Coupled systems mechanics

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Analysis of free vibration in bi-directional power law-based FG beams employing RSD theory

  • Nafissa Zouatnia (Department of Civil Engineering, University of Tiaret) ;
  • Lazreg Hadji (Department of Civil Engineering, University of Tiaret) ;
  • Hassen Ait Atmane (Laboratory of Structures Geotechnics and Risks, Department of Civil Engineering, Hassiba Benbouali University of Chlef) ;
  • Mokhtar Nebab (Laboratory of Structures Geotechnics and Risks, Department of Civil Engineering, Hassiba Benbouali University of Chlef) ;
  • Royal Madan (Department of Mechanical Engineering, Graphic Era (Deemed to be University)) ;
  • Riadh Bennai (Laboratory of Structures Geotechnics and Risks, Department of Civil Engineering, Hassiba Benbouali University of Chlef) ;
  • Mouloud Dahmane (Ecole National Superieur D'hydraulique)
  • Received : 2024.01.17
  • Accepted : 2024.07.18
  • Published : 2024.08.25
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Abstract

The present study aims to investigate the free vibration of bi-directional functionally graded (BDFG) beams using a refined shear deformation (RSD) theory. Power law variation of material composition was considered along thickness and longitudinal directions. The beams are considered simply supported. The methodology adopted is the Hamilton principle and the governing equation was solved using Navier's method for simply supported boundary conditions. A metal-ceramic combination of materials was used to provide gradation as per power law variation. The equivalent elasticity modulus and density of BDFG were computed using the rule of mixture. The results of the study were related to published works and found to be a good match. The effect of grading parameters in the thickness and longitudinal direction was studied to investigate its impact on the natural frequency.

Keywords

References

  1. Abdalla, H.M.A., Casagrande, D., De Bona, F., De Monte, T., Sortino, M. and Totis, G. (2021), "An optimized pressure vessel obtained by metal additive manufacturing: Preliminary results", Int. J. Press. Ves. Pip., 192, 104434. https://doi.org/10.1016/j.ijpvp.2021.104434.
  2. Ait Atmane, R., Mahmoudi, N. and Bennai, R. (2021), "Investigation on the dynamic response of porous FGM beams resting on variable foundation using a new higher order shear deformation theory", Steel Compos. Struct., 39(1), 95-107. https://doi.org/10.12989/scs.2021.39.1.095.
  3. Akinwamide, S.O., Abe, B.T., Akinribide, O.J., Obadele, B.A. and Olubambi, P.A. (2020), "Characterization of microstructure, mechanical properties and corrosion response of aluminium-based composites fabricated via casting-A review", Int. J. Adv. Manuf. Technol., 109, 975-991. https://doi.org/10.1007/s00170-020-05703-1.
  4. Ansari, M., Jabari, E. and Toyserkani, E. (2021), "Opportunities and challenges in additive manufacturing of functionally graded metallic materials via powder-fed laser directed energy deposition: A review", J. Mater. Proc. Technol., 294, 117117. https://doi.org/10.1016/j.jmatprotec.2021.117117.
  5. Avcar, M. (2019), "Free vibration of imperfect sigmoid and power law functionally graded beams", Steel Compos. Struct., 30(6), 603-615. https://doi.org/10.12989/scs.2019.30.6.603.
  6. Ayache, B., Bennai, R., Fahsi, B., Fourn, H., Ait Atmane, H. and Tounsi, A. (2018), "Analysis of wave propagation and free vibration of functionally graded porous material beam with a novel four variable refined theory", Earthq. Struct., 15(4), 369-382. https://doi.org/10.12989/eas.2018.15.4.369.
  7. Aydogdu, M. and Taskin, V. (2007), "Free vibration analysis of functionally graded beams with simply supported edges", Mater. Des., 28(5), 1651-1656. https://doi.org/10.1016/j.matdes.2006.02.007.
