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Dynamic responses of functionally graded and layered composite beams

  • Kirlangic, O. (The General Directorate of Highways) ;
  • Akbas, S.D. (Department of Civil Engineering, Bursa Technical University)
  • Received : 2020.05.17
  • Accepted : 2020.10.17
  • Published : 2021.01.25
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Abstract

This paper presents and compares the free and damped forced vibrations of layered and functionally graded composite beams. In the considered study, a cantilever beam subjected to a harmonic point load at the free end is investigated with layered and functionally graded materials. In the kinematics of the beam, the Timoshenko beam theory is used. The governing equations of problem are derived by using the Lagrange procedure. In the solution of the problem, the Ritz method is used. Algebraic polynomials are used with the trial functions for the Ritz method. In the obtaining of free vibration results, the eigenvalue procedure is implemented. In the solution of the damped forced vibration problem, the Newmark average acceleration method is used in the time history. In the damping effect, the Kelvin-Voigt viscoelastic model is used with the constitutive relations. In the numerical examples, the effects of material distribution parameter and dynamic parameters on the natural frequencies and forced vibration responses of functionally graded beams are obtained and compared with the results of the layered composite beam. Also, comparison studies are performed in order to validate the used formulations.

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References

  1. Akbas, S.D. (2013), "Geometrically nonlinear static analysis of edge cracked Timoshenko beams composed of functionally graded material", Mathe. Problems Eng., 2013. https://doi.org/10.1155/2013/871815
  2. Akbas, S.D. (2014), "Free vibration of axially functionally graded beams in thermal environment", Int. J. Eng. Appl. Sci., 6(3), 37-51. https://doi.org/10.24107/ijeas.251224
  3. Akbas, S.D. (2015a), "Wave propagation of a functionally graded beam in thermal environments", Steel Compos. Struct., Int. J., 19(6), 1421-1447. https://doi.org/10.12989/scs.2015.19.6.1421
  4. Akbas, S.D. (2015b), "Free vibration and bending of functionally graded beams resting on elastic foundation", Res. Eng. Struct. Mater., 1(1), 25-37. http://dx.doi.org/10.17515/resm2015.03st0107
  5. Akbas, S.D. (2017a), "Free vibration of edge cracked functionally graded microscale beams based on the modified couple stress theory", Int. J. Struct. Stabil. Dyn., 17(3), 1750033. https://doi.org/10.1142/S021945541750033X.
  6. Akbas, S.D. (2017b), "Nonlinear static analysis of functionally graded porous beams under thermal effect", Coupl. Syst. Mech., Int. J., 6(4), 399-415. https://doi.org/10.12989/csm.2017.6.4.399
  7. Akbas, S.D. (2017c), "Stability of a non-homogenous porous plate by using generalized differantial quadrature method", Int. J. Eng. Appl. Sci., 9(2), 147-155. https://doi.org/10.24107/ijeas.322375
  8. Akbas, S.D. (2018a), "Nonlinear thermal displacements of laminated composite beams", Coupl. Syst. Mech., Int. J., 7(6), 691-705. https://doi.org/10.12989/csm.2018.7.6.691
  9. Akbas, S.D. (2018b), "Post-buckling responses of a laminated composite beam", Steel Compos. Struct., Int. J., 26(6), 733-743. https://doi.org/10.12989/scs.2018.26.6.733
  10. Akbas, S.D. (2018c), "Bending of a cracked functionally graded nanobeam", Adv. Nano Res., Int. J., 6(3), 219-242. https://doi.org/10.12989/anr.2018.6.3.219
  11. Akbas, S.D. (2018d), "Geometrically nonlinear analysis of functionally graded porous beams", Wind Struct., Int. J., 27(1), 59-70. https://doi.org/10.12989/was.2018.27.1.059
  12. Akbas, S.D. (2018e), "Thermal post-buckling analysis of a laminated composite beam", Struct. Eng. Mech., Int. J., 67(4), 337-346. https://doi.org/10.12989/sem.2018.67.4.337
  13. Akbas, S.D. (2018f), "Geometrically nonlinear analysis of a laminated composite beam", Struct. Eng. Mech., Int. J., 66(1), 27-36. https://doi.org/10.12989/sem.2018.66.1.027
  14. Akbas, S.D. (2018g), "Large deflection analysis of a fiber reinforced composite beam", Steel Compos. Struct., Int. J., 27(5), 567-576. https://doi.org/10.12989/scs.2018.27.5.567
