Steel and Composite Structures

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Investigating wave propagation in sigmoid-FGM imperfect plates with accurate Quasi-3D HSDTs

  • Mokhtar Nebab (Department of Civil Engineering, Faculty of Technology, University of M'Hamed BOUGARA Boumerdes) ;
  • Hassen Ait Atmane (Laboratory of Structures, Geotechnics and Risks, Department of Civil Engineering, Hassiba Benbouali University of Chlef) ;
  • Riadh Bennai (Laboratory of Structures, Geotechnics and Risks, Department of Civil Engineering, Hassiba Benbouali University of Chlef)
  • Received : 2024.01.29
  • Accepted : 2024.03.22
  • Published : 2024.04.25
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Abstract

In this research paper, and for the first time, wave propagations in sigmoidal imperfect functionally graded material plates are investigated using a simplified quasi-three-dimensionally higher shear deformation theory (Quasi-3D HSDTs). By employing an indeterminate integral for the transverse displacement in the shear components, the number of unknowns and governing equations in the current theory is reduced, thereby simplifying its application. Consequently, the present theories exhibit five fewer unknown variables compared to other Quasi-3D theories documented in the literature, eliminating the need for any correction coefficients as seen in the first shear deformation theory. The material properties of the functionally graded plates smoothly vary across the cross-section according to a sigmoid power law. The plates are considered imperfect, indicating a pore distribution throughout their thickness. The distribution of porosities is categorized into two types: even or uneven, with linear (L)-Type, exponential (E)-Type, logarithmic (Log)-Type, and Sinus (S)-Type distributions. The current quasi-3D shear deformation theories are applied to formulate governing equations for determining wave frequencies, and phase velocities are derived using Hamilton's principle. Dispersion relations are assumed as an analytical solution, and they are applied to obtain wave frequencies and phase velocities. A comprehensive parametric study is conducted to elucidate the influences of wavenumber, volume fraction, thickness ratio, and types of porosity distributions on wave propagation and phase velocities of the S-FGM plate. The findings of this investigation hold potential utility for studying and designing techniques for ultrasonic inspection and structural health monitoring.

Keywords

References

  1. Abazid, M.A., Zenkour, A.M. and Sobhy, M. (2020), "Wave propagation in FG porous GPLs-reinforced nanoplates under in-plane mechanical load and Lorentz magnetic force via a new quasi 3D plate theory", Mech. Based Des. Struct. Mach. 1-20. https://doi.org/10.1080/15397734.2020.1769651.
  2. Abualnour, M., Houari, M.S.A., Tounsi, A., Bedia, E.A.A. and Mahmoud, S.R. (2018), "A novel quasi-3D trigonometric plate theory for free vibration analysis of advanced composite plates", Compos. Struct., 184 688-697. https://doi.org/10.1016/j.compstruct.2017.10.047.
  3. Alghanmi, R.A. (2022), "Nonlocal strain gradient theory for the bending of functionally graded porous nanoplates", Materials. 15(23), 8601.
  4. Alghanmi, R.A. (2023), "Hygrothermal bending analysis of sandwich nanoplates with FG porous core and piezomagnetic faces via nonlocal strain gradient theory", Nanotechnol. Rev., 12(1). https://doi.org/10.1515/ntrev-2023-0123.
  5. Alghanmi, R.A. and Zenkour, A.M. (2021), "An electromechanical model for functionally graded porous plates attached to piezoelectric layer based on hyperbolic shear and normal deformation theory", Compos. Struct., 274, 114352. https://doi.org/10.1016/j.compstruct.2021.114352.
  6. Aminipour, H., Janghorban, M. and Li, L. (2018), "A new model for wave propagation in functionally graded anisotropic doubly-curved shells", Compos. Struct., 190, 91-111. https://doi.org/10.1016/j.compstruct.2018.02.003.
  7. Asghari Ardalani, A.-R., Amiri, A., Talebitooti, R. and Safizadeh, M.S. (2020), "On wave dispersion characteristics of fluid-conveying smart nanotubes considering surface elasticity and flexoelectricity approach", Proc. Inst. Mech. Eng., Part C: J. Mech. Eng. Sci. 095440622096561. https://doi.org/10.1177/0954406220965611.
  8. Attia, A., Tounsi, A., Bedia, E. and Mahmoud, S. (2015), "Free vibration analysis of functionally graded plates with temperature-dependent properties using various four variable refined plate theories", Steel Compos. Struct. 18(1), 187-212. https://doi.org/10.12989/scs.2015.18.1.187
  9. Ayache, B., Bennai, R., Fahsi, B., Fourn, H., Atmane, H.A. 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.
  10. Azizi, N., Saadatpour, M.M. and Mahzoon, M. (2019), "Analyzing first symmetric and antisymmetric Lamb wave modes in functionally graded thick plates by using spectral plate elements", Int. J. Mech. Sci., 150, 484-494. https://doi.org/10.1016/j.ijmecsci.2018.10.030.
