Steel and Composite Structures

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Application of the exact spectral element method in the analysis of the smart functionally graded plate

  • Farhad Abad (Department of Mechanical and Aerospace Engineering, Shiraz University of Technology) ;
  • Jafar Rouzegar (Department of Mechanical and Aerospace Engineering, Shiraz University of Technology) ;
  • Saeid Lotfian (Department of Naval Architecture, Ocean and Marine Engineering, University of Strathclyde)
  • Received : 2022.12.26
  • Accepted : 2023.03.02
  • Published : 2023.04.25
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Abstract

This study aims to extend the application of the spectral element method (SEM) to wave propagation and free vibration analysis of functionally graded (FG) plates integrated with thin piezoelectric layers, plates with tapered thickness and structure on elastic foundations. Also, the dynamic response of the smart FG plate under impact and moving loads is presented. In this paper, the dynamic stiffness matrix of the smart rectangular FG plate is determined by using the exact dynamic shape functions based on Mindlin plate assumptions. The low computational time and results' independence with the number of elements are two significant features of the SEM. Also, to prove the accuracy and efficiency of the SEM, results are compared with Abaqus simulations and those reported in references. Furthermore, the effects of boundary conditions, power-law index, piezoelectric layers thickness, and type of loading on the results are studied.

Keywords

References

  1. Abad, F. and Rouzegar, J. (2017), "An exact spectral element method for free vibration analysis of FG plate integrated with piezoelectric layers", Compos. Struct., 180, 696-708. https://doi.org/10.1016/j.compstruct.2017.08.030.
  2. Abad, F. and Rouzegar, J. (2019), "Exact wave propagation analysis of moderately thick Levy-type plate with piezoelectric layers using spectral element method", Thin Wall. Struct., 141, 319-331. https://doi.org/10.1016/j.tws.2019.04.007.
  3. Abbaspour, F. and Arvin, H. (2021), "Thermo-electro-mechanical buckling analysis of sandwich nanocomposite microplates reinforced with graphene platelets integrated with piezoelectric facesheets resting on elastic foundation", Comput. Math. Applicat., 101, 38-50. https://doi.org/10.1016/j.camwa.2021.09.009.
  4. Ahmed, R.A., Khalaf, B.S., Raheef, K.M., Fenjan, R.M. and Faleh, N.M. (2021), "Investigating dynamic response of nonlocal functionally graded porous piezoelectric plates in thermal environment", Steel Compos. Struct., 40(2), 243-254. https://doi.org/10.12989/scs.2021.40.2.243.
  5. Al-Osta, M.A. (2022), "Wave propagation investigation of a porous sandwich FG plate under hygrothermal environments via a new first-order shear deformation theory", Steel Compos. Struct., 43(1), 117-127. https://doi.org/10.12989/SCS.2022.43.1.117
  6. Askari Farsangi, M.A. and Saidi, A.R. (2012), "Levy type solution for free vibration analysis of functionally graded rectangular plates with piezoelectric layers", Smart Mater. Struct., 21(9), 094017. https://doi.org/10.1088/0964-1726/21/9/094017.
  7. Azandariani, M.G., Gholami, M. and Zare, E. (2022), "Development of spectral element method for free vibration of axially-loaded functionally-graded beams using the first-order shear deformation theory", Eur. J. Mech. A Solids, 104759. https://doi.org/10.1016/j.euromechsol.2022.104759.
  8. Baferani, A.H., Saidi, A. and Jomehzadeh, E. (2011), "An exact solution for free vibration of thin functionally graded rectangular plates", Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science. 225(3), 526-536. https://doi.org/10.1243/09544062JMES2171
  9. Ebrahimi, F. and Barati, M.R. (2016), "A nonlocal higher-order refined magneto-electro-viscoelastic beam model for dynamic analysis of smart nanostructures", Int. J. Eng. Sci., 107, 183-196. https://doi.org/10.1016/j.ijengsci.2016.08.001
