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Prediction of vibration response of functionally graded sandwich plates by zig-zag theory

  • Simmi, Gupta (Department of Civil Engineering, National Institute of Technology) ;
  • H.D., Chalak (Department of Civil Engineering, National Institute of Technology)
  • Received : 2022.05.25
  • Accepted : 2022.11.07
  • Published : 2022.11.25
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Abstract

This study is aimed to accurately predict the vibration response of two types of functionally graded sandwich plates, one with FGM core and another with FGM face sheets. The gradation in FGM layer is quantified by exponential method. An efficient zig-zag theory is used and the zigzag impacts are established via a linear unit Heaviside step function. The present theory fulfills interlaminar transverse stress continuity at the interface and zero condition at the top and bottom surfaces of the plate for transverse shear stresses. Nine-noded C-0 FE having 8DOF/node is utilized throughout analysis. The present model is free from the obligation of any penalty function or post-processing technique and hence is computationally efficient. Numerical results have been presented on the free vibration behavior of sandwich FGM for different end conditions, lamination schemes and layer orientations. The applicability of present model is confirmed by comparing with published results. Several new results are also specified, which will serve as the benchmark for future studies.

Keywords

Acknowledgement

First author of this paper was financially supported jointly by MHRD, GoI, and Director, NIT Kurukshetra, through a Ph.D. scholarship grant (2K18/NITK/PHD/6180093).