  8. Beheshti-Aval, S.B. and Lezgy-Nazargah, M. (2012), "A coupled refined high-order global-local theory and finite element model for static electromechanical response of smart multilayered/sandwich beams", Arch. Appl. Mech., 82(12), 1709-1752. https://doi.org/10.1007/s00419-012-0621-9
  9. Benaberrahmane, I., Benyoucef, S., Sekkal, M., Mekerbi, M., Bouiadjra, R.B., Selim, M.M. and Hussain, M. (2021), "Investigating of free vibration behavior of bidirectional FG beams resting on variable elastic foundation", Geomech. Eng., 25(5), 383-394. https://doi.org/10.12989/gae.2021.25.5.383.
  10. Benferhat, R., Hassaine Daouadji, T., Said Mansour, M. and Hadji, L. (2016), "Free vibration analysis of FG plates resting on the elastic foundation and based on the neutral surface concept using higher order shear deformation theory", Earthq. Struct., 10(5), 1033-1048. https://doi.org/10.12989/eas.2016.10.5.1033.
  11. Benkhellat, S., Kada, O., Seghir, A. and Kadri, M. (2021), "Seismic damage assessment of reinforced concrete grain silos", Int. J. Struct. Stab. Dyn., 22(01), 2250005. https://doi.org/10.1142/S0219455422500055.
  12. Bennai, R., Ait Atmane, R., Bernard, F., Nebab, M., Mahmoudi, N., Ait Atmane, H., Aldosari, S.M. and Tounsi, A. (2022), "Study on stability and free vibration behavior of porous FGM beams", Steel Compos. Struct., 45(1), 67-82. https://doi.org/10.12989/scs.2022.45.1.067.
  13. Benoit, M.J., Mazur, M., Easton, M.A. and Brandt, M. (2021), "Effect of alloy composition and laser powder bed fusion parameters on the defect formation and mechanical properties of Inconel 625", Int. J. Adv. Manuf. Technol., 114, 915-927. https://doi.org/10.1007/s00170-021-06957-z.
  14. Dahmane, M., Benadouda, M., Bennai, R., Saimi, A. and Ait Atmane, H. (2024), "Effect of crack on the dynamic response of bidirectional porous functionally graded beams on an elastic foundation based on finite element method", Acta Mechanica, 235(6), 3849-3860. https://doi.org/10.1007/s00707-024-03906-1.
  15. Fenjan, R.M., Ahmed, R.A., Hamad, L.B. and Faleh, N.M. (2020), "A review of numerical approach for dynamic response of strain gradient metal foam shells under constant velocity moving loads", Adv. Comput. Des., 5(4), 349-362. https://doi.org/10.12989/acd.2020.5.4.349.
  16. Frahlia, H., Bennai, R., Nebab, M., Ait Atmane, H. and Tounsi, A. (2023), "Assessing effects of parameters of viscoelastic foundation on the dynamic response of functionally graded plates using a novel HSDT theory", Mech. Adv. Mater. Struct., 30(13), 2765-2779. https://doi.org10.1080/15376494.2022.2062632.
  17. Ghouilem, K., Mehaddene, R., Ghouilem, J., Kadri, M. and Boulifa, D. (2022), "ANSYS modeling interface and creep behavior of concrete matrix on waste glass powder under constant static stress", Mater. Today: Proc., 49, 1084-1092. https://doi.org/10.1016/j.matpr.2021.09.387.
  18. Hadji, L. and Avcar, M. (2021), "Free vibration analysis of FG Porous Sandwich Plates under various boundary conditions", J. Appl. Comput. Mech., 7(2), 505-519. https://doi.org/10.22055/JACM.2020.35328.2628.
  19. Karamanli, A., Wattanasakulpong, N., Lezgy-Nazargah, M. and Vo, T.P. (2023), "Bending, buckling and free vibration behaviours of 2D functionally graded curved beams", Struct., 55, 778-798. https://doi.org/10.1016/j.istruc.2023.06.052.
