Advances in nano research

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Free vibration analysis of FGP nanobeams with classical and non-classical boundary conditions using State-space approach

  • Tlidji, Youcef (Department of Civil Engineering, University of Tiaret) ;
  • Benferhat, Rabia (Department of Civil Engineering, University of Tiaret) ;
  • Daouadji, Tahar Hassaine (Department of Civil Engineering, University of Tiaret) ;
  • Tounsi, Abdelouahed (YFL (Yonsei Frontier Lab), Yonsei University) ;
  • Trinh, L.Cong (Faculty of Civil Engineering and Applied Mechanics, University of Technical Education Ho Chi Minh City)
  • Received : 2021.10.03
  • Accepted : 2022.05.01
  • Published : 2022.11.25
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Abstract

This paper aims to investigate the vibration analysis of functionally graded porous (FGP) beams using State-space approach with several classical and non-classical boundary conditions. The materials properties of the porous FG beams are considered to have even and uneven distributions profiles along the thickness direction. The equation of motion for FGP beams with various boundary conditions is obtained through Hamilton's principle. State-space approach is used to obtain the governing equation of porous FG beam. The comparison of the results of this study with those in the literature validates the present analysis. The effects of span-to-depth ratio (L/h), of distribution shape of porosity and others parameters on the dynamic behavior of the beams are described. The results show that the boundary conditions, the geometry of the beams and the distribution shape of porosity affect the fundamental frequencies of the beams.

Keywords

References

  1. Avcar, M. (2019), "Free vibration of imperfect sigmoid and power law functionally graded beams", Steel Compos. Struct., 30(6), 603-615.http://doi.org/10.12989/scs.2019.30.6.603.
  2. Zohra, A., Benferhat, R., Hassaine Daouadji, T. and Tounsi, A. (2021), "Analysis on the buckling of imperfect functionally graded sandwich plates using new modified power-law formulations", Struct. Eng. Mech., 77(6), 797-807. https://doi.org/10.12989/sem.2021.77.6.797.
  3. Abdelhak, Z., Hadji, L., Hassaine Daouadji, T. and Adda Bedia, E.A. (2016), "Thermal buckling response of functionally graded sandwich plates with clamped boundary conditions", Smart Struct. Syst., 18(2), 267-291. https://doi.org/10.12989/sss.2016.18.2.267.
  4. Abdedezak, 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.
  5. Adim, B., Hassaine Daouadji, T., Rabahi, A. and Boussad, A. (2018), "Mechanical buckling analysis of hybrid laminated composite plates under different boundary conditions", Struct. Eng. Mech., 6(6), 761-769. https://doi.org/10.12989/sem.2018.66.6.761.
  6. Adim, B., Hassaine Daouadji, T., Rabia, B. and Hadji, L. (2016a), "An efficient and simple higher order shear deformation theory for bending analysis of composite plates under various boundary conditions", Earthq. Struct., 11(1), 63-82. https://doi.org/10.12989/eas.2016.11.1.063.
  7. Adim, B. and Hassaine Daouadji, T. (2016b), "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.
  8. Aydogdu, M. and Taskin, V. (2007), "Free vibration analysis of functionally graded beams simply supported edges", Mater. Des., 28, 1651-1656. https://doi.org/10.1016/j.matdes.2006.02.007.
  9. Akhavan, A., Mohammadimehr, M. and Ejtahed, S. (2021), "Vibration analysis and control of porous beam integrated with FG-CNT distributed piezoelectric sensor and actuator", Steel Compos. Struct., 41(4), 595-608. https://doi.org/10.12989/scs.2021.41.4.595.
  10. Ammar, B., Bensattalah, T., Zidour, M. and Adda Bedia E.A. (2020), "Buckling of carbon nanotube reinforced composite plates supported by Kerr foundation using Hamilton's energy principle", Steel Compos. Struct., 73(2), 209-223. https://doi.org/10.12989/sem.2020.9.73.209.
  11. Bian, PL. and Qing, H. (2022), "Structural analysis of nonlocal nanobeam via FEM using equivalent nonlocal differential model", EngComput. 1-17. https://doi.org/10.1007/s00366-021-01575-5.
  12. Benhenni, M., Abbes, B., Hassaine Daouadji, T. and Adim, B. (2021), "Numerical modeling of hygrothermal effect on the dynamic behavior of hybrid composite plates", Steel Compos. Struct., 39(6), 751-763. http://doi.org/10.12989/scs.2021.39.6.751.