  11. Batou, B., Nebab, M., Bennai, R., Atmane, H.A., Tounsi, A. and Bouremana, M. (2019), "Wave dispersion properties in imperfect sigmoid plates using various HSDTs", Steel Compos. Struct., 33(5), 699. https://doi.org/10.12989/scs.2019.33.5.699.
  12. Belkhodja, Y., Ouinas, D., Fekirini, H., Olay, J.V. and Touahmia, M. (2020), "Three new hybrid quasi-3D and 2D higher-order shear deformation theories for free vibration analysis of functionally graded material monolayer and sandwich plates with stretching effect", Adv. Compos. Lett., 29 0963693520941865.
  13. Benadouda, M., Atmane, H.A., Tounsi, A., Bernard, F. and Mahmoud, S. (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.
  14. Benahmed, A., Houari, M.S.A., Benyoucef, S., Belakhdar, K. and Tounsi, A. (2017), "A novel quasi-3D hyperbolic shear deformation theory for functionally graded thick rectangular plates on elastic foundation", Geomech. Eng., 12(1), 9-34. https://doi.org/10.12989/gae.2017.12.1.009.
  15. Bennai, R., Fourn, H., Nebab, M., Atmane, R.A., Mellal, F., Atmane, H.A., Benadouda, M. and Touns, A. (2022), "On the wave dispersion and vibration characteristics of FG plates resting on elastic Kerr foundations via HSDT", Adv. Concr Constr., 14(3), 169-183. https://doi.org/10.12989/acc.2022.14.3.169.
  16. Bennai, R., Mellal, F., Nebab, M., Fourn, H., Benadouda, M., Atmane, H.A., Tounsi, A. and Hussain, M. (2022), "On wave dispersion properties of functionally graded plates resting on elastic foundations using quasi-3D and 2D HSDT", Earthq. Struct., 22(5), 447-460. https://doi.org/10.12989/eas.2022.22.5.447.
  17. Besseghier, A., Tounsi, A., Houari, M.S.A., Benzair, A., Boumia, L. and Heireche, H. (2011), "Thermal effect on wave propagation in double-walled carbon nanotubes embedded in a polymer matrix using nonlocal elasticity", Physica E. 43(7), 1379-1386. https://doi.org/10.1016/j.physe.2011.03.008.
  18. Bin, W., Jiangong, Y. and Cunfu, H. (2008), "Wave propagation in non-homogeneous magneto-electro-elastic plates", J. Sound Vib., 317(1-2), 250-264. https://doi.org/10.1016/j.jsv.2008.03.008.
  19. Carrera, E., Brischetto, S. and Robaldo, A. (2008), "Variable kinematic model for the analysis of functionally graded material plates", AIAA J., 46(1), 194-203. https://doi.org/10.2514/1.32490.
  20. Chen, W.Q., Wang, H.M. and Bao, R.H. (2007), "On calculating dispersion curves of waves in a functionally graded elastic plate", Compos. Struct., 81(2), 233-242. https://doi.org/10.1016/j.compstruct.2006.08.009.
  21. Chi, S.-H. and Chung, Y.-L. (2006), "Mechanical behavior of functionally graded material plates under transverse load-Part I: Analysis", Int. J. Solids Struct., 43(13), 3657-3674. https://doi.org/10.1016/j.ijsolstr.2005.04.011.
  22. Ebrahimi, F. and Barati, M.R. (2016), "Flexural wave propagation analysis of embedded S-FGM nanobeams under longitudinal magnetic field based on nonlocal strain gradient theory", Arab. J. Sci. Eng., 42(5), 1715-1726. https://doi.org/10.1007/s13369-016-2266-4.
  23. Ebrahimi, F. and Sedighi, S.B. (2020), "Wave propagation analysis of a rectangular sandwich composite plate with tunable magneto-rheological fluid core", J. Vib. Control. 27(11-12), 1231-1239. https://doi.org/10.1177/1077546320938189.
  24. Ebrahimi, F. and Seyfi, A. (2021), "A wave propagation study for porous metal foam beams resting on an elastic foundation", Waves Random Complex Medium. 1-15. https://doi.org/10.1080/17455030.2021.1905909.
  25. Fazzolari, F.A. (2018), "Generalized exponential, polynomial and trigonometric theories for vibration and stability analysis of porous FG sandwich beams resting on elastic foundations", Compos., Part B. 136, 254-271. https://doi.org/10.1016/j.compositesb.2017.10.022.