  20. Kehli, A., Nebab, M., Bennai, R., Ait Atmane, H. and Dahmane, M. (2024), "Dynamic characteristics analysis of functionally graded cracked beams resting on viscoelastic medium using a new quasi-3D HSDT", Mech. Adv. Mater. Struct., 1-14. https://doi.org10.1080/15376494.2024.2326983.
  21. Lahdiri, A. and Kadri, M. (2022), "Free vibration behaviour of multi-directional functionally graded imperfect plates using 3D isogeometric approach", Earthq. Struct., 22(5), 538. https://doi.org/10.12989/eas.2022.22.5.538.
  22. Latroch, N., Dahmane, M., Benosman, A.S., Bennai, R., Ait Atmane, H. and Benadouda, M. (2023), "Inclined crack identification in bidirectional FG beams on an elastic foundation using the h-version of the finite element method", Mech. Adv. Mater. Struct., 1-7. https://doi.org/10.1080/15376494.2023.2290226.
  23. Lezgy-Nazargah, M. (2015), "Fully coupled thermo-mechanical analysis of bi-directional FGM beams using NURBS isogeometric finite element approach", Aerosp. Sci. Technol., 45, 154-164. https://doi.org/10.1016/j.ast.2015.05.006.
  24. Lezgy-Nazargah, M. (2017), "Assessment of refined high-order global-local theory for progressive failure analysis of laminated composite beams", Acta Mechanica, 228(5), 1923-1940. https://doi.org/10.1007/s00707-017-1807-6.
  25. Lezgy-Nazargah, M., Karamanli, A. and Vo, T.P. (2023), "Bending, buckling and free vibration analyses of shallow-to-deep FG curved sandwich beams using a global-local refined shear deformation theory", Struct., 52, 568-581. https://doi.org/10.1016/j.istruc.2023.04.008.
  26. Lezgy-Nazargah, M., Shariyat, M. and Beheshti-Aval, S.B. (2011), "A refined high-order global-local theory for finite element bending and vibration analyses of laminated composite beams", Acta Mechanica, 217(3), 219-242. https://doi.org/10.1007/s00707-010-0391-9.
  27. Lezgy-Nazargah, M., Trinh, L.C., Wattanasakulpong, N. and Vo, T.P. (2024), "Finite element model for stability and vibration analyses of bi-directional FG curved sandwich beams", Int. J. Mech. Mater. Des., 1-27. https://doi.org/10.1007/s10999-023-09700-6.
  28. Lu, Y. and Chen, X. (2020), "Nonlinear parametric dynamics of bidirectional functionally graded beams", Shock Vib, Article ID 8840833, 1-13. https://doi.org/10.1155/2020/8840833.
  29. Madan, R. and Bhowmick, S. (2020), "A review on application of FGM fabricated using solid-state processes", Adv. Mater. Proc. Technol., 6(3), 608-619. https://doi.org/10.1080/2374068X.2020.1731153.
  30. Madan, R. and Bhowmick, S. (2022), "Modeling of functionally graded materials to estimate effective thermo-mechanical properties", World J. Eng., 19(3), 291-301. https://doi.org/10.1108/WJE-09-2020-0445.
  31. Madan, R. and Bhowmick, S. (2023), "Fabrication and microstructural characterization of Al-SiC based functionally graded disk", Aircraft Eng. Aerosp. Technol., 95(2), 292-301. https://doi.org/10.1108/aeat-03-2022-0096.
  32. Mellal, F., Bennai, R., Avcar, M., Nebab, M. and Ait Atmane, H. (2023), "On the vibration and buckling behaviors of porous FG beams resting on variable elastic foundation utilizing higher-order shear deformation theory", Acta Mechanica, 234(9), 3955-3977. https://doi.org10.1007/s00707-023-03603-5.