  13. Benhenni, M., Hassaine Daouadji, T., Abbes, B., Adim, B., Yuming, L. and Abbes, F. (2018), "Dynamic analysis for antisymmetric 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.
  14. Benhenni, M., Hassaine Daouadji, T., Abbes, B., Abbes, F. and Adim, B. (2019), "Numerical analysis for free vibration of hybrid laminated composite plates for different boundary conditions", Steel Compos. Struct., 70(5), 535-549. https://doi.org/10.12989/sem.2019.70.5.535.
  15. Bensattalah, T. and Hassaine Daouadji, T. (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.
  16. Bensattalah, T., Zidour, M. and Hassaine Daouadji, T. (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.
  17. Bensattalah, T., Zidour, M. and Hassaine Daouadji, T. (2019), "A new nonlocal beam model for free vibration analysis of chiral single-walled carbon nanotubes", Compos. Mater. Eng., 1(1), 21-31. http://dx.doi.org/10.12989/cme.2019.1.1.021.
  18. Bensatallah, T., Hassaine Daouadji, T., Rabahi, A. and Tounsi, A. (2021), "Structural bonding for civil engineering structures: New model of composite I-steel-concrete beam strengthened with CFRP plate", Steel Compos. Struct., 41(3), 417-435. https://doi.org/10.12989/scs.2021.41.3.417.
  19. Rabia, B., Abderezak, R., Hassaine Daouadji, T., 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.
  20. Rabia, B., Hassaine Daouadji, T. 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.
  21. Benferhat, R., Hassaine Daouadji, T. and Abderezak, R. (2021), "Effect of porosity on fundamental frequencies of FGM sandwich plates", Compos. Mater. Eng., 3(1), 25-40. http://doi.org/10.12989/cme.2021.3.1.025.
  22. Benferhat, R., Hassaine Daouadji, T. and Rabahi, A. (2021a), "Effect of porosity on fundamental frequencies of FGM sandwich plates", Compos. Mater. Eng., 3(1), 25-40. http://doi.org/10.12989/cme.2021.3.1.025.
  23. Benferhat, R., Hassaine Daouadji, T. andRabahi, A.(2021b), "Effect of air bubbles in concrete on the mechanical behavior of RC beams strengthened in flexion by externally bonded FRP plates under uniformly distributed loading", Compos. Mater. Eng., 3(1), 41-55. http://dx.doi.org/ 10.12989/cme.2021.3.1.041.
  24. Benferhat, R., Hassaine Daouadji, T. and Rabahi, A. (2021c), "Analysis and sizing of RC beams reinforced by external bonding of imperfect functionally graded plate", Adv. Mater. Res., 10(2), 77-98. http://doi.org/10.12989/amr.2021.10.2.077.
  25. 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.2019.28.1.019.
  26. Berghouti, H., Adda Bedia, E.A., Benkhedda, A. and Tounsi, A. (2019), "Vibration analysis of nonlocal porous nanobeams of functionally graded material", Adv. Nano Res., 7(5), 351-364. https://doi.org/10.12989/anr.2019.7.5.351.
  27. 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.
  28. Hadj, B., Rabia, B. and Hassaine Daouadji, T. (2021), "Vibration analysis of porous FGM plate resting on elastic foundations: Effect of the distribution shape of porosity", Coupled Syst. Mech., 10(1),61-77. http://doi.org/10.12989/csm.2021.10.1.061.
  29. Chergui, S., Hassaine Daouadji, T., Mostefa, H., 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.
  30. Chaded, A., Hassaine Daouadji, T., Rabahi, A., Adim, B., Benferhat, R. and Fazilay, A. (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.
  31. Civalek, O. and U. Busra (2020), "Frequency, bending and buckling loads of nanobeams with cross sections", Adv. Nano Res.,9(2), 91-104. https://doi.org/10.12989/anr.2020.9.2.091.
  32. Dehshahri, K., Nejad, M.Z., Ziaee, S., Niknejad, A. and Hadi, A. (2020), "Free vibrations analysis of arbitrary three-dimensionally FGM nanoplates", Adv. Nano Res., 8(2), 115-134. https://doi.org/10.12989/anr.2020.8.2.115.
  33. Demir, E., Callioglu, H., Sayer, M. andKavla, F. (2020), "Effect of chitosan/carbon nanotube fillers on vibration behaviors of drilled composite plates", Steel Compos. Struct., 35(6), 789-798. https://doi.org/10.12989/scs.2020.35.6.789.
