Geomechanics and Engineering

Techno-Press (테크노프레스)
권호 표지
DOI QR코드

DOI QR Code

Study on the characteristics of wave propagation in functionally graded porous square plates

  • Xiao, Hang (College of Mechanical and Electrical Engineering, Changsha University) ;
  • Yan, Kunming (China Aviation Changsha Design and Research Co. Ltd) ;
  • She, Guilin (College of Mechanical and Vehicle Engineering, Chongqing University)
  • Received : 2021.06.16
  • Accepted : 2021.09.27
  • Published : 2021.09.25
⟨ Previous Next ⟩

Abstract

Considering the modified power function form of material parameters, the wave equation of porous functionally graded material plate was established according to Hamilton principle based on the concept of physical medium surface and Reddy high-order shear deformed plate theory. The dispersion relations of five different elastic waves were obtained by using eigenvalue method. Then, the effects of functional gradient index and porosity on the propagation characteristics of five kinds of elastic waves are discussed. Finally, it is found that the pore volume fraction can simultaneously characterize the stiffness strengthening effect and stiffness softening effect, which depends on the power law index.

Keywords

References

  1. Ahmadi, H. and Foroutan, K. (2019), "Combination resonance analysis of FG porous cylindrical shell under two-term excitation", Steel Compos. Struct., 32(2), 253-264. http://doi.org/10.12989/scs.2019.32.2.253.
  2. Ahmed, A., Fenjan, R.M. and Faleh, N.M. (2019), "Analyzing post-buckling behavior of continuously graded FG nanobeams with geometrical imperfections", Geomech. Eng., 17(2), 175-180. http://doi.org/10.12989/gae.2019.17.2.175.
  3. Alnujaie, A., Akbas, S.D., Eltaher, M.A. and Assie, A. (2021), "Forced vibration of a functionally graded porous beam resting on viscoelastic foundation", Geomech. Eng., 24(1), 91-103. http://doi.org/10.12989/gae.2021.24.1.091
  4. Arefi, M. and Meskini, M. (2019), "Application of hyperbolic shear deformation theory to free vibration analysis of functionally graded porous plate with piezoelectric face-sheets", Struct. Eng. Mech., 71(5), 459-467. http://doi.org/10.12989/sem.2019.71.5.459.
  5. Arefi, M., Kiani, M. and Rabczuk, T. (2019), "Application of nonlocal strain gradient theory to size dependent bending analysis of a sandwich porous nanoplate integrated with piezomagnetic face-sheets", Compos. Part B Eng., 168, 320-333. http://doi.org/10.1016/j.compositesb.2019.02.057.
  6. Arefi, M., Firouzeh, S., Bidgoli, E.M.R., and Civalek, O. (2020), "Analysis of porous micro-plates reinforced with FG-GNPs based on Reddy plate theory", Compos. Struct., 247(1), 112391. https://doi.org/10.1016/j.compstruct.2020.112391.
  7. Arefi, M. and Zenkour, A.M. (2017), "Wave propagation analysis of a functionally graded magneto-electro-elastic nanobeam rest on Visco-Pasternak foundation", Mech. Res. Commun., 79, 51-62. https://doi.org/10.1016/j.mechrescom.2017.01.004.
  8. Arefi, M. (2016), "Analysis of wave in a functionally graded magneto-electro-elastic nano-rod using nonlocal elasticity model subjected to electric and magnetic potentials", Acta Mech., 227(9), 2529-2542. https://doi.org/10.1007/s00707-016-1584-7.
  9. Arshid, E., Khorshidvand, A.R. and Khorsandijou, S.M. (2019), "The effect of porosity on free vibration of SPFG circular plates resting on visco-Pasternak elastic foundation based on CPT, FSDT and TSDT", Struct. Eng. Mech., 70(1), 97-112. http://doi.org/10.12989/sem.2019.70.1.097.