  15. Akbas, S.D. (2018h), "Investigation on free and forced vibration of a bi-material composite beam", Journal of Polytechnic-Politeknik Dergisi, 21(1), 65-73. https://doi.org/10.2339/politeknik.386841
  16. Akbas, S.D. (2018i), "Investigation of static and vibration behaviors of a functionally graded orthotropic beam", Balikesir universitesi Fen Bilimleri Enstitusu Dergisi, 1-14. https://doi.org/10.25092/baunfbed.343227
  17. Akbas, S.D. (2019a), "Forced vibration analysis of functionally graded sandwich deep beams", Coupl. Syst. Mech., Int. J., 8(3), 259-271. https://doi.org/10.12989/csm.2019.8.3.259
  18. Akbas, S.D. (2019b), "Hygro-thermal nonlinear analysis of a functionally graded beam", J. Appl. Computat. Mech., 5(2), 477-485. https://doi.org/10.22055/JACM.2018.26819.1360
  19. Akbas, S.D. (2019c), "Hygrothermal post-buckling analysis of laminated composite beams", Int. J. Appl. Mech., 11(1), 1950009. https://doi.org/10.1142/S1758825119500091
  20. Akbas, S.D. (2019d), "Hygro-thermal post-buckling analysis of a functionally graded beam", Coupl. Syst. Mech., Int. J., 8(5), 459-471. https://doi.org/10.12989/csm.2019.8.5.459
  21. Akbas, S.D. (2019e), "Post-buckling analysis of a fiber reinforced composite beam with crack", Eng. Fract. Mech., 212, 70-80. https://doi.org/10.1016/j.engfracmech.2019.03.007
  22. Akbas, S.D. (2019f), "Nonlinear static analysis of laminated composite beams under hygro-thermal effect", Struct. Eng. Mech., Int. J., 72(4), 433-441. https://doi.org/10.12989/sem.2019.72.4.433
  23. Akbas, S.D. (2019g), "Nonlinear behavior of fiber reinforced cracked composite beams", Steel Compos. Struct., Int. J., 30(4), 327-336. https://doi.org/10.12989/scs.2019.30.4.327
  24. Babilio, E. (2014), "Dynamics of functionally graded beams on viscoelastic foundation", Int. J. Struct. Stabil. Dyn., 14(8), 1440014. https://doi.org/10.1142/S0219455414400148
  25. 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, Int. J., 24(4), 369-378. https://doi.org/10.12989/cac.2019.24.4.369
  26. Eltaher, M.A., Emam, S.A. and Mahmoud, F.F. (2012), "Free vibration analysis of functionally graded size-dependent nanobeams", Appl. Mathe. Computat., 218(14), 7406-7420. https://doi.org/10.1016/j.amc.2011.12.090
  27. Ghayesh, M.H. (2018), "Mechanics of tapered AFG shear-deformable microbeams", Microsyst. Technol., 24(4), 1743-1754. https://doi.org/10.1007/s00542-018-3764-y
  28. 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., Int. J., 62(2), 143-149. https://doi.org/10.12989/sem.2017.62.2.143
  29. Hein, H. and Feklistova, L. (2011), "Free vibrations of non-uniform and axially functionally graded beams using Haar wavelets", Eng. Struct., 33(12), 3696-3701. https://doi.org/10.1016/j.engstruct.2011.08.006
  30. Mehar, K., Panda, S.K. and Mahapatra, T.R. (2018), "Nonlinear frequency responses of functionally graded carbon nanotube-reinforced sandwich curved panel under uniform temperature field", Int. J. Appl. Mech., 10(3), 1850028. https://doi.org/10.1142/S175882511850028X
  31. Mohanty, S.C., Dash, R.R. and Rout, T. (2015), "Vibration and dynamic stability of pre-twisted thick cantilever beam made of functionally graded material", Int. J. Struct. Stabil. Dyn., 15(4), 1450058. https://doi.org/10.1142/S0219455414500588
  32. Nguyen, T.K., Nguyen, N.D., Vo, T. and Thai, T. (2016), "Trigonometric-series solution for analysis of laminated composite beams", Compos. Struct., 160, 142-151. https://doi.org/10.1016/j.compstruct.2016.10.033
  33. Palanivel, S. (2006), "Dynamic analysis of laminated composite beams using higher order theories and finite elements", Compos. Struct., 73(3), 342-353. https://doi.org/10.1016/j.compstruct.2005.02.002
  34. Safa, A., Hadji, L., Bourada, M. and Zouatnia, N. (2019), "Thermal vibration analysis of FGM beams using an efficient shear deformation beam theory", Earthq. Struct., Int. J., 17(3), 329-336. https://doi.org/10.12989/eas.2019.17.3.329
  35. Tornabene, F., Fantuzzi, N., Viola, E. and Reddy, J.N. (2014), "Winkler-Pasternak foundation effect on the static and dynamic analyses of laminated doubly-curved and degenerate shells and panels", Compos. Part B: Eng., 57, 269-296. https://doi.org/10.1016/j.compositesb.2013.06.020
  36. Yang, J. and Chen, Y. (2008), "Free vibration and buckling analyses of functionally graded beams with edge cracks", Compos. Struct., 83, 48-60. https://doi.org/10.1016/j.compstruct.2007.03.006
  37. 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