  34. Ebrahimi, F., Barati, M.R. and Civalek, O . (2019), "Application of Chebyshev-Ritz method for static and vibration analysis of nonlocal microstructure-dependent nanostructures", Eng. Comput., 36, 953-964. https://doi.org/10.1007/s00366-0190742.
  35. Ebrahimi, F., Karimiasl, M. and Mahesh, V. (2021), "Chaotic dynamics and forced harmonic vibration analysis of magnetoelectro-viscoelastic multiscale composite nanobeam", Eng. Comput., 37, 937-950. https://doi.org/10.1007/s00366-019-00865-3.
  36. Ebrahimi, F. and Hosseini, S.H.S. (2020), "Effect of residual surface stress on parametrically excited nonlinear dynamics and instability of double-walled nanobeams: an analytical study", Eng. Comput., 37, 1219-1230. https://doi.org/10.1007/s00366-019-00879-x.
  37. Fakher, M. and Hosseini-Hashemi, S. (2022), "Vibration of twophase local/nonlocal Timoshenko nanobeams with an efficient shear-locking-free finite-element model and exact solution", Eng. Comput., 38, 231-245. https://doi.org/ 10.1007/s00366-020-01058-z.
  38. Ebrahimi, F., Hosseini, S.H.S. and Selvamani, R. (2020), "Thermo-electro-elastic nonlinear stability analysis of viscoelastic double-piezo nanoplates under magnetic field", Struct. Eng. Mech.,73(5), 565-584. https://doi.org/10.12989/sem.2020.73.5.565.
  39. She, G.L., Liu, H.B. andKarami, B. (2020), "On resonance behavior of porous FG curved nanobeams", Steel Compos. Struct,36(2), 179-186. https://doi.org/10.12989/scs.2020.36.2.179.
  40. She, G.L. (2020), "Wave propagation of FG polymer composite nanoplates reinforced with GNPs", Steel Compos. Struct.,37(1), 27-35. https://doi.org/10.12989/scs.2020.37.1.027.
  41. Hamrat, M., Bouziadi, F., Bensaid, B., Hassaine Daouadji, T., Chergui, S., Labed, A. and Amziane, S. (2020), "Experimental and numerical investigation on the deflection behavior of precracked and repaired reinforced concrete beams with fiberreinforced polymer", Construct. Build. Mater., 249,1-13. http://doi.org/10.1016/j.conbuildmat.2020.118745.
  42. Hassaine Daouadji, 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.
  43. Hassaine Daouadji, T., Bensattalah, T., Rabahi, A. and Tounsi, A. (2021a), "New approach of composite wooden beam- reinforced concrete slab strengthened by external bonding of prestressed composite plate: Analysis and modeling", Struct. Eng. Mech. 78(3), 319-332. http://doi.org/10.12989/sem.2021.78.3.31.
  44. Hassaine Daouadji, T., Rabahi, A., Benferhat, R. and Tounsi, A. (2021b), "Performance of damaged RC continuous beams strengthened by prestressed laminates plate: Impact of mechanical and thermal properties on interfacial stresses", Coupled Syst. Mech., 10(2), 161-184. http://doi.org/10.12989/csm.2021.10.2.161.
  45. Hassaine Daouadji, T., Rabahi, A., Benferhat, R., and Tounsi, A. (2021c), "Impact of thermal effects in FRP-RC hybrid cantilever beams", Struct. Eng. Mech.,78(5), 573-583. http://doi.org/10.12989/sem.2021.78.5.573.
  46. Hassaine Daouadji, T., Rabahi, A. and Benferhat, R. (2021d), "A new model for adhesive shear stress in damaged RC cantilever beam strengthened by composite taking into account the effect of creep shrinkage", Struct. Eng. Mech., 79(5), 531-540. http://doi.org/10.12989/sem.2021.79.5.531.
  47. Hassaine Daouadji, T., Rabahi, A. and Benferhat, R. (2021e), "Hyperstatic steel structure strengthened with prestressed carbon/glass hybrid laminated plate", Coupled Syst. Mech., 10(5), 393-414. https://doi.org/10.12989/csm.2021.10.5.393.
