DOI QR코드

DOI QR Code

Wave propagation of bi-directional porous FG beams using Touratier's higher-order shear deformation beam theory

  • Slimane Debbaghi (LDDI, Hydrocarbons and Renewable Energies) ;
  • Mouloud Dahmane (Department of Planning and Hydraulic Engineering, Higher National School of Hydraulics) ;
  • Mourad Benadouda (Material and Hydrology Laboratory, Faculty of Technology, Civil Engineering Department, University of Sidi Bel Abbes) ;
  • Hassen Ait Atmane (Civil Engineering Department, University of Hassiba Ben Bouali) ;
  • Nourddine Bendenia (Material and Hydrology Laboratory, Faculty of Technology, Civil Engineering Department, University of Sidi Bel Abbes) ;
  • Lazreg Hadji (Laboratory of Geomatics and Sustainable Development, University of Tiaret)
  • 투고 : 2023.08.03
  • 심사 : 2023.10.23
  • 발행 : 2024.02.25

초록

This work presents an analytical approach to investigate wave propagation in bi-directional functionally graded cantilever porous beam. The formulations are based on Touratier's higher-order shear deformation beam theory. The physical properties of the porous functionally graded material beam are graded through the width and thickness using a power law distribution. Two porosities models approximating the even and uneven porosity distributions are considered. The governing equations of the wave propagation in the porous functionally graded beam are derived by employing the Hamilton's principle. Closed-form solutions for various parameters and porosity types are obtained, and the numerical results are compared with those available in the literature.The numerical results show the power law index, number of wave, geometrical parameters and porosity distribution models affect the dynamic of the FG beam significantly.