  10. Ebrahimi, F. and Barati, M.R. (2018), "Vibration analysis of smart piezoelectrically actuated nanobeams subjected to magnetoelectrical field in thermal environment", J. Vib. Control, 24(3), 549-564. https://doi.org/10.1177/1077546316646239.
  11. Farsangi, M.A. and Saidi, A. (2012), "Levy type solution for free vibration analysis of functionally graded rectangular plates with piezoelectric layers", Smart Mater. Struct., 21(9), 094017.
  12. Farsangi, M.A., Saidi, A. and Batra, R. (2013), "Analytical solution for free vibrations of moderately thick hybrid piezoelectric laminated plates", J. Sound Vib., 332(22), 5981-5998. https://doi.org/10.1016/j.jsv.2013.05.010.
  13. Fazeli, S., Stokes-Griffin, C., Gilbert, J. and Compston, P. (2021), "An analytical solution for the vibrational response of stepped smart cross-ply laminated composite beams with experimental validation", Compos. Struct., 266, 113823. https://doi.org/10.1016/j.compstruct.2021.113823.
  14. Fenjan, R.M., Ahmed, R.A. and Faleh, N.M. (2021), "Post-buckling analysis of imperfect nonlocal piezoelectric beams under magnetic field and thermal loading", Struct. Eng. Mech. 78(1), 15-22. https://doi.org/10.12989/sem.2021.78.1.015.
  15. Fenjan, R.M., Ahmed, R.A., Faleh, N.M. and Hani, FM (2020), "Static stability analysis of smart nonlocal thermo-piezomagnetic plates via a quasi-3D formulation", Smart Struct. Syst., 26(1), 77-87. https://doi.org/10.12989/sss.2020.26.1.077.
  16. Hosseini-Hashemi, S., Taher, H.R.D., Akhavan, H. and Omidi, M. (2010), "Free vibration of functionally graded rectangular plates using first-order shear deformation plate theory", Appl. Math. Model., 34(5), 1276-1291. https://doi.org/10.1016/j.apm.2009.08.008.
  17. Jiang, W.-W., Gao, X.-W., Xu, B.-B. and Lv, J. (2021), "Analysis of piezoelectric problems using zonal free element method", Eng. Anal. Bound. Elem., 127, 40-52. https://doi.org/10.1016/j.enganabound.2021.03.010.
  18. Joglekar, D.M. and Mitra, M. (2016), "Analysis of flexural wave propagation through beams with a breathing crack using wavelet spectral finite element method", Mech. Syst. Signal Process., 76, 576-591. https://doi.org/10.1016/j.ymssp.2016.02.010.
  19. Khalili, A., Jha, R. and Samaratunga, D. (2017), "The Wavelet Spectral Finite Element-based user-defined element in Abaqus for wave propagation in one-dimensional composite structures", Simulation, 93(5), 397-408. https://doi.org/10.1177/0037549716687377.
  20. Koizumi, M. (1993), "The concept of FGM", Ceramic Transactions, 34, 3-10.
  21. Kulkarni, H., Zohaib, K., Khusru, A. and Shravan Aiyappa, K. (2018), "Application of piezoelectric technology in automotive systems", Mater. Today: Proc., 5(10, Part 1), 21299-21304. https://doi.org/10.1016/j.matpr.2018.06.532.
  22. Kulkarni, R.B., Gopalakrishnan, S. and Trikha, M. (2022), "Material property identification in composite structures using time domain spectral elements", Compos. Struct., 292, 115656.
  23. Lee, U. (2009), Spectral Element Method in Structural Dynamics, John Wiley & Sons
  24. Liu, C., Yu, J., Zhang, B., Zhang, X. and Elmaimouni, L. (2021), "Analysis of Lamb wave propagation in a functionally graded piezoelectric small-scale plate based on the modified couple stress theory", Compos. Struct., 265, 113733. https://doi.org/10.1016/j.compstruct.2021.113733.
  25. Liu, J., Zhang, X., Wang, J., Gu, L., Chu, P.K. and Yu, X.-F. (2022), "Global structure search for new 2D PtSSe allotropes and their potential for thermoelectirc and piezoelectric applications", Chem. Phys. Letters, 805, 139913.
  26. Liu, X. (2016), "Spectral dynamic stiffness formulation for inplane modal analysis of composite plate assemblies and prismatic solids with arbitrary classical/nonclassical boundary conditions", Compos. Struct., 158, 262-280. https://doi.org/10.1016/j.compstruct.2016.09.019.