  48. Kablia, A., Benferhat, R., Hassaine Daouadji, T. and Bouzidene, A. (2020), "Effect of porosity distribution rate for bending analysis of imperfect FGM plates resting on Winkler-Pasternak foundations under various boundary conditions", Coupled Syst. Mech., 9(6), 575-597. http://doi.org/10.12989/csm.2020.9.6.575.
  49. Karama, M., Afaq K.S. and Mistou, S. (2003), "Mechanical behavior of laminated composite beam by the new multi-layered laminated composite structures model with transverse shear stress continuity", Int. J. Solids Struct.,40(5), 25-46. http://doi.org/10.1016/S0020-7683(02)00647-9.
  50. Lei, Y.L., Kang, G., Xinwei, W. and Jie, Y. (2020), "Dynamic behaviors of single- and multi-span functionally graded porous beams with flexible boundary constraints", Appl. Math. Modell., 83, 754-776. https://doi.org/10.1016/j.apm.2020.03.017.
  51. Mahsa, N. and Isa, A. (2021), "A nonlocal Layerwise theory for free vibration analysis of nanobeams with various boundary conditions on Winkler-Pasternak foundation", Steel Compos. Struct., 40(1), 101-119. https://doi.org/10.12989/scs.2021.40.1.101.
  52. Mohsen, M. and Arameh, E. (2020), "Post-buckling analysis of Mindlin Cut out-plate reinforced by FG-CNTs", Steel Compos. Struct, 34(2), 289-297. https://doi.org/10.12989/scs.2020.34.2.289.
  53. Mohammad, A. and Kamil Zur, K. (2020), "Free vibration analysis of functionally graded nanoshells resting on Pasternak foundation based on two-dimensional analysis", Steel Compos. Struct, 34(4), 615-623. https://doi.org/10.12989/scs.2020.34.4.615.
  54. Nazemnezhad, R., Rabiei, M. and Pouyan, S. (2021), "Large amplitude free torsional vibration analysis of size-dependent circular nanobars using elliptic functions", Struct. Eng. Mech.,77(4), 535-547. https://doi.org/10.12989/sem.2021.77.4.535.
  55. Noroozi, R., Kazemi, A., Norouzi, S. and Hadi, A. (2020), "Torsional vibration analysis of bi-directional FG nano-cone with arbitrary cross-section based on nonlocal strain gradient elasticity", Adv. Nano Res., 8(1), 13-24. https://doi.org/10.12989/anr.2020.8.1.013.
  56. Noori, A.R., Timucin, A.A. and Beytullah, T. (2021), "Dynamic analysis of functionally graded porous beams using complementary functions method in the laplace domain", Compos. Struct.,256, 113094. https://doi.org/10.1016/j.compstruct.2020.113094.
  57. Ran, B., Gao, J., and Seyedmahmoodreza, A. (2021), "Higher order plate theory for buckling analysis of plates based on exact solution", Steel Compos. Struct.,40(3), 451-459. https://doi.org/10.12989/scs.2021.40.3.451.
  58. Reza, N. and Shokrollahi, H. (2020), "Free axial vibration of cracked axially functionally graded nanoscale rods incorporating surface effect", Steel Compos. Struct, 35(3), 449-462. https://doi.org/10.12989/scs.2020.35.3.449.
  59. Rabahi, A., Hassaine Daouadji, T. and Benferhat, R. (2021a), "Modeling and analysis of the imperfect FGM-damaged RC hybrid beams", Adv. Comput. Des., 6(2), 117-133. http://doi.org/10.12989/acd.2021.6.2.117.
  60. Rabahi, A., Hassaine Daouadji, T. and Benferhat, R.(2021b), "Aluminum beam reinforced by externally bonded composite materials", Adv. Mater. Res., 10(1), 23-44. http://doi.org/10.12989/amr.2021.10.1.023.
  61. Rabahi, A., Hassaine Daouadji, T., Benferhat, R. and Tounsi, A. (2021c), "Mechanical behavior of RC cantilever beams strengthened with FRP laminate plate", Adv. Comput. Des., 6(3), 169-190. http://doi.org/10.12989/acd.2021.6.3.169.
  62. Rabahi, A., Hassaine Daouadji, T., Benferhat. R. and Tounsi, A. (2021d), "New proposal for flexural strengthening of a continuous I-steel beam using FRP laminate under thermomechanical loading", Struct. Eng. Mech.,78(6), 703-714. http://doi.org/10.12989/sem.2021.78.6.703.