키워드

참고문헌

  1. Abdelhak, Z., Hadji, L., Daouadji, T.H. and Bedia, E.A. (2015), "Thermal buckling of functionally graded plates using a n-order four variable refined theory", Adv. Mater. Res, 4(1), 31-44. https://doi.org/10.12989/amr.2015.4.1.31.
  2. Aliaga, J.W. and Reddy, J.N. (2004), "Nonlinear thermoelastic analysis of functionally graded plates using the third-order shear deformation theory", Int. J. Comput. Eng. Sci., 5, 753-779. https://doi.org/10.1142/S1465876304002666.
  3. Alshorbagy, A.E., Eltaher, M.A. and Mahmoud, F.F. (2011), "Free vibration characteristics of a functionally graded beam by finite element method", Appl. Math. Model., 35, 412-425. https://doi.org/10.1016/j.apm.2010.07.006.
  4. Amoozgar, M. and Gelman, L. (2022), "Vibration analysis of rotating porous functionally graded material beams using formulation", J. Vib. Control, 28(22), 3195-3206. https://doi.org/10.1177/10775463211027883.
  5. 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.
  6. Batou, B., Nebab, M., Bennai, R., Ait Atmane, H., Tounsi, A. and Bouremana, M. (2019), "Wave dispersion properties in imperfect sigmoid plates using various HSDTs", Steel Compos. Struct., 33(5), 699-716. https://doi.org/10.12989/scs.2019.33.5.699.
  7. Benadouda, M., Ait Atmane, H., Tounsi, A., Bernard, F. and Mahmoud, S.R. (2017), "An efficient shear deformation theory for wave propagation in functionally graded material beams with porosities", Earthq. Struct., 13(3), 255-265. https://doi.org/10.12989/eas.2017.13.3.255.
  8. Bennai, R., Fourn, H., Ait Atmane, H., Tounsi, A. and Bessaim, A. (2019), "Dynamic and wave propagation investigation of FGM plates with porosities using a four variable plate theory", Wind Struct., 28(1), 49-62. https://doi.org/10.12989/was.2019.28.1.049.
  9. Bouremana, M., Houari, M.S.A., Tounsi, A., Kaci, A. and Adda Bedia, E.A. (2013), "A new first shear deformation beam theory based on neutral surface position for functionally graded beams", Steel Compos. Struct., 15(5), 467-479. https://doi.org/10.12989/scs.2013.15.5.467.
  10. Chen, D., Yang, J. and Kitipornchai, S. (2016), "Free and forced vibrations of shear deformable functionally graded porous beams", Int. J. Mech. Sci., 108-109, 14-22. https://doi.org/10.1016/j.ijmecsci.2016.01.025.
  11. Cong, P.H., Chien, T.M., Khoa, N.D. and Duc, N.D. (2018), "Nonlinear thermomechanical buckling and post-buckling response of porous FGM plates using Reddy's HSDT", Aerosp. Sci. Technol., 77, 419-428. https://doi.org/10.1016/j.ast.2018.03.020.
  12. Dahmane, M., Benadouda, M., Fellahc, A., Saimi, A., Hassen, A.A. and Bensaid, I. (2023), "Porosities-dependent wave propagation in bidirectional functionally graded cantilever beam with higher-order shear model", Adv. Mater. Struct., 1-11. https://doi.org/10.1080/15376494.2023.2253546.
  13. Daouadji, T.H., Henni, A.H., Tounsi, A. and Bedia, E.A.A. (2013), "Elasticity solution of a cantilever functionally graded beam", Appl. Compos. Mater., 20, 1-15. https://doi.org/10.1007/s10443-011-9243-6.
  14. Ding, J.H., Huang, D.J. and Chen, W.Q. (2007), "Elasticity solutions for plane anisotropic functionally graded beams", Int. J. Solid. Struct., 44(1), 176-196. https://doi.org/10.1016/j.ijsolstr.2006.04.026.
  15. Eiadtrong, S., Wattanasakulpong, N. and Vo, T.P. (2023), "Thermal vibration of functionally graded porous beams with classical and non-classical boundary conditions using a modified Fourier method", Acta Mechanica, 234(2), 729-750. https://doi.org/10.1007/s00707-022-03401-5.
  16. Gokhan, A. (2022), "Free vibration analysis of a porous functionally graded beam using higher-order shear deformation theory", J. Struct. Eng. Appl. Mech., 5(4), 277-288. https://doi.org/10.31462/jseam.2022.04277288.
  17. Habib, E.S., El-Hadek, M.A. and El-Megharbel, A. (2019), "Stress analysis for cylinder made of FGM and subjected to thermo-mechanical loadings", Metal., 9(4), 1-14. https://doi.org/10.3390/met9010004.
  18. Hadji, L., Bernard, F. and Zouatnia, N. (2022), "Bending and free vibration analysis of Porous-Functionally-Graded (PFG) beams resting on elastic foundations", Fluid Dyn. Mater. Pr., 19(4), 1143-1155. https://doi.org/10.32604/fdmp.2022.022327.
  19. Hadji, L., Daouadji, T.H., Meziane, M.A.A., Tlidji, Y. and Bedia, E.A.A. (2016), "Analysis of functionally graded beam using a new first-order shear deformation theory", Struct. Eng. Mech., 57(2), 315-325. https://doi.org/10.12989/sem.2016.57.2.315.
  20. Hadji, L., Khelifa, Z. and Bedia, E.A.A. (2016), "A new higher order shear deformation model for functionally graded beams", KSCE J. Civil Eng., 20, 1835-1841. https://doi.org/10.1007/s12205-015-0252-0.
  21. Hassaine, N., Touat, N., Dahak, M., Fellah, A. and Saimi, A. (2022), "Study of crack's effect on the natural frequencies of bi-directional functionally graded beam", Mech. Bas. Des. Struct. Mach., 1-11. https://doi.org/10.1080/15397734.2022.2113408.
