DOI QR코드

DOI QR Code

Dynamic analysis of a laminated composite beam under harmonic load

  • Akbas, S.D. (Department of Civil Engineering, Bursa Technical University)
  • 투고 : 2020.08.30
  • 심사 : 2020.11.13
  • 발행 : 2020.12.25

초록

Dynamic responses of a laminated composite cantilever beam under a harmonic are investigated in this study. The governing equations of problem are derived by using the Lagrange procedure. The Timoshenko beam theory is considered and the Ritz method is implemented in the solution of the problem. The algebraic polynomials are used with the trivial functions for the Ritz method. In the solution of dynamic problem, the Newmark average acceleration method is used in the time history. In the numerical examples, the effects of load parameter, the fiber orientation angles and stacking sequence of laminas on the dynamic responses of the laminated beam are investigated.

키워드

참고문헌

  1. Akbas, S.D. (2013), "Geometrically nonlinear static analysis of edge cracked Timoshenko beams composed of functionally graded material", Math. Prob. Eng., 2013, Article ID 871815. 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., 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. Stab. 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., 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., 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., 26(6), 733-743. http://dx.doi.org/10.12989/scs.2018.26.6.733.
  10. Akbas, S.D. (2018c), "Bending of a cracked functionally graded nanobeam", Adv. Nano Res., 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., 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., 67(4), 337-346. http://dx.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., 66(1), 27-36. http://dx.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., 27(5), 567-576. http://dx.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", J. Polytech.-Politeknik Dergisi, 21(1), 65-73. http://dx.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., 8(3), 259-271. http://dx.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. Comput. Mech., 5(2), 477-485. http://dx.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(01), 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., 8(5), 459-471. http://dx.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., 72(4), 433-441. http://dx.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., 30(4), 327-336. http://dx.doi.org/10.12989/scs.2019.30.4.327.
  24. Al-Furjan, M.S.H., Habibi, M., Chen, G., Safarpour, H., Safarpour, M. and Tounsi, A. (2020a), "Chaotic oscillation of a multi-scale hybrid nano-composites reinforced disk under harmonic excitation via GDQM", Composite Structures, 252, 112737. http://dx.doi.org/10.1016/j.compstruct.2020.112737.
  25. 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.
  26. 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.
  27. Alimirzaei, S., Mohammadimehr, M. and Tounsi, A. (2019), "Nonlinear analysis of viscoelastic microcomposite beam with geometrical imperfection using FEM: MSGT electro-magneto-elastic bending, buckling and vibration solutions", Struct. Eng. Mech., 71(5), 485-502. http://dx.doi.org/10.12989/sem.2019.71.5.485.
  28. Bahmyari, E., Mohebpour, S.R. and Malekzadeh, P. (2014), "Vibration analysis of inclined laminated composite beams under moving distributed masses", Shock Vib., 2014, Article ID 750916. http://dx.doi.org/10.1155/2014/750916.
  29. 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.
  30. 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. http://dx.doi.org/10.12989/scs.2019.33.1.081.
  31. 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. http://dx.doi.org/10.12989/cac.2020.25.6.485.
  32. Bousahla, A.A., Bourada, F., Mahmoud, S.R., Tounsi, A., Algarni, A., Bedia, E.A. and Tounsi, A. (2020), "Buckling and dynamic behavior of the simply supported CNT-RC beams using an integral-first shear deformation theory", Comput. Concrete, 25(2), 155-166. http://dx.doi.org/10.12989/cac.2020.25.2.155.
  33. Bozyigit, B., Yesilce, Y. and Wahab, M.A. (2020b), "Single variable shear deformation theory for free vibration and harmonic response of frames on flexible foundation", Eng. Struct., 208, 110268. http://dx.doi.org/10.12989/sem.2020.74.1.033.
  34. Bozyigit, B., Yesilce, Y. and Wahab, M.A. (2020a), "Free vibration and harmonic response of cracked frames using a single variable shear deformation theory", Struct. Eng. Mech., 74(1), 33-54. http://dx.doi.org/10.12989/sem.2020.74.1.033.
  35. Bozyigit, B., Yesilce, Y. and Wahab, M.A. (2020c), "Transfer matrix formulations and single variable shear deformation theory for crack detection in beam-like structures", Struct. Eng. Mech., 73(2), 109-121. http://dx.doi.org/10.12989/sem.2020.73.2.109.