  33. Nebab, M., Atmane, H.A., Bennai, R. and Dahmane, M. (2024), "Warping and porosity effects on the mechanical response of FG-Beams on non-homogeneous foundations via a Quasi-3D HSDT", Struct. Eng. Mech., 90(1), 83-94. https://doi.org/10.12989/sem.2024.90.1.083.
  34. Nakamura, T., Wang, T. and Sampath, S. (2000), "Determination of properties of graded materials by inverse analysis and instrumented indentation", Acta Materialia, 48(17), 4293-4306. https://doi.org/10.1016/S1359-6454(00)00217-2.
  35. Nebab, M., Ait Atmane, H., Bennai, R. and Dahmane, M. (2024), "Warping and porosity effects on the mechanical response of FG-Beams on non-homogeneous foundations via a Quasi-3D HSDT", Struct. Eng. Mech., 90(1), 83-94. https://doi.org/10.12989/sem.2024.90.1.083.
  36. Nebab, M., Dahmane, M., Belqassim, A., Ait Atmane, H., Bernard, F., Benadouda, M., Bennai, R. and Hadji, L. (2023), "Fundamental frequencies of cracked FGM beams with influence of porosity and Winkler/Pasternak/Kerr foundation support using a new quasi-3D HSDT", Mech. Adv. Mater. Struct., 1-13. https://doi.org/10.1080/15376494.2023.2294371.
  37. Nguyen, D.K., Nguyen, Q.H., Tran, T.T. and Bui, V.T. (2017), "Vibration of bi-dimensional functionally graded Timoshenko beams excited by a moving load", Acta Mechanica, 228, 141-155. https://doi.org/10.1007/s00707-016-1705-3.
  38. Norio, H., Hideaki, I. and Takuji, N. (1992), "Stress intensity factors of cracks initiating from a rhombic hole due to uniform heat flux", Eng. Fract. Mech., 42(2), 331-337. https://doi.org/10.1016/0013-7944(92)90223-2.
  39. Ould Larbi, L., Kaci, A., Houari, M.S.A. and Tounsi, A. (2013), "An efficient shear deformation beam theory based on neutral surface position for bending and free vibration of functionally graded beams", Mech. Bas. Des. Struct. Mach., 41(4), 421-433. https://doi.org/10.1080/15397734.2013.763713.
  40. Rabahi, A., Hassaine Daouadji, T. and Benferhat, R. (2021), "Modeling and analysis of the imperfect FGM-damaged RC hybrid beams", Adv. Comput. Des., 6(2), 117-133. https://doi.org/10.12989/acd.2021.6.2.117.
  41. Sankar, B.V. (2001), "An elasticity solution for functionally graded beams", Compos. Sci. Technol., 61(5), 689-696. https://doi.org/10.1016/S0266-3538(01)00007-0.
  42. 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.
  43. Singh, A. and Kumari, P. (2020), "Analytical free vibration solution for angle-ply piezolaminated plate under cylindrical bending: A piezo-elasticity approach", Adv. Comput. Des., 5(1), 55-89. https://doi.org/10.12989/acd.2020.5.1.055.
  44. 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(1), 57-66. https://doi.org/10.1016/j.ijmecsci.2012.05.014.
  45. Thom, T.T. and Kien, N.D. (2018), "Free vibration analysis of 2-D FGM beams in thermal environment based on a new third-order shear deformation theory", Vietnam J. Mech., 40(2), 121-140. https://doi.org/10.15625/0866-7136/10503.
  46. Verma, R.K., Parganiha, D. and Chopkar, M. (2021), "A review on fabrication and characteristics of functionally graded aluminum matrix composites fabricated by centrifugal casting method", SN Appl. Sci., 3, 227. https://doi.org/10.1007/s42452-021-04200-8.
  47. Ying, J., Lu, C.F. and Chen, W.Q. (2008), "Two-dimensional elasticity solutions for functionally graded beams resting on elastic foundations", Compos. Struct., 84(3), 209-219. https://doi.org/10.1016/j.compstruct.2007.07.004.