Coupled systems mechanics

Techno-Press (테크노프레스)
권호 표지
DOI QR코드

DOI QR Code

Effects of changing materials properties for vibration of FGM beam using integral shear deformation model

  • Mokhtar Ellali (Smart Structures Laboratory, University of Ain Temouchent-Belhadj Bouchaib) ;
  • Mashhour A. Alazwari (Mechanical Engineering Department, Faculty of Engineering, King Abdulaziz University) ;
  • Mokhtar Bouazza (Department of Civil Engineering, University Tahri Mohammed of Bechar) ;
  • Mohamed A. Eltaher (Mechanical Design and Production Department, Faculty of Engineering, Zagazig University) ;
  • Noureddine Benseddiq (Mechanics Laboratory of Lille, CNRS UMR 8107, University of Lille 1)
  • Received : 2024.02.24
  • Accepted : 2024.05.13
  • Published : 2024.08.25
⟨ Previous Next ⟩

Abstract

The objective of this work is to study the effects of the modification of material properties on the vibration of the FGM beam using an integral shear strain model. In the present theory, the rotational displacement is replaced by an integral term in the displacement fields. The use of a shear correction factor is not necessary because our model gives a parabolic description of shear stress through the thickness while satisfying the conditions of zero shear stresses on the bottom and top surfaces of the beam. The FGM beam is assumed that the beam is a mixture of metal and ceramic, and that its properties change depending on the power functions of the thickness of the beam such as: linear, quadratic, cubic and inverse quadratic. By applying Hamilton's principle, general formulas were obtained to obtain the frequencies of the FGM beam. The effects of changing compositional characteristics of materials presented by volume fraction of FGM beams with simply supported edges on free vibration and some mode shapes are investigated.