  26. Fourn, H., Ait Atmane, H., Bourada, M., Bousahla, A.A., Tounsi, A. and Mahmoud, S. (2018), "A novel four variable refined plate theory for wave propagation in functionally graded material plates", Steel Compos. Struct., 27(1), 109-122. https://doi.org/10.12989/scs.2018.27.1.109.
  27. Fourn, H., Atmane, H.A., Bourada, M., Bousahla, A.A., Tounsi, A. and Mahmoud, S. (2018), "A novel four variable refined plate theory for wave propagation in functionally graded material plates", Steel Compos. Struct., 27(1), 109-122. https://doi.org/10.12989/scs.2018.27.1.109.
  28. 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.
  29. Ghorbanpour Arani, A., Jamali, M., Mosayyebi, M. and Kolahchi, R. (2016), "Wave propagation in FG-CNT-reinforced piezoelectric composite micro plates using viscoelastic quasi3D sinusoidal shear deformation theory", Compos., Part B. 95, 209-224. https://doi.org/10.1016/j.compositesb.2016.03.077.
  30. Gupta, A. and Talha, M. (2018), "Static and Stability Characteristics of Geometrically Imperfect FGM Plates Resting on Pasternak Elastic Foundation with Microstructural Defect", Arabian J. Sci. Eng., 43(9), 4931-4947. https://doi.org/10.1007/s13369-018-3240-0.
  31. Hadj, B., Rabia, B. and Daouadji, T.H. (2021), "Vibration analysis of porous FGM plate resting on elastic foundations: Effect of the distribution shape of porosity", Coupl. Syst. Mech.. 10(1), 61-77.
  32. Idesman, A. (2014), "Accurate finite-element modeling of wave propagation in composite and functionally graded materials", Compos. Struct., 117 298-308. https://doi.org/10.1016/j.compstruct.2014.06.032.
  33. Jung, W.-Y., Han, S.-C. and Park, W.-T. (2016), "Four-variable refined plate theory for forced-vibration analysis of sigmoid functionally graded plates on elastic foundation", Int. J. Mech. Sci.. 111-112, 73-87. https://doi.org/10.1016/j.ijmecsci.2016.03.001.
  34. Karami, B., Janghorban, M. and Li, L. (2018), "On guided wave propagation in fully clamped porous functionally graded nanoplates", Acta Astronaut., 143 380-390. https://doi.org/10.1016/j.actaastro.2017.12.011.
  35. Lezgy-Nazargah, M. and Meshkani, Z. (2018), "An efficient partial mixed finite element model for static and free vibration analyses of FGM plates rested on two-parameter elastic foundations", Struct. Eng. Mech., 66(5), 665-676. https://doi.org/10.12989/sem.2018.66.5.665.
  36. Mantari, J.L. (2016), "A simple polynomial quasi-3D HSDT with four unknowns to study FGPs. Reddy's HSDT assessment", Compos. Struct., 137 114-120. https://doi.org/10.1016/j.compstruct.2015.11.006.
  37. Matsunaga, H. (2008), "Free vibration and stability of functionally graded plates according to a 2-D higher-order deformation theory", Compos. Struct., 82(4), 499-512. https://doi.org/10.1016/j.compstruct.2007.01.030.
  38. 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 Mech., 234(9), 3955-3977. https://doi.org10.1007/s00707-023-03603-5.
  39. Mirjavadi, S.S., Khan, I., Forsat, M., Barati, M.R. and Hamouda, A. (2020), "Analyzing nonlinear vibration of metal foam stiffened toroidal convex/concave shell segments considering porosity distribution", Mech. Based Des. Struct. Mach. 1-17.
  40. Mohamed, S., Assie, A.E., Mohamed, N. and Eltaher, M.A. (2022), "Static and stress analyses of bi-directional FG porous plate using unified higher order kinematics theories", Steel Compos. Struct., 45(3), 305-330. https://doi.org/10.12989/scs.2022.45.3.305.
  41. Mohammadimehr, M. and Alimirzaei, S. (2017), "Buckling and free vibration analysis of tapered FG-CNTRC micro Reddy beam under longitudinal magnetic field using FEM", Smart Struct. Syst. 19(3), 309-322. https://doi.org/10.12989/sss.2017.19.3.309.
  42. Nebab, M., Ait Atmane, H., Bennai, R. and Tounsi, A. (2019), "Effect of variable elastic foundations on static behavior of functionally graded plates using sinusoidal shear deformation", Arabian J. Geosci., 12(24), 809. https://doi.org/10.1007/s12517-019-4871-5.
  43. Nebab, M., Atmane, H.A., Bennai, R. and Tahar, B. (2019), "Effect of nonlinear elastic foundations on dynamic behavior of FG plates using four-unknown plate theory", Earthq. Struct., 17(5), 447-462. https://doi.org/10.12989/eas.2019.17.5.447.
  44. Nebab, M., Atmane, H.A., Bennai, R., Tounsi, A. and Bedia, E.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.org10.12989/sem.2019.69.5.511.