  63. Rabahi, A., Hassaine Daouadji, T. and Benferhat, R. (2021e), "Fiber reinforced polymer in civil engineering: Shear lag effect on damaged RC cantilever beams bonded by prestressed plate", Coupled Syst. Mech.,10, 299-316. http://doi.org/10.12989/csm.2021.10.4.299.
  64. Rabahi, A., Hassaine Daouadji, T. and Benferhat, R. (2021f), "New solution for damaged porous RC cantilever beamsstrengthening by composite plate", Adv. Mater. Res., 10(3), 169-194. http://doi.org/10.12989/amr.2021.10.3.169.
  65. Reddy, J.N. (1984), "A simple higher-order theory for laminated composite plates", J. Appl. Mech., 51(4), 745-752. https://doi.org/10.1115/1.3167719.
  66. Simsek, M. (2009), "Fundamental frequency analysis of functionally graded beams by using different higher-order beam theories", Nuclear Eng. Des., 240(4), 697-705. http://doi.org/10.1016/j.nucengdes.2009.12.013.
  67. Shanab, R.A. and Attia, M.A. (2020), "Semi-analytical solutions for static and dynamic responses of bi-directional FG nonuniform nanobeams with surface energy effect", Eng. Comput., 1-44. https://doi.org/10.1007/s00366-020-01205-6.
  68. Sayyid, H. and Hashemi, K. (2020), "Nonlinear and nonclassical vibration analysis of double walled piezoelectric cylindrical nanoshell", Adv. Nano Res., 9(4), 277-294. https://doi.org/10.12989/anr.2020.9.4.277.
  69. Singh Piyush, P. and Azam, M.S. (2021), "Size dependent vibration of functionally graded nanoplate in hygrothermal environment by Rayleigh-Ritz method", Adv. Nano Res., 10(1), 25-42. https://doi.org/10.12989/anr.2021.10.1.025.
  70. Tlidji, Y., Benferhat, R. and Hassaine Daouadji, T. (2021a), "Study and analysis of the free vibration for FGM microbeam containing various distribution shape of porosity", Struct. Eng. Mech.,77(2), 217-229. http://doi.org/10.12989/sem.2021.77.2.217.
  71. Tlidji, Y., Benferhat, R., Luan C.T., Hassaine Daouadji, T. and Tounsi, A. (2021b), "New state-space approach to dynamic analysis of porous FG beam under different boundary conditions", Adv. Nano Res., 11(4), 347-359. https://doi.org/10.12989/.2021.11.4.347.
  72. Tounsi, A., Al-Dulaijan, S.U., Al-Osta, A., Abdelbaki, C., Alzahrani, M.M. and Alfarabi, S. (2020), "A four variable trigonometric integral plate theory for hygro-thermo-mechanical bending analysis of AFG ceramic-metal plates resting on a twoparameter elastic foundation", Steel Compos. Struct., 34(4), 511-524. https://doi.org/10.12989/scs.2020.34.4.511.
  73. Wattanasakulpong, N. and Ungbhakorn, V. (2012), "Free vibration analysis of functionally graded beams with general elastically end constraints by DTM", World J. Mech., 2(6), 297-312. http://doi.org/10.4236/wjm.2012.26036.
  74. Wattanasakulpong, N. and Ungbhakorn, V. (2014), "Linear and nonlinear vibration analysis elastically restrained FGM beams with porosities", Aerosp. Sci. Technol.,32(1), 111-120, http://doi.org/10.1016/j.ast.2013.12.002.
  75. Xinli, X., Chunwei, Z., Farayi, M., Tamer, A.S. and Afrasyab, K. (2021), "Dispersion of waves characteristics of laminated composite nanoplate", Steel Compos. Struct., 40(3), 355-367. https://doi.org/10.12989/scs.2021.40.3.355.
  76. Yaser, S.F., Mohamadreza, S. and Seyed, M., Mosavi, N. (2020), "Meshless Local Petrov-Galerkin (MLPG) method for dynamic analysis of non-symmetric nanocomposite cylindrical shell", Struct. Eng. Mech., 74(5), 679-698. https://doi.org/10.12989/sem.2020.74.5.679.
  77. Zaoui, F.Z., Younsi, A., Meradjah, M., Tounsi A. and Ouinas, D. (2017), "Free vibration analysis of functionally graded beams using a higher-order shear deformation theory", Math. Model. Eng. Probl., 4(1), 7-12. https://doi.org/10.18280/mmep.040102.