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. Abdelrahman, A.A., Shanab, R.A., Esen, I. and Eltaher, M.A. (2022), "Effect of moving load on dynamics of nanoscale Timoshenko CNTs embedded in elastic media based on doublet mechanics theory", Steel Compos. Struct., 44(2), 241-256. https://doi.org/10.12989/scs.2022.44.2.241.
  3. Alazwari, M.A., Daikh, A.A. and Eltaher, M.A. (2022), "Novel quasi 3D theory for mechanical responses of FG-CNTs reinforced composite nanoplates", Adv. Nano Res., 12(2), 117-137. https://doi.org/10.12989/anr.2022.12.2.117.
  4. Alhijazi, M., Safaei, B., Zeeshan, Q., Arman, S. and Asmael, M. (2023)., "Prediction of elastic properties of thermoplastic composites with natural fibers", J. Textile Inst., 114(10), 1488-1496. https://doi.org/10.1080/00405000.2022.2131352.
  5. Amara, K., Bouazza, M. and Fouad, B (2016), "Postbuckling analysis of functionally graded beams using nonlinear model", Per. Polytech. Mech. Eng., 60(2), 121-128. https://doi.org/10.3311/PPme.8854.
  6. Atmane, H.A., Bedia, E.A.A., Bouazza, M., Tounsi, A. and Fekrar, A. (2016), "On the thermal buckling of simply supported rectangular plates made of a sigmoid functionally graded Al/Al2O3 based material", Mech. Solid., 51, 177-187. https://doi.org/10.3103/S0025654416020059.
  7. Basha, M., Daikh, A.A., Melaibari, A., Wagih, A., Othman, R., Almitani, K.H. and Eltaher, M.A. (2022), "Nonlocal strain gradient theory for buckling and bending of FG-GRNC laminated sandwich plates", Steel Compos. Struct., 43, 639-660. https://doi.org/10.12989/scs.2022.43.5.639.
  8. Bharti, I., Gupta, N. and Gupta, K.M. (2013), "Novel applications of functionally graded nano, optoelectronic and thermoelectric materials", Int. J. Mater. Mech Manuf., 1(3), 221-224. https://doi.org/10.7763/IJMMM.2013.V1.47.
  9. Bouazza, M. and Adda-Bedia, E.A. (2013), "Elastic stability of functionally graded rectangular plates under mechanical and thermal loadings", Sci. Res. Essay., 8(39), 1933-1943. https://doi.org/10.5897/SRE11.251.
  10. Bouazza, M. and Benseddiq, N. (2015), "Analytical modeling for the thermoelastic buckling behavior of functionally graded rectangular plates using hyperbolic shear deformation theory under thermal loadings", Multidisc. Model. Mater. Struct., 11(4), 558-578. https://doi.org/10.1108/MMMS-02-2015-0008.
  11. Bouazza, M. and Zenkour, A.M. (2021), "Vibration of inhomogeneous fibrous laminated plates using an efficient and simple polynomial refined theory", J. Comput. Appl. Mech., 52, 233-245. https://doi.org/10.22059/jcamech.2021.320751.605.
  12. Bouazza, M., Antar, K., Amara, K., Benyoucef, S. and Bedia, E.A.A. (2019), "Influence of temperature on the beams behavior strengthened by bonded composite plates", Geomech. Eng., 18(5), 555-566. https://doi.org/10.12989/gae.2019.18.5.555.
  13. Bouazza, M., Becheri, T., Boucheta, A. and Benseddiq, N. (2019), "Bending behavior of laminated composite plates using the refined four-variable theory and the finite element method", Earthq. Struct., 17(3), 257-270. https://doi.org/10.12989/eas.2019.17.3.257.
  14. Bouazza, M., Boucheta, A., Becheri, T. and Benseddiq, N, (2017), "Thermal stability analysis of functionally graded plates using simple refined plate theory", Int. J. Autom. Mech. Eng., 14(1), 4013-4029. https://doi.org/10.15282/ijame.14.1.2017.15.0325.
  15. Bouazza, M., Tounsi, A. and Megueni, A. (2011), "Thermal buckling of simply supported FGM square plates", Appl. Mech. Mater., 61, 25-32. https://doi.org/10.4028/www.scientific.net/AMM.61.25.
  16. Bouazza, M., Zenkour, A.M. and Benseddiq, N. (2017), "Effect of material composition on bending analysis of FG plates via a two-variable refined hyperbolic theory", Arch. Mech., 70(2), 107-129.
  17. Bouazza, M., Zenkour, A.M. and Benseddiq, N. (2018), "Closed-from solutions for thermal buckling analyses of advanced nanoplates according to a hyperbolic four-variable refined theory with small-scale effects", Acta Mechanica, 229(5), 2251-2265. https://doi.org/10.1007/s00707-017-2097-8.
  18. Boucheta, A., Bouazza, M., Becheri, T. and Benseddiq, N. (2016), "Hyperbolic four variable refined shear deformation theory for mechanical buckling analysis of functionally graded plates", UPB. Sci. Bull. Ser. D, 78(4), 65-78.
  19. Boucheta, A., Bouazza, M., Becheri, T., Eltaher, M.A., Tounsi, A. and Benseddiq, N. (2024), "Bending of sandwich FGM plates with a homogeneous core either hard or soft via a refined hyperbolic shear deformation plate theory", Iran. J. Sci. Technol. Tran. Civil Eng., 1-15. https://doi.org/10.1007/s40996-024-01386-w.
  20. Derbale, A., Bouazza, M. and Benseddiq, N. (2021), "Analysis of the mechanical and thermal buckling of laminated beams by new refined shear deformation theory", Iran. J. Sci. Technol. Trans. Civil Eng., 45, 89-98. https://doi.org/10.1007/s40996-020-00417-6.
