Structural Engineering and Mechanics

Techno-Press (테크노프레스)
권호 표지
DOI QR코드

DOI QR Code

Influence of the distribution pattern of porosity on the free vibration of functionally graded plates

  • Hadji, Lazreg (Department of Civil Engineering, University of Tiaret) ;
  • Fallah, Ali (Sabanci University Integrated Manufacturing Technologies Research and Application Center) ;
  • Aghdam, Mohammad Mohammadi (Mechanical Engineering Department, Amirkabir University of Technology)
  • Received : 2021.07.30
  • Accepted : 2022.01.06
  • Published : 2022.04.25
⟨ Previous Next ⟩

Abstract

In this study, the effect of porosity distribution pattern on the free vibration analysis of porous FG plates with various boundary conditions is studied. The material properties of the plate and the porosities within the plate are considered to vary continuously through the thickness direction according to the volume fraction of constituents defined by the modified rule of the mixture, this includes porosity volume fraction with four different types of porosity distribution over the cross-section. The governing partial differential equation of motion for the free vibration analysis is obtained using hyperbolic shear deformation theory. An analytical solution is presented for the governing PDEs for various boundary conditions. Results of the presented solution are compared and validated by the available results in the literature. Moreover, the effects of material and porosity distribution and geometrical parameters on vibrational properties are investigated.