  27. Liu, X., Kassem, H. and Banerjee, J. (2016), "An exact spectral dynamic stiffness theory for composite plate-like structures with arbitrary non-uniform elastic supports, mass attachments and coupling constraints", Compos. Struct., 142, 140-154. https://doi.org/10.1016/j.compstruct.2016.01.074.
  28. Lv, J., Shao, M., Cui, M. and Gao, X. (2019), "An efficient collocation approach for piezoelectric problems based on the element differential method", Compos. Struct., 230, 111483. https://doi.org/10.1016/j.compstruct.2019.111483.
  29. Manna, M. (2006), "A sub-parametric shear deformable element for free vibration analysis of thick/thin rectangular plates with tapered thickness", Appl. Mech. Eng., 11(4), 901.
  30. Martinez-Ayuso, G., Friswell, M.I., Khodaparast, H.H., Roscow, JI and Bowen, C.R. (2019), "Electric field distribution in porous piezoelectric materials during polarization", Acta Materialia. 173, 332-341. https://doi.org/10.1016/j.actamat.2019.04.021
  31. Mirjavadi, S.S., Forsat, M., Barati, M.R. and Hamouda, A.S. (2022), "Geometrically nonlinear vibration analysis of eccentrically stiffened porous functionally graded annular spherical shell segments", Mech. Base. Des. Struct. Mach., 50(6), 2206-2220. https://doi.org/10.1080/15397734.2020.1771729
  32. Mlzusawa, T. (1993), "Vibration of rectangular Mindlin plates with tapered thickness by the spline strip method", Comput. Struct., 46(3), 451-463. https://doi.org/10.1016/0045-7949(93)90215-Y.
  33. Mokhtari, A., Mirdamadi, H.R. and Ghayour, M. (2017), "Wavelet-based spectral finite element dynamic analysis for an axially moving Timoshenko beam", Mech. Syst. Signal Process., 92, 124-145. https://doi.org/10.1016/j.ymssp.2017.01.029.
  34. Nanda, N. and Kapuria, S. (2015), "Spectral finite element for wave propagation analysis of laminated composite curved beams using classical and first order shear deformation theories", Compos. Struct., 132, 310-320. https://doi.org/10.1016/j.compstruct.2015.04.061.
  35. Narayanan, G. and Beskos, D. (1978), "Use of dynamic influence coefficients in forced vibration problems with the aid of fast Fourier transform", Comput. Struct., 9(2), 145-150. https://doi.org/10.1016/0045-7949(78)90132-3.
  36. Newland, D.E. (2012), An introduction to random vibrations, spectral & wavelet analysis, Courier Corporation
  37. Panda, S., Hajra, S., Mistewicz, K., In-na, P., Sahu, M., Rajaitha, P.M. and Kim, H.J. (2022), "Piezoelectric energy harvesting systems for biomedical applications", Nano Energy, 100, 107514. https://doi.org/10.1016/j.nanoen.2022.107514.
  38. Rouzegar, J. and Abad, F. (2015), "Free vibration analysis of FG plate with piezoelectric layers using four-variable refined plate theory", Thin Wall. Struct., 89, 76-83. https://doi.org/10.1016/j.tws.2014.12.010.
  39. Rouzegar, J., Lotfavar, A. and Abad, F. (2015), "Free vibration analysis of FG plate with piezoelectric layers on elastic foundation using refined shear deformation theory", The 23rd Annual International Conference on Mechanical Engineering-ISME2015. Tehran, May.
  40. Shirmohammadi, F., Bahrami, S., Saadatpour, M.M. and Esmaeily, A. (2015), "Modeling wave propagation in moderately thick rectangular plates using the spectral element method", Appl. Math. Model., 39(12), 3481-3495. https://doi.org/10.1016/j.apm.2014.11.044.
  41. Szilard, R. (2004), "Theories and applications of plate analysis: classical, numerical and engineering methods", Appl. Mech. Rev., 57(6), B32-B33. https://doi.org/10.1115/1.1849175
  42. Taherifar, R., Zareei, S.A., Bidgoli, M.R. and Kolahchi, R. (2020), "Seismic analysis in pad concrete foundation reinforced by nanoparticles covered by smart layer utilizing plate higher order theory", Steel Compos. Struct., Int. J., 37(1), 99-115.
  43. Tran, H.-Q., Vu, V.-T. and Tran, M.-T. (2023), "Free vibration analysis of piezoelectric functionally graded porous plates with graphene platelets reinforcement by pb-2 Ritz method", Compos. Struct., 305, 116535. https://doi.org/10.1016/j.compstruct.2022.116535.