  21. Dihaj, A., Zidour, M., Meradjah, M., Rakrak, K., Heireche, H. and Chemi, A. (2018), "Free vibration analysis of chiral double-walled carbon nanotube embedded in an elastic medium using non-local elasticity theory and Euler Bernoulli beam model", Struct. Eng. Mech., 65(3), 335-342. https://doi.org/10.12989/sem.2018.65.3.335.
  22. Ding, H.X., Eltaher, M.A. and She, G.L. (2023), "Nonlinear low-velocity impact of graphene platelets reinforced metal foams cylindrical shell: Effect of spinning motion and initial geometric imperfections", Aerosp. Sci. Technol., 140, 108435. https://doi.org/10.1016/j.ast.2023.108435.
  23. Ellali, M., Amara, K. and Bouazza, M. (2024d), "Thermal buckling of porous FGM plate integrated surface-bonded piezoelectric", Couple. Syst. Mech., 13(2), 171-186. https://doi.org/10.12989/csm.2024.13.2.171.
  24. Ellali, M., Amara, K., Bouazza, M. and Bourada, F. (2018), "The buckling of piezoelectric plates on pasternak elastic foundation using higher-order shear deformation plate theories", Smart Struct. Syst., 21(1), 113-122. https://doi.org/10.12989/sss.2018.21.1.113.
  25. Ellali, M., Bouazza, M. and Amara, K (2022a), "Thermal buckling of a sandwich beam attached with piezoelectric layers via the shear deformation theory", Arch. Appl. Mech., 92, 657-665. https://doi.org/10.1007/s00419-021-02094-x.
  26. Ellali, M., Bouazza, M. and Zenkour, A.M (2024a), "Hygrothermal vibration of FG nanobeam via nonlocal unknown integral variables secant-tangential shear deformation coupled theory with temperature-dependent material properties", Eur. J. Mech. A/Solid., 105, 105243. https://doi.org/10.1016/j.euromechsol.2024.105243.
  27. Ellali, M., Bouazza, M. and Zenkour, A.M (2023)., "Wave propagation in functionally-graded nanoplates embedded in a winkler-pasternak foundation with initial stress effect", Phys. Mesomech., 26, 282-294. https://doi.org/10.1134/S1029959923030049.
  28. Ellali, M., Bouazza, M. and Zenkour, A.M (2023a), "Wave propagation of FGM plate via new integral inverse cotangential shear model with temperature-dependent material properties", Geomech. Eng., 33(5), 427-437. https://doi.org/10.12989/gae.2023.33.5.427.
  29. Ellali, M., Bouazza, M. and Zenkour, A.M. (2022b), "Impact of micromechanical approaches on wave propagation of FG plates via indeterminate integral variables with a hyperbolic secant shear model", Int. J. Comput. Meth., 19(9), 2250019. https://doi.org/10.1142/S0219876222500190.
  30. Ellali, M., Bouazza, M., Zenkour, A.M. and Benseddiq, N. (2024b), "Polynomial-exponential integral shear deformable theory for static stability and dynamic behaviors of FG-CNT nanobeams", Arch. Appl. Mech., 1-20. https://doi.org/10.1007/s00419-024-02582-w.
  31. Ellali, M., Zenkour, A.M., Bouazza, M. and Benseddiq, N. (2024c), "Thermal buckling of FG nanobeams via an indeterminate integral variable with trigonometric displacement models in conjunction with the gradient elasticity theory", J. Nano Res., 82, 117-138. https://doi.org/10.4028/p-PCOnh6.
  32. Fattahi, A.M., Safaei, B., Qin, Z. and Chu, F. (2021), "Experimental studies on elastic properties of high density polyethylene-multi walled carbon nanotube nanocomposites", Steel Compos. Struct., 38(2), 177-187. https://doi.org/10.12989/scs.2021.38.2.177.
  33. Feng, J., Safaei, B., Qin, Z. and Chu, F. (2023), "Nature-inspired energy dissipation sandwich composites reinforced with high-friction graphene", Compos. Sci. Tech., 233, 109925. https://doi.org/10.1016/j.compscitech.2023.109925.
  34. Kieback, B., Neubrand, A. and Riedel, H. (2003), "Processing techniques for functionally graded materials", Mater. Sci. Eng. A, 362(1-2), 81-106. https://doi.org/10.1016/S0921-5093(03)00578-1.
  35. Kumar, P. and Srinivas, J. (2017), "Free vibration, bending and buckling of a FG-CNT reinforced composite beam: Comparative analysis with hybrid laminated composite beam", Multidisc. Model. Mater. Struct., 13(4), 590-611. https://doi.org/10.1108/MMMS-05-2017-0032.
  36. Mamen, B., Bouhadra, A., Bourada, F., Bourada, M., Tounsi, A., Mahmoud, S.R. and Hussain, M. (2022), "Combined effect of thickness stretching and temperature-dependent material properties on dynamic behavior of imperfect FG beams using three variable quasi-3D model", J. Vib. Eng. Technol., 11(5), 2309-2331. https://doi.org/10.1007/s42417-022-00704-8.
  37. Mellouli, H., Jrad, H., Wali, M. and Dammak, F. (2019), "Geometrically nonlinear meshfree analysis of 3D-shell structures based on the double directors shell theory with finite rotations", Steel Compos. Struct., 31(4), 397-408. https://doi.org/10.12989/scs.2019.31.4.397.
  38. Nguyen, D.K. and Tran, T.T. (2018), "Free vibration of tapered BFGM beams using an efficient shear deformable finite element model", Steel Compos. Struct., 29(3), 363-377. https://doi.org/10.12989/scs.2018.29.3.363.
  39. Niino, M. (1987), "Design of functionally gradient material", Sci. Technol. JPN, 18(3), 18-46.
  40. Nuhu, A.A. and Safaei, B. (2022), "A comprehensive review on the vibration analyses of small-scaled plate-based structures by utilizing the nonclassical continuum elasticity theories", Thin Wall. Struct., 179, 109622. https://doi.org/10.1016/j.tws.2022.109622.