  10. Avcar, M. (2019), "Free vibration of imperfect sigmoid and power law functionally graded beams", Steel Compos. Struct., 30(6), 603-615. http://dx.doi.org/10.12989/scs.2019.30.6.603
  11. Bamdad, M., Mohammadimehr, M., and Alambeigi, K. (2020), "Bending and buckling analysis of sandwich Reddy beam considering shape memory alloy wires and porosity resting on Vlasov's foundation", Steel Compos. Struct., 36(6), 671-687. http://doi.org/10.12989/scs.2020.36.6.671
  12. Barretta, R. and de Sciarra, F.M. (2019), "Variational nonlocal gradient elasticity for nano-beams", Int. J. Eng. Sci., 143, 73-91. https://doi.org/10.1016/j.ijengsci.2019.06.016.
  13. Batou, B., Nebab, M., Bennai, R., Atmane, H.T., Tounsi, A. and Bouremana, M. (2019), "Wave dispersion properties in imperfect sigmoid plates using various HSDTs", Steel Compos. Struct., 33(5), 699-716. http://doi.org/10.12989/scs.2019.33.5.699.
  14. Benahmed, A., Fahsi, B., Benzair, A., Zidour, M., Bourada, F. and Tounsi, A. (2019), "Critical buckling of functionally graded nanoscale beam with porosities using nonlocal higher-order shear deformation", Struct. Eng. Mech., 69(4), 457-466. http://doi.org/10.12989/sem.2019.69.4.457.
  15. Bennai, R., Fourn, H., Atmane, H.A., 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.
  16. Civalek, O., Uzun, B., Yayli, M.O. and Akgoz, B. (2020), "Sizedependent transverse and longitudinal vibrations of embedded carbon and silica carbide nanotubes by nonlocal finite element method", Eur. Phys. J. Plus, 135, 381. https://doi.org/10.1140/epjp/s13360-020-00385-w.
  17. Ebrahim, F., Jafaril, A., and Mahesh, V. (2019), "Assessment of porosity influence on dynamic characteristics of smart heterogeneous magneto-electro-elastic plates", Struct. Eng. Mech., 72(1), 113-129. http://doi.org/10.12989/sem.2019.72.1.113
  18. Ebrahimi, F. and Seyfi, A. (2020), "Studying propagation of wave of metal foam rectangular plates with graded porosities resting on Kerr substrate in thermal environment via analytical method", Wave Random Complex. https://doi.org/10.1080/17455030.2020.1802531
  19. Faghidian, S.A. (2021), "Contribution of nonlocal integral elasticity to modified strain gradient theory", Eur. Phys. J. Plus, 136(5), 559. https://doi.org/10.1140/epjp/s13360-021-01520-x
  20. Faghidian, S.A. (2020), "Higher-order nonlocal gradient elasticity: A consistent variational theory", Int. J. Eng. Sci., 154, 103337. https://doi.org/10.1016/j.ijengsci.2020.103337.
  21. Fenjan, R.M., Faleh, N.M. and Ridha, A.A. (2020), "Strain gradient based static stability analysis of composite crystalline shell structures having porosities", Steel Compos. Struct., 36(6), 631-642. http://doi.org/10.12989/scs.2020.36.6.631.
  22. Gao, W., Qin, Z. and Chu, F. (2020), "Wave propagation in functionally graded porous plates reinforced with graphene platelets", Aerosp. Sci. Technol., 102, 105860. https://doi.org/10.1016/j.ast.2020.105860.
  23. Ghandourh, E.E. and Abdraboh, A.M. (2020), "Dynamic analysis of functionally graded nonlocal nanobeam with different porosity models", Steel Compos. Struct., 36(3), 293-305. http://doi.org/10.12989/scs.2020.36.3.293.
  24. Ghayesh, M.H. and Farokhi, H. (2020), "Extremely large dynamics of axially excited cantilevers", Thin Walled Struct., 154, 106275. http://doi.org/10.1016/j.tws.2019.106275.