Keywords

References

  1. Abdelhak, Z., Hadji, L., Hassaine Daouadji, T. and Adda Bedia, E.A. (2015), "Thermal buckling of functionally graded plates using a n-order four variable refined theory", Adv. Mater. Res., 4(1), 31. https://doi.org/10.12989/amr.2015.4.4.031.
  2. Abrate, S. (2008), "Functionally graded plates behave like homogeneous plates", Compos. Part B: Eng., 39(1), 151-158. https://doi.org/10.1016/j.compositesb.2007.02.026.
  3. Ait Atmane, H., Tounsi, A. and Bernard, F. (2015), "A computational shear displacement model for vibrational analysis of functionally graded beams with porosities", Steel Compos. Struct., 19(2), 369-384. https://doi.org/10.12989/scs.2015.19.2.369.
  4. Ait Yahia, S., Ait Atmane, H., 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.
  5. Bekki, H., Benfarhat, R. and Hassaine Daouadji, T. (2019), "Influence of the distribution shape of porosity on the bending FGM new plate model resting on elastic foundations", Struct. Eng. Mech., 72(1), 823-832. https://doi.org/10.12989/sem.2019.72.1.061.
  6. Chen, D., Yang, J. and Kitipornchai, S. (2019), "Buckling and bending analyses of a novel functionally graded porous plate using Chebyshev-Ritz method", Arch. Civil Mech. Eng., 19(1), 157-170. https://doi.org/10.1016/j.acme.2018.09.004.
  7. Ebrahimi, F. and Rastgo, A. (2008), "An analytical study on the free vibration of smart circular thin FGM plate based on classical plate theory", Thin Wall. Struct., 46(12), 1402-1408. https://doi.org/10.1016/j.tws.2008.03.008.
  8. Fallah, A., Aghdam, M.M. and Kargarnovin, M.H. (2013), "Free vibration analysis of moderately thick functionally graded plates on elastic foundation using the extended Kantorovich method", Arch. Appl. Mech., 83(2), 177-191. https://doi.org/10.1007/s00419-012-0645-1.
  9. Gupta, A. and Talha, M. (2018), "Influence of porosity on the flexural and free vibration responses of functionally graded plates in thermal environment", Int. J. Struct. Stab. Dyn., 18(01), 1850013. https://doi.org/10.1142/S021945541850013X.
  10. Hadji, L., Hassaine Daouadji, T., Tounsi, A. and Adda Bedia, E.A. (2014), "A higher order shear deformation theory for static and free vibration of FGM beam", Steel Compos. Struct., 16(5), 507-519. https://doi.org/10.12989/scs.2014.16.5.507.
  11. Hadji, L. and Avcar, M. (2020), "Free vibration analysis of FG porous sandwich plates under various boundary conditions", J. Appl. Comput. Mech., 7(2), 505-519. 10.22055/JACM.2020.35328.2628.
  12. Hosseini-Hashemi, S., Fadaee, M. and Atashipour, S.R. (2011), "Study on the free vibration of thick functionally graded rectangular plates according to a new exact closed-form procedure", Compos. Struct., 93(2), 722-735. https://doi.org/10.1016/j.compstruct.2010.08.007.
  13. Hosseini-Hashemi, S., Fadaee, M. and Atashipour, S.R. (2011), "A new exact analytical approach for free vibration of Reissner-Mindlin functionally graded rectangular plates", Int. J. Mech. Sci., 53(1), 11-22. https://doi.org/10.1016/j.ijmecsci.2010.10.002.
  14. Jahromi, H.N., Aghdam, M.M. and Fallah, A. (2013), "Free vibration analysis of Mindlin plates partially resting on Pasternak foundation", Int. J. Mech. Sci., 75, 1-7. https://doi.org/10.1016/j.ijmecsci.2013.06.001.
  15. Jalaei, M. and Civalek, O. (2019), "On dynamic instability of magnetically embedded viscoelastic porous FG nanobeam", Int. J. Mech. Sci., 143, 14-32. https://doi.org/10.1016/j.ijengsci.2019.06.013.
  16. Karami, B., Shahsavari, D. and Janghorban, M. (2018), "Wave propagation analysis in functionally graded (FG) nanoplates under in-plane magnetic field based on nonlocal strain gradient theory and four variable refined plate theory", Mech. Adv. Mater. Struct., 25(12), 1047-1057. https://doi.org/10.1080/15376494.2017.1323143.
  17. Kumar, S., Ranjan, V. and Jana, P. (2018), "Free vibration analysis of thin functionally graded rectangular plates using the dynamic stiffness method", Compos. Struct., 197, 39-53. https://doi.org/10.1016/j.compstruct.2018.04.085.
  18. Li, J.F. (2003), "Fabrication and evaluation of porous piezoelectric ceramics and porosity-graded piezoelectric actuators", J. Am. Ceram. Soc., 86(7), 1094-1098. https://doi.org/10.1111/j.1151-2916.2003.tb03430.x.
  19. Mantari, J. and Granados, E. (2015), "Dynamic analysis of functionally graded plates using a novel FSDT", Compos. Part B: Eng., 75, 148-155. https://doi.org/10.1016/j.compositesb.2015.01.028.
  20. Mashat, D.S., Zenkour, A.M. and Radwan, A.F. (2020), "A quasi-3D higher-order plate theory for bending of FG plates resting on elastic foundations under hygro-thermo-mechanical loads with porosity", Eur. J. Mech.-A/Solid., 82, 103985. https://doi.org/10.1016/j.euromechsol.2020.103985.
  21. Mechab, I., Ait Atmane, H., Tounsi, A., Belhadj, H.A. and Adda Bedia, E.A. (2010), "A two variable refined plate theory for the bending analysis of functionally graded plates", Acta Mechanica Sinica, 26(6), 941-949. https://doi.org/10.1007/s10409-010-0372-1.
  22. Mueller, 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.