  41. Nuhu, A.A. and Safaei, B. (2022), "State-of-the-art of vibration analysis of small-sized structures by using nonclassical continuum theories of elasticity", Arch. Comput. Meth. Eng., 29, 4959-5147. https://doi.org/10.1007/s11831-022-09754-3.
  42. Pan, S., Feng, J., Safaei, B., Qin, Z., Chu, F. and Hui, D. (2022), "A comparative experimental study on damping properties of epoxy nanocomposite beams reinforced with carbon nanotubes and graphene nanoplatelets", Nanotechnol. Rev., 11(1), 1658-1669. https://doi.org/10.1515/ntrev-2022-0107.
  43. Rahmani, A., Safaei, B. and Qin, Z (2022), "On wave propagation of rotating viscoelastic nanobeams with temperature effects by using modified couple stress-based nonlocal Eringen's theory", Eng. Comput., 38(Suppl 4), 2681-2701. https://doi.org/10.1007/s00366-021-01429-0.
  44. 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.
  45. Safaei, B., Onyibo, E.C., Goren, M., Kotrasova, K., Yang, Z., Arman, S. and Asmael, M. (2023), "Free vibration investigation on rve of proposed honeycomb sandwich beam and material selection optimization", Facta Universitatis, Ser.: Mech. Eng., 21(1), 31-50. https://doi.org/10.22190/FUME220806042S.
  46. Safaei, B. (2020), "The effect of embedding a porous core on the free vibration behavior of laminated composite plates", Steel Compos. Struct., 35(5), 659-670. https://doi.org/10.12989/scs.2020.35.5.659.
  47. Safaei, B. (2021), "Frequency-dependent damped vibrations of multifunctional foam plates sandwiched and integrated by composite faces", Eur. Phys. J. Plus, 136, 646. https://doi.org/10.1140/epjp/s13360-021-01632-4.
  48. Safaei, B., Chukwueloka Onyibo, E. and Hurdoganoglu, D. (2022), "Thermal buckling and bending analyses of carbon foam beams sandwiched by composite faces under axial compression", Facta Universitatis, Ser.: Mech. Eng., 20(3), 589-615. https://doi.org/10.22190/FUME220404027S.
  49. Safaei, B., Chukwueloka Onyibo, E. and Hurdoganoglu, D. (2022), "Effect of static and harmonic loading on the honeycomb sandwich beam by using finite element method", Facta Universitatis, Ser.: Mech. Eng., 20(2), 279-306. https://doi.org/10.22190/FUME220201009S.
  50. Sahnoun, M., Ouinas, D., Benderdouche, N., Bouazza, M. and Vina, J. (2013), "Hygrothermal effect on stiffness reduction modeling damage evolution in cross-ply composite laminates", Adv. Mater. Res., 629, 79-84. https://doi.org/10.4028/www.scientific.net/amr.629.79.
  51. Sayyad, A.S. and Ghugal, Y.M. (2018), "Analytical solutions for bending, buckling, and vibration analyses of exponential functionally graded higher order beams", Asia. J. Civil Eng., 19, 607-623. https://doi.org/10.1007/s42107-018-0046-z.
  52. Selmi, A. (2020), "Dynamic behavior of axially functionally graded simply supported beams", Smart Struct. Syst., 25(6), 669-678. https://doi.org/10.12989/sss.2020.25.6.669.
  53. Shanab, R., Mohamed, S., Tharwan, M.Y., Assie, A.E. and Eltaher, M.A. (2022), "Buckling of 2D FG Porous unified shear plates resting on elastic foundation based on neutral axis", Steel Compos. Struct., 45(5), 729. https://doi.org/10.12989/scs.2022.45.5.729.
  54. Simsek, M. (2010), "Fundamental frequency analysis of functionally graded beams by using different higher-order beam theories", Nucl. Eng. Des., 240(4), 697-705. https://doi.org/10.1016/j.nucengdes.2009.12.013.
  55. 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.
  56. Timoshenko, S.P. (1921), "On the correction for shear of the differential equation for transverse vibrations of prismatic bars", Philos. Mag., 41, 742-746.
  57. Tounsi, A., Bouazza, M., Meftah, S. and Adda-Bedia, E. (2005), "On the transient hygroscopic stresses in polymer matrix laminated composites plates with cyclic and unsymmetric environmental conditions the moisture concentration", Polym. Polym. Compos., 13(5), 489-503. https://doi.org/10.1177/096739110501300506.
  58. Tounsi, T., Bouazza, M. and Adda-Bedia, E.A. (2004), "Computation of transient hygroscopic stresses in unidirectional laminated composite plates with cyclic and asymmetrical environmental conditions", Int. J. Mech. Mater. Des., 1, 271-286. https://doi.org/10.1007/s10999-005-0222-7.
  59. Vo, T.P., Thai, H.T., Nguyen, T.K., Maheri, A. and Lee, J. (2014), "Finite element model for vibration and buckling of functionally graded sandwich beams based on a refined shear deformation theory", Eng. Struct., 64, 12-22. https://doi.org/10.1016/j.engstruct.2014.01.029.
  60. Xin, L. and Kiani, Y. (2023), "Vibration characteristics of arbitrary thick sandwich beam with metal foam core resting on elastic medium", Struct., 49, 1-11. https://doi.org/10.1016/j.istruc.2023.01.108.
  61. Xu, Y., Li, Z. and Guo, K. (2018), "Active vibration robust control for FGM beams with piezoelectric layers", Struct. Eng. Mech., 67(1), 33-43. https://doi.org/10.12989/sem.2018.67.1.033.