  36. DeValve, C. and Pitchumani, R. (2014), "Analysis of vibration damping in a rotating composite beam with embedded carbon nanotubes", Compos. Struct., 110, 289-296. https://doi.org/10.1016/j.compstruct.2013.12.007.
  37. 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.
  38. Draoui, A., Zidour, M., Tounsi, A. and Adim, B. (2019), "Static and dynamic behavior of nanotubes-reinforced sandwich plates using (FSDT)", J. Nano Res., 57, 117-135. https://doi.org/10.4028/www.scientific.net/JNanoR.57.117.
  39. Eltaher, M.A., Emam, S.A. and Mahmoud, F.F. (2012), "Free vibration analysis of functionally graded sizedependent nanobeams", Appl. Math. Comput., 218(14), 7406-7420. https://doi.org/10.1016/j.amc.2011.12.090.
  40. 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.
  41. Gillich, G.R., Praisach, Z.I., Abdel Wahab, M., Gillich, N., Mituletu, I.C. and Nitescu, C. (2016), "Free vibration of a perfectly clamped-free beam with stepwise eccentric distributed masses", Shock Vib., 2016, Article ID 2086274. https://doi.org/10.1155/2016/2086274.
  42. 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.
  43. Karami, B., Janghorban, M. and Tounsi, A. (2019), "Galerkin's approach for buckling analysis of functionally graded anisotropic nanoplates/different boundary conditions", Eng. Comput., 35(4), 1297-1316. https://doi.org/10.1007/s00366-018-0664-9.
  44. Li, Y.H., Wang, L. and Yang, E.C. (2018), "Nonlinear dynamic responses of an axially moving laminated beam subjected to both blast and thermal loads", Int. J. Nonlin. Mech., 101, 56-67. https://doi.org/10.1016/j.ijnonlinmec.2018.02.007.
  45. 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. Stab. Dyn., 15(4), 1450058. https://doi.org/10.1142/S0219455414500588.
  46. Nguyen, H.X., Nguyen, T.N., Abdel-Wahab, M., Bordas, S.P., Nguyen-Xuan, H. and Vo, T.P. (2017), "A refined quasi-3D isogeometric analysis for functionally graded microplates based on the modified couple stress theory", Comput. Meth. Appl. Mech. Eng., 313, 904-940. https://doi.org/10.1016/j.cma.2016.10.002.
  47. 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.
  48. Phung-Van, P., Thai, C.H., Nguyen-Xuan, H. and Abdel-Wahab, M. (2019a), "An isogeometric approach of static and free vibration analyses for porous FG nanoplates", Eur. J. Mech.-A/Solid., 78, 103851. https://doi.org/10.1016/j.euromechsol.2019.103851.
  49. Phung-Van, P., Thai, C.H., Nguyen-Xuan, H. and Wahab, M.A. (2019b), "Porosity-dependent nonlinear transient responses of functionally graded nanoplates using isogeometric analysis", Compos. Part B: Eng., 164, 215-225. https://doi.org/10.1016/j.compositesb.2018.11.036.
  50. Phung-Van, P., Tran, L.V., Ferreira, A.J.M., Nguyen-Xuan, H. and Abdel-Wahab, M. (2017), "Nonlinear transient isogeometric analysis of smart piezoelectric functionally graded material plates based on generalized shear deformation theory under thermo-electro-mechanical loads", Nonlin. Dyn., 87(2), 879-894. https://doi.org/10.1007/s11071-016-3085-6.
  51. Semmah, A., Heireche, H., Bousahla, A.A. and Tounsi, A. (2019), "Thermal buckling analysis of SWBNNT on Winkler foundation by nonlocal FSDT", Adv. Nano Res., 7(2), 89. http://dx.doi.org/10.12989/anr.2019.7.2.089.
  52. Shariati, A., Ghabussi, A., Habibi, M., Safarpour, H., Safarpour, M., Tounsi, A. and Safa, M. (2020), "Extremely large oscillation and nonlinear frequency of a multi-scale hybrid disk resting on nonlinear elastic foundation", Thin Wall. Struct., 154, 106840. http://dx.doi.org/10.1016/j.tws.2020.106840.
  53. Thanh, C.L., Tran, L.V., Vu-Huu, T. and Abdel-Wahab, M. (2019), "The size-dependent thermal bending and buckling analyses of composite laminate microplate based on new modified couple stress theory and isogeometric analysis", Comput. Meth. Appl. Mech. Eng., 350, 337-361. https://doi.org/10.1016/j.cma.2019.02.028.
  54. 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.
  55. Vinson, J.R. and Sierakowski, R.L. (2008), The behavior of Structures Composed of Composite Materials, Springer, Netherlands. https://doi.org/10.1007/0-306-48414-5.
  56. Wang, K., Inman, D.J. and Farrar, C.R. (2005), "Modeling and analysis of a cracked composite cantilever beam vibrating in coupled bending and torsion", J. Sound Vib., 284(1-2), 23-49. https://doi.org/10.1016/j.jsv.2004.06.027.
  57. Yayli, M.O. (2019), "Free vibration analysis of a rotationally restrained (FG) nanotube", Microsyst. Technol., 25(10), 3723-3734. https://doi.org/10.1007/s00542-019-04307-4.
  58. 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.