  25. Farokhi, H. and Ghayesh, M.H. (2020), "Motion limiting nonlinear dynamics of initially curved beams", Thin Walled Struct., 158, 106346. http://doi.org/10.1016/j.tws.2019.106346.
  26. Hadj, B., Rabia, B., 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), 61-70. http://doi.org/10.12989/sem.2019.72.1.061
  27. Hadji, L., Zouatnia, N. and Bernard, F. (2019), "An analytical solution for bending and free vibration responses of functionally graded beams with porosities: Effect of the micromechanical models", Struct. Eng. Mech., 69(2), 231-241. http://doi.org/10.12989/sem.2019.69.2.231.
  28. Hamed, M.A., Sadoun, A.M. and Eltaher, M.A. (2019), "Effects of porosity models on static behavior of size dependent functionally graded beam", Struct. Eng. Mech., 71(1), 89-98. http://doi.org/10.12989/sem.2019.71.1.089
  29. Jalaei, M.H. and Civalek, O. (2019), "On dynamic instability of magnetically embedded viscoelastic porous FG nanobeam", Int. J. Eng. Sci., 143, 14-32. https://doi.org/10.1016/j.ijengsci.2019.06.013.
  30. Jia, A., Liu, H., Ren, L., Yun, Y. and Tahouneh, V. (2020), "Influence of porosity distribution on vibration analysis of GPLs-reinforcement sectorial plate", Steel Compos. Struct., 35(1), 111-127. http://doi.org/10.12989/scs.2020.35.1.111.
  31. Khazaei, P. and Mohammadimehr, M. (2020), "Size dependent effect on deflection and buckling analyses of porous nanocomposite plate based on nonlocal strain gradient theory", Struct. Eng. Mech., 76(1), 27-56. http://doi.org/10.12989/sem.2020.76.1.027.
  32. Liang, C. and Wang, Y.Q. (2020), "A quasi-3D trigonometric shear deformation theory for wave propagation analysis of FGM sandwich plates with porosities resting on viscoelastic foundation", Compos. Struct., 247, 112478. https://doi.org/10.1016/j.compstruct.2020.112478.
  33. Lu, L., She, G.L. and Guo, X. (2021a), "Size-dependent postbuckling analysis of graphene reinforced composite microtubes with geometrical imperfection", Int. J. Mech. Sci., 199, 106428. https://doi.org/10.1016/j.ijmecsci.2021.106428.
  34. Lu, L., Wang, S., Li, M. and Guo, X. (2021b), "Free vibration and dynamic stability of functionally graded composite microtubes reinforced with graphene platelets", Compos. Struct., 272(15), 114231. https://doi.org/10.1016/j.compstruct.2021.114231.
  35. Lu, L., Zhu, L., Guo, X., Zhao, J. and Liu, G. (2019), "A nonlocal strain gradient shell model incorporating surface effects for vibration analysis of functionally graded cylindrical nanoshells", Appl. Math. Mech., 40(12), 1695-1722. https://doi.org/10.1007/s10483-019-2549-7.
  36. Malikan, M., Krasheninnikov, M., Eremeyev, V.A. (2020b), "Torsional stability capacity of a nano-composite shell based on a nonlocal strain gradient shell model under a three-dimensional magnetic field", Int. J. Eng. Sci., 148, 103210. http://dx.doi.org/10.1016/j.ijengsci.2019.103210
  37. Malikan, M., Uglov, N.S. and Eremeyev, V.A. (2020a), "Oninstabilities and post-buckling of piezomagnetic andflexomagnetic nanostructures", Int. J. Eng. Sci., 157, 103395. http://doi.org/10.1016/j.ijengsci.2020.103395.
  38. Mekerbi, M., Benyoucef, S., Mahmoudi, A., Bourada, F., and Tounsi, A. (2019), "Investigation on thermal buckling of porous FG plate resting on elastic foundation via quasi 3D solution", Struct. Eng. Mech., 72(4), 513-524. http://doi.org/10.12989/sem.2019.72.4.513.
