Geomechanics and Engineering

  • 제39권3호
  • /
  • Pages.257-271
  • /
  • 2024
  • /
  • 2005-307X(pISSN)
  • /
  • 2092-6219(eISSN)
테크노프레스 (Techno-Press)
권호 표지
DOI QR코드

DOI QR Code

Dynamic analysis of viscoelastic porous functionally graded plates resting on elastic foundation

  • Omer Faruk Capar (Department of Civil Engineering, Adana Alparslan Turkes Science and Technology University) ;
  • Mehmet Halil Calim (Department of Civil Engineering, Cukurova University) ;
  • Mehmet Bugra Ozbey (Department of Civil Engineering, Adana Alparslan Turkes Science and Technology University) ;
  • Yavuz Cetin Cuma (Department of Civil Engineering, Adana Alparslan Turkes Science and Technology University)
  • 투고 : 2023.02.27
  • 심사 : 2024.10.22
  • 발행 : 2024.11.10
⟨ 이전 논문 다음 논문 ⟩

초록

In this study, free and forced vibration behaviour of viscoelastic porous functionally graded (VPFG) plates resting on elastic foundations are investigated. Differential equations are obtained via higher order shear deformation theory. Equations of motion are obtained through energy formulations and Hamilton's principle. Navier's method based on double Fourier series is employed for the solution. Damping effect is implemented into the analysis by means of Kelvin and linear standard viscoelastic models. Viscoelastic material properties are used instead of elastic properties by means of the correspondence principle. Displacements of the plates are determined in Laplace domain and transformed into time domain by using Durbin's Modified Inverse Laplace transform method. The proposed algorithm's accuracy is validated through free and damped vibration analyses on VPFG plate, with results compared to existing studies in the literature. The study examines the influence of viscoelastic damping parameters, porosity volume fraction indexes, foundation characteristics, porosity distribution patterns and material property variations on the damped forced vibration response.