  45. Nebab, M., Benguediab, S., Atmane, H.A. and Bernard, F. (2020), "A simple quasi-3D HDST for dynamic behavior of advanced composite plates with the effect of variables elastic foundations", Geomech. Eng., 22(5), 415-431. https://doi.org/10.12989/gae.2020.22.5.415.
  46. Nebab, M., Dahmane, M., Belqassim, A., Atmane, H.A., 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. 10.1080/15376494.2023.2294371.
  47. 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. https://doi.org/10.12989/scs.2018.29.3.363.
  48. Nguyen, T.-K., Nguyen, V.-H., Chau-Dinh, T., Vo, T.P. and Nguyen-Xuan, H. (2016), "Static and vibration analysis of isotropic and functionally graded sandwich plates using an edge-based MITC3 finite elements", Compos., Part B. 107 162-173. https://doi.org/10.1016/j.compositesb.2016.09.058
  49. Radwan, A.F. (2019), "Quasi-3D integral model for thermomechanical buckling and vibration of FG porous nanoplates embedded in an elastic medium", Int. J. Mech. Sci., 157-158 320-335. https://doi.org/10.1016/j.ijmecsci.2019.04.031.
  50. Reddy, J. (2000), "Analysis of functionally graded plates", Int. J. Numer. Methods Eng., 47(1-3), 663-684. https://doi.org/10.1002/(SICI)1097-0207(20000110/30)47:1/3%3C663::AIDNME787%3E3.0.CO;2-8.
  51. Shahmohammadi, M.A., Azhari, M. and Saadatpour, M.M. (2020), "Free vibration analysis of sandwich FGM shells using isogeometric B-spline finite strip method", Steel Compos. Struct., 34(3), 361-376. https://doi.org/10.12989/scs.2020.34.3.361.
  52. Shahsavari, D., Karami, B. and Li, L. (2018), "A high-order gradient model for wave propagation analysis of porous FG nanoplates", Steel Compos. Struct., 29(1), 53-66. https://doi.org/10.12989/scs.2018.29.1.053.
  53. 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.
  54. 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.2021.40.1.139.
  55. Shufrin, I. and Eisenberger, M. (2005), "Stability and vibration of shear deformable plates--first order and higher order analyses", Int. J. Solids Struct., 42(3-4), 1225-1251. https://doi.org/10.1016/j.ijsolstr.2004.06.067.
  56. Thai, H.-T. and Choi, D.-H. (2012), "A refined shear deformation theory for free vibration of functionally graded plates on elastic foundation", Compos., Part B. 43(5), 2335-2347. https://doi.org/10.1016/j.compositesb.2011.11.062.
  57. Tran, T.T., Tran, V.K., Pham, Q.-H. and Zenkour, A.M. (2021), "Extended four-unknown higher-order shear deformation nonlocal theory for bending, buckling and free vibration of functionally graded porous nanoshell resting on elastic foundation", Compos. Struct., 264 113737. https://doi.org/10.1016/j.compstruct.2021.113737.
  58. 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.
  59. Xi, F. (2022), "Vibrational characteristics of sandwich annular plates with damaged core and FG face sheets", Steel Compos. Struct., 44(1), 65. https://doi.org/10.12989/scs.2022.44.1.065.
  60. Yahia, S.A., Atmane, H.A., Houari, M.S.A. and Tounsi, A. (2015), "Wave propagation in functionally graded plates with porosities using various higher-order shear deformation plate theories", Struct. Eng. Mech., 53(6), 1143-1165. https://doi.org/10.12989/sem.2015.53.6.1143.
  61. Yu, J., Wu, B. and He, C. (2010), "Guided thermoelastic waves in functionally graded plates with two relaxation times", Int. J. Eng. Sci., 48(12), 1709-1720. https://doi.org/10.1016/j.ijengsci.2010.10.002.
  62. Zaoui, F.Z., Ouinas, D. and Tounsi, A. (2019), "New 2D and quasi-3D shear deformation theories for free vibration of functionally graded plates on elastic foundations", Compos., Part B. 159 231-247. https://doi.org/10.1016/j.compositesb.2018.09.051.
  63. Zenkour, A.M. and Alghanmi, R.A. (2022), "A refined quasi-3D theory for the bending of functionally graded porous sandwich plates resting on elastic foundations", Thin-Wall. Struct., 181 110047. https://doi.org/10.1016/j.tws.2022.110047.
  64. Zhang, L.W., Lei, Z.X. and Liew, K.M. (2016), "Free vibration analysis of FG-CNT reinforced composite straight-sided quadrilateral plates resting on elastic foundations using the IMLS-Ritz method", J. Vib. Control. 23(6), 1026-1043. https://doi.org/10.1177/1077546315587804.