  39. Mirjavadi, S.S., Forsat, M., Yahya, Y.Z., Barati, M.R., Jayasimha, A.N. and Hamouda, A.M.S. (2020), "Porosity effects on post-buckling behavior of geometrically imperfect metal foam doubly-curved shells with stiffeners", Struct. Eng. Mech., 75(6), 701-711. http://doi.org/10.12989/sem.2020.75.6.701.
  40. Nebab, M., Atmane, H.A., Bennai, R., Tounis., A. and Bedia, E.A.A. (2019), "Vibration response and wave propagation in FG plates resting on elastic foundations using HSDT", Struct. Eng. Mech., 69(5), 511-525. https://doi.org/10.12989/sem.2019.69.5.511.
  41. Rabia, B., Daouadji, T.H. and Abderezak, R. (2019), "Effect of porosity in interfacial stress analysis of perfect FGM beams reinforced with a porous functionally graded materials plate", Struct. Eng. Mech., 72(3), 293-304. http://doi.org/10.12989/sem.2019.72.3.293.
  42. Rahmani, M., Mohammadi, Y. and Kakavand, F. (2019), "Vibration analysis of sandwich truncated conical shells with porous FG face sheets in various thermal surroundings", Steel Compos. Struct., 32(2), 239-252. http://doi.org/10.12989/scs.2019.32.2.239.
  43. Sadoughifar, A., Farhatnia, F., Izadinia, M. and Tal, S.B. (2019), "Nonlinear bending analysis of porous FG thick annular/circular nanoplate based on modified couple stress and two-variable shear deformation theory using GDQM", Steel Compos. Struct., 33(2), 307-318. http://doi.org/10.12989/scs.2019.33.2.307.
  44. Sadoughifar, A., Farhatnia, F., Izadinia, M. and Talaeetaba, S.B. (2020), "Size-dependent buckling behaviour of FG annular/circular thick nanoplates with porosities resting on Kerr foundation based on new hyperbolic shear deformation theory", Struct. Eng. Mech., 73(3), 225-238. http://doi.org/10.12989/sem.2020.73.3.225.
  45. She, G.L., Liu, H.B. and Karami, B. (2021), "Resonance analysis of composite curved microbeams reinforced with graphene nanoplatelets", Thin Wall. Struct., 160, 107407. https://doi.org/10.1016/j.tws.2020.107407
  46. Sun, D. and Luo, S.N. (2011), "Wave propagation of functionally graded material plates in thermal environments", Ultrasonics, 51(8), 940-952. http://doi.org/10.1016/j.ultras.2011.05.009.
  47. Xu, K., Yuan, Y. and Li, M. (2019), "Buckling behavior of functionally graded porous plates integrated with laminated composite faces sheets", Steel Compos. Struct., 32(5), 633-642. http://doi.org/10.12989/scs.2019.32.5.633.
  48. Yahia, S.A., Atmane, H.A., Houari, M.S.A, and Tounis., A. (2019), "Wave propagation in functionally graded plates with porosities using various higher-order shear deformation plate theories", Struct. Eng. Sci., 53(6), 1143-1165. https://doi.org/10.12989/sem.2015.53.6.1143.
  49. Zhang, D.G. (2013), "Modeling and analysis of FGM rectangular plates based on physical neutral surface and high order shear deformation theory", Int. J. Mech. Sci., 68, 92-104. http://doi.org/10.1016/j.ijmecsci.2013.01.002.
  50. Zhang, D.G. (2014), "Nonlinear bending analysis of FGM rectangular plates with various supported boundaries resting on two-parameter elastic foundations", Arch. Appl. Mech., 84(1), 1-20. http://doi.org/10.1007/s00419-013-0775-0.
  51. Zhang, Y.Y., Wang, X.Y., Zhang, X., Shen, H.M., and She, G.L. (2021), "On snap-buckling of FG-CNTR curved nanobeams considering surface effects", Steel Compos. Struct., 38(3), 293-304. https://doi.org/10.12989/scs.2021.38.3.293.