  23. Niknam, H., Fallah, A. and Aghdam, M.M. (2014), "Nonlinear bending of functionally graded tapered beams subjected to thermal and mechanical loading", Int. J. Nonlin. Mech., 65, 141-147. https://doi.org/10.1016/j.ijnonlinmec.2014.05.011.
  24. Nguyen, T.K. (2015), "A higher-order hyperbolic shear deformation plate model for analysis of functionally graded materials", Int. J. Mech. Mater. Des., 11(2), 203-219. https://doi.org/10.1007/s10999-014-9260-3.
  25. Nguyen, L.B., Nguyen, N.V., Thai, C.H., Ferreira, A.M.J. and Nguyen-Xuan, H. (2019), "An isogeometric Bezier finite element analysis for piezoelectric FG porous plates reinforced by graphene platelets", Compos. Struct., 214, 227-245. https://doi.org/10.1016/j.compstruct.2019.01.077.
  26. Pradhan, K. and Chakraverty, S. (2015), "Free vibration of functionally graded thin elliptic plates with various edge supports", Struct. Eng. Mech., 53(2), 337-354. https://doi.org/10.12989/sem.2015.53.2.337.
  27. Reddy, J.N. (2002), Energy Principles and Variational Methods in Applied Mechanics, John Wiley & Sons Inc.
  28. 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.
  29. Shimpi, R. and Patel, H. (2006), "Free vibrations of plate using two variable refined plate theory", J. Sound Vib., 296(4-5), 979-999. https://doi.org/10.1016/j.jsv.2006.03.030.
  30. Shimpi, R. and Patel, H. (2006), "A two variable refined plate theory for orthotropic plate analysis", Int. J. Solid. Struct., 43(22-23), 6783-6799. https://doi.org/10.1016/j.ijsolstr.2006.02.007.
  31. Shahsavari, D. and Janghorban, M. (2017), "Bending and shearing responses for dynamic analysis of single-layer graphene sheets under moving load", J. Brazil. Soc. Mech. Sci. Eng., 39(10), 3849-3861. https://doi.org/10.1007/s40430-017-0863-0.
  32. 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.
  33. Sobhy, M. (2013), "Buckling and free vibration of exponentially graded sandwich plates resting on elastic foundations under various boundary conditions", Compos. Struct., 99, 76-87. https://doi.org/10.1016/j.compstruct.2012.11.018.
  34. Talha, M. and Singh, B. (2010), "Static response and free vibration analysis of FGM plates using higher order shear deformation theory", Appl. Math. Model., 34(12), 3991-4011. https://doi.org/10.1016/j.apm.2010.03.034.
  35. Thai, H.T. and Kim, S.E. (2012), "Analytical solution of a two variable refined plate theory for bending analysis of orthotropic Levy-type plates", Int. J. Mech. Sci., 54(1), 269-276. https://doi.org/10.1016/j.ijmecsci.2011.11.007.
  36. Thai, H.T. and Choi, D.H. (2013), "A simple first-order shear deformation theory for the bending and free vibration analysis of functionally graded plates", Compos. Struct., 101, 332-340. https://doi.org/10.1016/j.compstruct.2013.02.019.
  37. Thai, H.T. and Choi, D.H. (2013), "Efficient higher-order shear deformation theories for bending and free vibration analyses of functionally graded plates", Arch. Appl. Mech., 83(12), 1755-1771. https://doi.org/10.1007/s00419-013-0776-z.
  38. Thai, H.T., Nguyen, T.K., Vo, T.P. and Lee, J. (2014), "Analysis of functionally graded sandwich plates using a new first-order shear deformation theory", Eur. J. Mech. A/Solid., 45, 211-225. https://doi.org/10.1016/j.euromechsol.2013.12.008.
  39. Thai, H.T. and Choi, D.H. (2014), "Levy solution for free vibration analysis of functionally graded plates based on a refined plate theory", KSCE J. Civil Eng., 18, 1813-1824. https://doi.org/10.1007/s12205-014-0409-2.
  40. Uymaz, B. and Aydogdu, M. (2007), "Three-dimensional vibration analyses of functionally graded plates under various boundary conditions", J. Reinf. Plast. Compos., 26(18), 1847-1863. https://doi.org/10.1177/0731684407081351.
  41. Vu, T.V., Nguyen, N.H., Khosravifard, A. and Quoc Bui, T. (2017), "A simple FSDT-based meshfree method for analysis of functionally graded plates", Eng. Anal. Bound. Elem., 79, 1-12. https://doi.org/10.1016/j.enganabound.2017.03.002.
  42. Watari, F., Yokoyama, A., Saso, F., Uo, M. and Kawasaki, T. (1997), "Fabrication and properties of functionally graded dental implant", Compos. Part B: Eng., 28(1-2), 5-11. https://doi.org/10.1016/S1359-8368(96)00021-2.
  43. Yin, S., Yu, T. and Liu, P. (2013), "Free vibration analyses of FGM thin plates by isogeometric analysis based on classical plate theory and physical neutral surface", Adv. Mech. Eng., 5, 634584. https://doi.org/10.1155/2013/634584.
  44. Yousfi, M., Ait Atmane, H., Meradjah, M., Tounsi, A. and Bennai, R. (2018), "Free vibration of FGM plates with porosity by a shear deformation theory with four variables", Struct. Eng. Mech., 66(3), 353-368. https://doi.org/10.12989/sem.2018.66.3.353.
  45. Zidi, M., Tounsi, A., Houari, M.S.A., Adda Bedia, E.A. and Beg, O.A. (2014), "Bending analysis of FGM plates under hygrothermo-mechanical loading using a four variable refined plate theory", Aerosp. Sci. Technol., 34, 24-34. https://doi.org/10.1016/j.ast.2014.02.001.
  46. Zhu, J., Lai, Z., Yin, Z., Jeon, J. and Lee, S. (2001), "Fabrication of ZrO2-NiCr functionally graded material by powder metallurgy", Mater. Chem. Phys., 68(1-3), 130-135. https://doi.org/10.1016/S0254-0584(00)00355-2.