  22. Hoang Lan, T.T. (2020), "A combined strain element to functionally graded structures in thermal environment", Acta Polytechnica, 60(6), 528-539. https://doi.org/10.14311/AP.2020.60.0528.
  23. Houari, M.S.A., Tounsi, A. and Anwar, B.O. (2013), "Thermo-elastic bending analysis of functionally graded sandwich plates using a new higher order shear and normal deformation theory", Int. J. Mech. Sci., 76, 102-111. https://doi.org/10.1016/j.ijmecsci.2013.09.004.
  24. Koochaki, G.R. (2011), "Free vibration analysis of functionally graded beams", Int. J. Mech. Aerosp. Indus. Mechatron. Manuf. Eng., 5(2), 514-517.
  25. Larbi Chaht, F., Kaci, A., Houari, M.S.A., Tounsi, A., Anwar Beg, O. and Mahmoud, S.R. (2015), "Bending and buckling analyses of functionally graded material (FGM) size-dependent nanoscale beams including the thickness stretching effect", Steel Compos. Struct., 18(2), 425-442. https://doi.org/10.12989/scs.2015.18.2.425.
  26. Lu, C.F., Lim, C.W. and Chen, W.Q. (2009), "Exact solutions for free vibrations of functionally graded thick plates on elastic foundations", Mech. Adv. Mater. Struct., 16(8), 576-584. https://doi.org/10.1080/15376490903138888.
  27. Medjdoubi, B.A., Houari, M.S.A., Sadoun, M., Bessaim, A., Daikh, A.A., Belarbi, M.O., ... & Ghazwani, M.H. (2023), "On the effect of porosity on the shear correction factors of functionally graded porous beams", Couple. Syst. Mech., 12(3), 199-220. https://doi.org/10.12989/csm.2023.12.3.199.
  28. Mellal, F., Bennai, R., Avcar, M., Nebab, M. and Atmane, H.A. (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.org/10.1007/s00707-023-03603-5.
  29. Muller, E., Drasar, C., Schilz, J. and Kaysser, W.A. (2003), "Functionally graded materials for sensor and energy applications", Mater. Sci. Eng. A, 362(1-2), 17-39. https://doi.org/10.1016/S0921-5093(03)00581-1.
  30. Reddy, J.N. (2000), "Analysis of functionally graded plates", Int. J. Numer. Meth. Eng., 47(1-3), 663-684. https://doi.org/10.1002/(SICI)1097-0207.
  31. Reddy, J.N. and Chin, C.D. (1998), "Thermomechanical analysis of functionally graded cylinders and plates", J. Therm. Stress., 21, 593-626. https://doi.org/10.1080/01495739808956165.
  32. Saffari, P.R., Thongchom, C., Jearsiripongkul, T., Saffari, P.R., Keawsawasvong, S. and Kongwat, S. (2023), "Porosity-dependent wave propagation in multi-directional functionally graded nano-plate with nonlinear temperature-dependent characteristics on Kerr-type substrate", Int. J. Thermofluid., 20, 1-17. https://doi.org/10.1016/j.ijft.2023.100408.
  33. Saimi, A., Bensaid, I. and Fellah, A. (2023), "Effect of crack presence on the dynamic and buckling responses of bidirectional functionally graded beams based on quasi-3D beam model and differential quadrature finiteelement method", Arch. Appl. Mech., 93, 3131-3151. https://doi.org/10.1007/s00419-023-02429-w.
  34. Sayyad, A.S. and Ghugal, Y.M. (2017), "A unified shear deformation theory for the bending of isotropic, functionally graded, laminated and sandwich beams and plates", Int. J. Appl. Mech., 9(1), 1-36. https://doi.org/10.1142/S1758825117500077.
  35. Shahsavari, D., Shahsavari, M., Li, L. and Karami, B. (2018), "A novel quasi-3D hyperbolic theory for free vibration of FG plates with porosities resting on Winkler/Pasternak/Kerr foundation", Aerosp. Sci. Technol., 72, 134-149. https://doi.org/10.1016/j.ast.2017.11.004.
  36. Sina, S.A., Navazi, H.M. and Haddadpour, H. (2009), "An analytical method for free vibration analysis of functionally graded beams", Mater. Des., 30(3), 741-747. https://doi.org/10.1016/j.matdes.2008.05.015.
  37. Slimane, S.A., Slimane, A., Guelaili, A., Boudjemai, A., Kebdani, S., Smahat A. and Dahmane, M. (2022). Hypervelocity impact on honeycomb structure reinforced with bi-layer ceramic/aluminum facesheets used for spacecraft shielding", Mech. Adv. Mater. Struct., 29(25), 4487-4505. https://doi.org/10.1080/15376494.2021.1931991.
  38. Sura, K.A.A. and Ahmad, R.N. (2023), "Finite element analysis for the static response of functionally graded porous sandwich beams", Int. J. Eng. Technol.-IJET, 8(1), 13-20. https://doi.org/10.19072/ijet.1161612.
  39. Touratier, M. (1991), "An efficient standard plate theory", Int. J. Eng. Sci., 29(8), 901-916. https://doi.org/10.1016/0020-7225(91)90165-Y.
  40. Wattanasakulpong, N. and Eiadtrong S. (2023), "transient responses of sandwich plates with a functionally graded porous core: Jacobi-Ritz method", Int. J. Struct. Stab. Dyn., 23(4), 2350039. https://doi.org/10.1142/S0219455423500396.
  41. Wattanasakulpong, N. and Ungbhakorn, V. (2014), "Linear and nonlinear vibration analysis of elastically restrained ends FGM beams with porosities", Aerosp. Sci. Technol., 32(1), 111-120. https://doi.org/10.1016/j.ast.2013.12.002.
  42. Zhong, Z. and Yu, T. (2007), "Analytical solution of a cantilever functionally graded beam", Compos. Sci. Technol., 67(3-4), 481-488. https://doi.org/10.1016/j.compscitech.2006.08.023.