키워드

참고문헌

  1. Akavci, S.S. (2014), "An efficient shear deformation theory for free vibration of functionally graded thick rectangular plates on elastic foundation", Compos. Struct., 108, 667-676. https://doi.org/10.1016/j.compstruct.2013.10.019.
  2. Akavci, S.S. and Tanrikulu, A.H. (2015), "Static and free vibration analysis of functionally graded plates based on a new quasi-3D and 2D shear deformation theories", Compos. B Eng., 83, 203-215. https://doi.org/10.1016/j.compositesb.2015.08.043.
  3. Alavi, S.K., Ayatollahi, M.R., Petru, M. and Koloor, S.S.R. (2022), "On the dynamic response of viscoelastic functionally graded porous plates under various hybrid loadings", Ocean Eng., 264, 112541. https://doi.org/10.1016/j.oceaneng.2022.112541.
  4. 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. https://doi.org/10.12989/gae.2021.24.1.091.
  5. 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 https://doi.org/10.12989/sem.2019.71.5.459.
  6. Baferani, A.H., Saidi, A.R. and Ehteshami, H. (2011), "Accurate solution for free vibration analysis of functionally graded thick rectangular plates resting on elastic foundation", Compos. Struct., 93, 1842-1853. https://doi.org/10.1016/j.compstruct.2011.01.020.
  7. Bardell, N.S. (1991), "Free vibration analysis of a flat plate using the hierarchical finite element method", J. Sound Vib., 151, 263-289. https://doi.org/10.1016/0022-460X(91)90855-E.
  8. 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.
  9. Boley, B.A., Weiner J.H. (1960), "Theory of thermal stresses", New York: John Wiley & Sons, Ltd.
  10. Boulefrakh, L., Hebali, H., Chikh, A., Bousahla, A.A., Tounsi, A. and Mahmoud, S.R. (2019), "The effect of parameters of visco- Pasternak foundation on the bending and vibration properties of a thick FG plate", Geomech. Eng., 18(2), 161-178. https://doi.org/10.12989/gae.2019.18.2.161.
  11. Burlayenko, V.N., Altenbach, H. and Sadowski, T. (2015), "An evaluation of displacement-based finite element models used for free vibration analysis of homogeneous and composite plates", J. Sound Vib., 358, 152-175 https://doi.org/10.1016/j.jsv.2015.08.010.
  12. Calim, F.F. (2003), "Dynamic analysis of viscoelastic, anisotropic curved spatial rod systems", Ph. D. Dissertation, Cukurova University, Adana, Turkey, 160.
  13. Calim, F.F. (2016), "Dynamic response of curved Timoshenko beams resting on viscoelastic foundation." Struct. Eng. Mech., 59(4), 761-774. http://dx.doi.org/10.12989/sem.2016.59.4.761
  14. Calim, F.F. and Cuma, Y.C. (2022), "Vibration analysis of nonuniform hyperboloidal and barrel helices made of functionally graded material", Mech. Based Des. Struct., 50(11), 3781-3795 https://doi.org/10.1080/15397734.2020.1822181.
  15. Calim, F.F. and Cuma, Y.C. (2023), "Forced vibration analysis of viscoelastic helical rods with varying cross-section and functionally graded material", Mech. Based Des. Struct., 51(7), 3620-3631 https://doi.org/10.1080/15397734.2021.1931307.
  16. Chikr, S.C., Kaci, A., Bousahla, A.A., Bourada, F., Tounsi, A., Bedia, E.A., Mahmoud, S.R., Benrahou, K.H. and Tounsi, A. (2020), "A novel four-unknown integral model for buckling response of FG sandwich plates resting on elastic foundations under various boundary conditions using Galerkin's approach", Geomech. Eng., 21(5), 471-487. https://doi.org/10.12989/gae.2020.21.5.471.
  17. Cho, K.N., Bert, C.W. and Striz, A.G. (1991), "Free vibrations of laminated rectangular plates analyzed by higher order individual-layer theory", J. Sound Vib., 145, 429-442 https://doi.org/10.1016/0022-460X(91)90112-W.
  18. Choe, K., Tang, J., Shui, C., Wang, A. and Wang, Q. (2018), "Free vibration analysis of coupled functionally graded (FG) doublycurved revolution shell structures with general boundary conditions", Compos. Struct., 194, 413-432 https://doi.org/10.1016/j.compstruct.2018.04.035.
  19. Cuma, Y.C. and Calim, F.F. (2021a). Free vibration analysis of functionally graded cylindrical helices with variable crosssection." J. Sound Vib., 494, 115856. https://doi.org/10.1016/j.jsv.2020.115856
  20. Cuma, Y.C. and Calim, F.F. (2021b), "Transient response of functionally graded non-uniform cylindrical helical rods", Steel Compos. Struct., 40(4), 571-580 https://doi.org/10.12989/scs.2021.40.4.571.
