j.compositesb.2016.10.039.
  21. Li, S.R. and Batra, R.C. (2013), "Relations between buckling loads of functionally graded Timoshenko and homogeneous Euler-Bernoulli beams", Compos. Struct., 95, 5-9. https://doi.org/10.1016/j.compstruct.2012.07.027.
  22. Mahmoud, S.R. and Tounsi, A. (2017), "A new shear deformation plate theory with stretching effect for buckling analysis of functionally graded sandwich plates", Steel Compos. Struct., 24(5), 569-578. https://doi.org/10.12989/scs.2017.24.5.569.
  23. Menasria, A., Bouhadra, A., Tounsi, A., Bousahla, A.A. and Mahmoud, S.R. (2017), "A new and simple HSDT for thermal stability analysis of FG sandwich plates", Steel Compos. Struct., 25(2), 157-175. https://doi.org/10.12989/scs.2017.25.2.157.
  24. Mokhtar, Y., Heireche, H., Bousahla, A.A., Houari, M.S.A., Tounsi, A. and Mahmoud, S.R. (2018), "A novel shear deformation theory for buckling analysis of single layer graphene sheet based on nonlocal elasticity theory", Smart Struct. Syst., 21(4), 397-405. https://doi.org/10.12989/sss.2018.21.4.397.
  25. Nguyen, T.K., Vo, T.P. and Thai, H.T. (2013), "Static and free vibration of axially loaded functionally graded beams based on the first-order shear deformation theory", Compos. Part B Eng., 55, 147-157. https://doi.org/10.1016/j.compositesb.2013.06.011.
  26. Ould Larbi, L., Hadji, L., Ait Amar Meziane, M. and Adda Bedia, E.A. (2018), "An analytical solution for free vibration of functionally graded beam using a simple first-order shear deformation theory", Wind Struct., 27(4), 247-254. https://doi.org/10.12989/was.2018.27.4.247.
  27. Pradhan, K.K. and Chakraverty, S. (2013), "Free vibration of Euler and Timoshenko functionally graded beams by Rayleigh-Ritz method", Compos. Part B: Eng., 51, 175-184. https://doi.org/10.1016/j.compositesb.2013.02.027.
  28. Sayyad, A.S. and Ghugal, Y.M. (2017), "Bending, buckling and free vibration of laminated composite and sandwich beams : A critical review of literature", Compos. Struct., 171, 486-504. https://doi.org/10.1016/j.compstruct.2017.03.053.
  29. Thai, H.T. and Vo, T.P. (2012), "Bending and free vibration of functionally graded beams using various higher-order shear deformation beam theories", Int. J. Mech. Sci., 62, 57-66. https://doi.org/10.1016/j.ijmecsci.2012.05.014.
  30. Tounsi, A., Houari, M.S.A., Benyoucef, S. and Adda Bedia, E.A. (2013), "A refined trigonometric shear deformation theory for thermoelastic bending of functionally graded sandwich plates", Aerosp. Sci. Technol., 24(1), 209-220. https://doi.org/10.1016/j.ast.2011.11.009.
  31. Xu, Y., Yu, T. and Zhou, D. (2014), "Two-dimensional elasticity solution for bending of functionally graded beams with variable thickness", Meccanica, 49, 2479-2489. https://doi.org/10.1007/s11012-014-9958-1.
  32. Younsi, A., Tounsi, A., Zaoui, F.Z., Bousahla, A.A. and Mahmoud, S.R. (2018), "Novel quasi-3D and 2D shear deformation theories for bending and free vibration analysis of FGM plates", Geomech. Eng., 14(6), 519-532. https://doi.org/10.12989/gae.2018.14.6.519.
  33. Zouatnia, N. and Hadji, L. (2019), "Effect of the micromechanical models on the bending of FGM beam using a new hyperbolic shear deformation theory", Earthq. Struct., 16(2), 177-183. https://doi.org/10.12989/eas.2019.16.2.177.
  34. Zouatnia, N., Hadji, L. and Kassoul, A. (2017), "Effect of the micromechanical models on the bending of FGM beam using a new hyperbolic shear deformation theory", Wind Struct., 25(4), 329-342. https://doi.org/10.12989/eas.2019.16.2.177.

피인용 문헌

  1. Free vibration analysis of angle-ply laminated composite and soft core sandwich plates vol.33, pp.5, 2019, https://doi.org/10.12989/scs.2019.33.5.663
  2. Influence of boundary conditions on the bending and free vibration behavior of FGM sandwich plates using a four-unknown refined integral plate theory vol.25, pp.3, 2020, https://doi.org/10.12989/cac.2020.25.3.225
  3. Effects of hygro-thermo-mechanical conditions on the buckling of FG sandwich plates resting on elastic foundations vol.25, pp.4, 2019, https://doi.org/10.12989/cac.2020.25.4.311
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