  21. Cuma, Y.C. and Calim, F.F. (2022), "Dynamic response of viscoelastic functionally graded barrel and hyperboloidal coil springs with variable cross-sectional area", Mech. Time Depend. Mater., 26, 923-937. https://doi.org/10.1007/s11043-021-09520-1.
  22. Cuma, Y.C., Ozbey, M.B. and Calim, F.F. (2023), "Vibration and damping analysis of functionally graded shells", Mech. Time Depend. Mater., https://doi.org/10.1007/s11043-023-09621-z.
  23. Dogan, A. (2022), "Quasi-static and dynamic response of functionally graded viscoelastic plates", Compos. Struct., 280, 114883. https://doi.org/10.1016/j.compstruct.2021.114883.
  24. Eratli, N., Argeso, H., Calim, F.F., Temel, B., Omurtag, M.H. (2014), "Dynamic analysis of linear viscoelastic cylindrical and conical helicoidal rods using the mixed FEM", J. Sound Vib., 333, 3671-3690. https://doi.org/10.1016/j.jsv.2014.03.017.
  25. Hajlaoui, A., Triki, E., Frikha, A., Wali, M. and Dammak, F. (2017), "Nonlinear dynamics analysis of FGM shell structures with a higher order shear strain enhanced solid-shell element", LAJSS, 14, 72-91 https://doi.org/10.1590/1679-78253323.
  26. 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.
  27. Leissa, A.W. (1973), "The free vibration of rectangular plates", J. Sound Vib., 31, 257-293. https://doi.org/10.1016/S0022-460X(73)80371-2.
  28. Mantari, J.L., Granados, E.V., Hinostroza, M.A. and Soares, C.G. (2014), "Modelling advanced composite plates resting on elastic foundation by using a quasi-3D hybrid type HSDT", Compos. Struct., 118, 455-471. https://doi.org/10.1016/j.compstruct.2014.07.039.
  29. Matsunaga, H. (2008), "Free vibration and stability of functionally graded plates according to a 2-D higher-order deformation theory", Compos. Struct., 82, 499-512. https://doi.org/10.1016/j.compstruct.2007.01.030.
  30. Messina, A. (2011), "Influence of the edge-boundary conditions on three-dimensional free vibrations of isotropic and cross-ply multilayered rectangular plates", Compos. Struct., 93, 2135-2151. https://doi.org/10.1016/j.compstruct.2010.11.010.
  31. Nagino, H., Mikami, T. and Mizusawa, T. (2008), "Threedimensional free vibration analysis of isotropic rectangular plates using the B-spline Ritz method", J. Sound Vib., 317, 329-353. https://doi.org/10.1016/j.jsv.2008.03.021.
  32. 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.
  33. Nedri, K., Meiche, N.E. and Tounsi, A. (2014), "Free vibration analysis of laminated composite plates resting on elastic foundations by using a refined hyperbolic shear deformation theory", Mech. Compos. Mater., 49, 629-640, https://doi.org/10.1007/s11029-013-9379-6.
  34. Neves, A.M.A., Ferreira, A.J.M., Carrera, E., Roque, C.M.C., Cinefra, M. and Jorge, R.M.N. (2012), "A quasi-3D sinusoidal shear deformation theory for the static and free vibration analysis of functionally graded plates", Compos. B Eng., 43, 711-725. https://doi.org/10.1016/j.compositesb.2011.08.009.
  35. Ozbey, M. B., Cuma, Y. C., Deneme, I.O. and Calim, F. F. (2024), "Free and forced vibration analysis of FG-CNTRC viscoelastic plate using high shear deformation theory", Adv. Nano Res., 16(4), 413-426. https://doi.org/10.12989/anr.2024.16.4.413.
  36. Pandit, M.K., Haldar, S. and Mukhopadhyay, M. (2007), "Free vibration analysis of laminated composite rectangular plate using finite element method", J. Reinf. Plast. Comp., 26, 69-80. https://doi.org/10.1177/0731684407069955.
  37. Rabhi, M., Benrahou, K.H., Kaci, A., Houari, M.S.A., Bourada, F., Bousahla, A.A., Tounsi, A., Bedia, E.A., Mahmoud, S.R. and Tounsi, A. (2020), "A new innovative 3-unknowns HSDT for buckling and free vibration of exponentially graded sandwich plates resting on elastic foundations under various boundary conditions", Geomech. Eng., 22(2), 119-132. https://doi.org/10.12989/gae.2020.22.2.119.
  38. Rachedi, M.A., Benyoucef, S., Bouhadra, A., Bouiadjra, R.B., Sekkal, M. and Benachour, A. (2020), "Impact of the homogenization models on the thermoelastic response of FG plates on variable elastic foundation", Geomech. Eng., 22(1), 65-80. https://doi.org/10.12989/gae.2020.22.1.065.
  39. Rad, S.A.F., Hassani, B. and Karamodin, A. (2017), "Isogeometric analysis of functionally graded plates using a new quasi-3D shear deformation theory based on physical neutral surface", Compos. B Eng., 108, 174-189. https://doi.org/10.1016/j.compositesb.2016.09.029.
  40. Ramu, I. and Mohanty, S.C. (2012), "Study on free vibration analysis of rectangular plate structures using finite element method", Procedia Eng., 38, 2758-2766. https://doi.org/10.1016/j.proeng.2012.06.323.
  41. Reddy, J.N. (2000), "Analysis of functionally graded plates", Int. J. Numer. Method. Eng., 47, 663-684. https://doi.org/10.1002/(SICI)1097-0207(20000110/30)47:1/3<663::AID-NME787>3.0.CO;2-8.
  42. Reddy, J.N. (2013), "An introduction to continuum mechanics", Cambridge university press.
  43. Sayyad, A.S. and Ghugal, Y.M. (2015), "On the free vibration analysis of laminated composite and sandwich plates: A review of recent literature with some numerical results", Compos. Struct., 129, 177-201. https://doi.org/10.1016/j.compstruct.2015.04.007.
  44. 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.
  45. Shao, D., Hu, S., Wang, Q. and Pang, F. (2017), "Free vibration of refined higher-order shear deformation composite laminated beams with general boundary conditions", Compos. B Eng., 108, 75-90. https://doi.org/10.1016/j.compositesb.2016.09.093.
  46. 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.
  47. Tabatabaei, S.J.S. and Fattahi, A.M. (2022), "A finite element method for modal analysis of FGM plates", Mech. Based Des. Struct., 50, 1111-1122, https://doi.org/10.1080/15397734.2020.1744004.
  48. Temel, B. and Sahan, M.F. (2018), "Investigation of the efficiency of the solution of a simple mechanical model by using laplace transformation", AJER, 7(10), 276-282. https://doi.org/10.47000/tjmcs.1378857.
  49. Temel, B., Calim, F.F. and Tutuncu, N. (2004), "Quasi-static and dynamic response of viscoelastic helical rods", J. Sound Vib., 271, 921-935. https://doi.org/10.1016/S0022-460X(03)00760-0.
  50. Thai, H.T. and Choi, DH. (2012), "A refined shear deformation theory for free vibration of functionally graded plates on elastic foundation", Compos. B Eng., 43, 2335-2347. https://doi.org/10.1016/j.compositesb.2011.11.062.
  51. Turker, H.T., Cuma, Y.C. and Calim, F.F. (2023), "An efficient approach for free vibration behaviour of non-uniform and nonhomogeneous helices", IJST-T Civ. Eng., 47(4), 1959-1970. https://doi.org/10.1007/s40996-023-01075-0.
  52. Van, V.T., Tai, N.H.T. and Hung, N.N. (2021), "Static bending and free vibration analysis of functionally graded porous plates laid on elastic foundation using the meshless method", J. Sci. Tech. Civil Eng., 15, 141-159. https://doi.org/10.31814/stce.nuce2021-15(2)-12.
  53. Vel, S.S. and Batra, R.C. (2004), "Three-dimensional exact solution for the vibration of functionally graded rectangular plates", J. Sound Vib., 272, 703-730, https://doi.org/10.1016/S0022-460X(03)00412-7.
  54. Vinh, P.V. and Huy, L.Q. (2021), "Influence of variable nonlocal parameter and porosity on the free vibration behavior of functionally graded nanoplates", Shock Vib., 2021(1), 1219429. https://doi.org/10.1155/2021/1219429.
  55. Vinh, P.V., Chinh, N.V. and Tounsi, A. (2022), "Static bending and buckling analysis of bi-directional functionally graded porous plates using an improved first-order shear deformation theory and FEM", Eur. J. Mech.-A Solid, 96, 104743. https://doi.org/10.1016/j.euromechsol.2022.104743.
  56. Xuan, H.N., Tran, L.V., Thai, C.H. and Thoi, T.N. (2012), "Analysis of functionally graded plates by an efficient finite element method with node-based strain smoothing", Thin Walled Struct., 54, 1-18. https://doi.org/10.1016/j.tws.2012.01.013.
  57. Xue, Y., Jin, G., Ma, X., Chen, H., Ye, T. and Chen, M. (2019), "Free vibration analysis of porous plates with porosity distributions in the thickness and in-plane directions using isogeometric approach", Int. J. Mech. Sci., 152, 346-362. https://doi.org/10.1016/j.ijmecsci.2019.01.004.
  58. Zhang, Y., Jin, G., Chen, M., Ye, T., Yang, C. and Yin, Y. (2020), "Free vibration and damping analysis of porous functionally graded sandwich plates with a viscoelastic core", Compos. Struct., 244, 112298. https://doi.org/10.1016/j.compstruct.2020.112298.
  59. Zhao, J., Choe, K., Xie, F., Wang, A., Shuai, C. and Wang, Q. (2018), "Three-dimensional exact solution for vibration analysis of thick functionally graded porous (FGP) rectangular plates with arbitrary boundary conditions", Compos. B Eng., 155, 369-381. https://doi.org/10.1016/j.compositesb.2018.09.001.