References

  1. Al-Fatlawi, A., Jarmai, K. and Kovacs, G. (2021), "Optimal design of a lightweight composite sandwich plate used for airplane containers", Struct. Eng. Mech., 78(5), 611-622. https://doi.org/10.12989/sem.2021.78.5.611.
  2. Anderson, T.A. (2003), "A 3-D elasticity solution for a sandwich composite with functionally graded core subjected to transverse loading by a rigid sphere", Compos. Struct., 60(3), 265-274. https://doi.org/10.1016/S0263-8223(03)00013-8.
  3. Antony, S., Cherouat, A. and Montay, G. (2019), "Hemp fibre woven fabric /polypropylene based honeycomb sandwich structure for aerospace applications", Adv. Aircraft Spacecraft Sci., 6(2), 87-103. https://doi.org/10.12989/aas.2019.6.2.087.
  4. Averill, R.C. (1994), "Static and dynamic response of moderately thick laminated beams with damage", Compos. Eng. J., 4, 381-395. https://doi.org/10.1016/S0961-9526(09)80013-0.
  5. Belabed, Z., Bousahla, A.A., Houari, M.S.A., Tounsi, A. and Mahmoud, S.R. (2018), "A new 3-unknown hyperbolic shear deformation theory for vibration of functionally graded sandwich plate", Earthq. Struct., 14(2), 103-115. https://doi.org/10.12989/eas.2018.14.2.103.
  6. Benferhat, R., Daouadji, T.H. and Abderezak, R. (2021), "Effect of porosity on fundamental frequencies of FGM sandwich plates", Compos. Mater. Eng., 3(1), 25-40. https://doi.org/10.12989/cme.2021.3.1.025.
  7. Brischetto, S., Carrera, E. and Demasi, L. (2009), "Improved bending analysis of sandwich plates using a zig-zag function", Compos. Struct., 89(3), 408-415. https://doi.org/10.1016/j.compstruct.2008.09.001.
  8. Carrera, E. (2003), "Historical review of zig-zag theories for multilayered plates and shells", Appl. Mech. Rev., 56(3), 287-308. https://doi.org/10.1115/1.1557614.
  9. Carrera, E. (2004), "On the use of the Murakami's zig-zag function in the modeling of layered plates and shells", Comput. Struct., 82(7-8), 541-554. https://doi.org/10.1016/j.compstruc.2004.02.006.
  10. Chakrabarti, A., Chalak, H.D., Iqbal, M.A. and Sheikh, A.H. (2011), "A new FE model based on higher order zigzag theory for the analysis of laminated sandwich beam with soft core", Compos. Struct., 93(2), 271-279. https://doi.org/10.1016/j.compstruct.2010.08.031.
  11. Chakraverty, S. and Pradhan, K.K. (2014), "Free vibration of exponential functionally graded rectangular plates in thermal environment with general boundary conditions", Aerosp. Sci. Technol., 36, 132-156. https://doi.org/10.1016/j.ast.2014.04.005.
  12. Chalak, H.D., Chakrabarti, A., Iqbal, M.A. and Sheikh, A. H. (2013), "Free vibration analysis of laminated soft core sandwich plates", J. Vib. Acoust., 135(1), 011013. https://doi.org/10.1115/1.4007262.
  13. Chareonsuk, J. and Vessakosol, P. (2011), "Numerical solutions for functionally graded solids under thermal and mechanical loads using a high-order control volume finite element method", Appl. Therm. Eng., 31(2-3), 213-227. https://doi.org/10.1016/j.applthermaleng.2010.09.001.
  14. Cho, Y.B. and Averill, R.C. (2000), "First order zigzag sub-laminate plate theory and finite element model for laminated composite and sandwich panels", Compos. Struct., 50, 1-15. https://doi.org/10.1016/S0263-8223(99)00063-X.
  15. Demasi, L. (2008), "∞3 Hierarchy plate theories for thick and thin composite plates: the generalized unified formulation", Compos. Struct., 84(3), 256-270. https://doi.org/10.1016/j.compstruct.2007.08.004.
  16. Di Sciuva, M. (1985), "Development of anisotropic multilayered shear deformable rectangular plate element", Comput. Struct., 21, 789-96. https://doi.org/10.1016/0045-7949(85)90155-5.
  17. Di Sciuva, M. (1993), "A general quadrilateral multilayered plate element with continuous interlaminar stresses", Comput. Struct., 47, 91-105. https://doi.org/10.1016/0045-7949(93)90282-I.
  18. Ebrahimi, F. and Barati, M.R. (2017), "A third-order parabolic shear deformation beam theory for nonlocal vibration analysis of magneto-electro-elastic nanobeams embedded in two-parameter elastic foundation", Adv. Nano Res., 59(4), 313-336. https://doi.org/10.12989/anr.2017.5.4.313.
  19. Ebrahimi, M.J. and Najafizadeh, M.M. (2014), "Free vibration analysis of two-dimensional functionally graded cylindrical shells", Appl. Math Model., 38(1), 308-324. https://doi.org/10.1016/j.apm.2013.06.015.
  20. El-Galy, I.M., Bassiouny, I.S. and Mahmoud, H.A. (2019), "Functionally graded materials classifications and development trends from industrial point of view", S.N. Appl. Sci., 1(11), 1-23. https://doi.org/10.1007/s42452-019-1413-4.
  21. Garg, A. and Chalak, H.D. (2019), "A review on analysis of laminated composite and sandwich structures under hygrothermal conditions", Thin Wall. Struct., 142, 205-226. https://doi.org/10.1016/j.tws.2019.05.005.
  22. Garg, A., Belarbi, M.O., Chalak, H.D. and Chakrabarti, A. (2021), "A review of the analysis of sandwich FGM structures", Compos. Struct., 258, 113427. https://doi.org/10.1016/j.compstruct.2020.113427.
  23. Garg, A., Chalak, H.D., Li, L., Belarbi, M.O., Sahoo, R. and Mukhopadhyay, T. (2022), "Vibration and buckling analyses of sandwich plates containing functionally graded metal foam core", Acta Mechanica Solida Sinica, 1-16. https://doi.org/10.1007/s10338-021-00295-z.
  24. Hirane, H., Belarbi, M.O., Houari, M.S.A. and Tounsi, A. (2021), "On the layerwise finite element formulation for static and free vibration analysis of functionally graded sandwich plates", Eng. Comput., 1-29. https://doi.org/10.1007/s00366-020-01250-1.
  25. Khalafi, V. and Fazilati, J. (2021), "Free vibration analysis of functionally graded plates containing embedded curved cracks", Struct. Eng. Mech., 79(2), 157-168. https://doi.org/10.12989/sem.2021.79.2.157.
  26. Koizumi, M. (1997), "FGM activities in Japan", Compos. Part B, 28(1-2), 1-4. https://doi.org/10.1016/S1359-8368(96)00016-9.
  27. Li, L. and Hu, Y. (2016), "Nonlinear bending and free vibration analyses of nonlocal strain gradient beams made of functionally graded material", Int. J. Eng. Sci., 107, 77-97. https://doi.org/10.1016/j.ijengsci.2016.07.011.
  28. Meksi, R., Benyoucef, S., Mahmoudi, A., Tounsi, A., Adda Bedia, E.A. and Mahmoud, S.R. (2019), "An analytical solution for bending, buckling and vibration responses of FGM sandwich plates", J. Sandw. Struct. Mater., 21(2), 727-757. https://doi.org/10.1177/1099636217698443.
  29. Moleiro, F., Correia, V.F., Araujo, A.L., Soares, C.M., Ferreira, A.J.M. and Reddy, J.N. (2019), "Deformations and stresses of multilayered plates with embedded functionally graded material layers using a layerwise mixed model", Compos. Part B: Eng., 156, 274-291. https://doi.org/10.1016/j.compositesb.2018.08.095.
  30. Murakami, H. (1986), "Laminated composite plate theory with improved in-plane responses.", J. Appl. Mech., 53(3), 661-666. https://doi.org/10.1115/1.3171828.
  31. Neves, A.M.A., Ferreira, A.J., Carrera, E., Cinefra, M., Jorge, R.M.N. and Soares, C.M.M. (2012), "Static analysis of functionally graded sandwich plates according to a hyperbolic theory considering Zig-Zag and warping effects", Adv. Eng. Softw., 52, 30-43. https://doi.org/10.1016/j.advengsoft.2012.05.005.
  32. Neves, A.M.A., Ferreira, A.J.M., Carrera, E., Cinefra, M., Jorge, R.M.N., Mota Soares, C.M. and Araujo, A.L. (2017), "Influence of zig-zag and warping effects on buckling of functionally graded sandwich plates according to sinusoidal shear deformation theories", Mech. Adv. Mater. Struct., 24(5), 360-376. https://doi.org/10.1080/15376494.2016.1191095.
  33. Nguyen, K., Thai, H.T. and Vo, T. (2015), "A refined higher-order shear deformation theory for bending, vibration and buckling analysis of functionally graded sandwich plates", Steel Compos. Struct., 18(1), 91-120. https://doi.org/10.12989/scs.2015.18.1.091.
  34. Owoputi, A.O., Inambao, F.L. and Ebhota, W.S. (2018), "A review of functionally graded materials: fabrication processes and applications", Int. J. Appl. Eng. Res., 13(23), 16141-16151.
  35. Pandey, S. and Pradyumna, S. (2018), "Analysis of functionally graded sandwich plates using a higher-order layerwise theory", Compos. Part B: Eng., 153, 325-336. https://doi.org/10.1016/j.compositesb.2018.08.121.
  36. Reddy, J. (2000), "Analysis of functionally graded plates", Int. J. Numer. Meth. Eng., 47(1-3), 663-684. https://doi.org/10.1002/(SICI)1097-0207(20000110/30)47:1/3<663::AID-NME787>3.0.CO;2-8.
  37. Sahouane, A., Hadji, L. and Bourada, M. (2019), "Numerical analysis for free vibration of functionally graded beams using an original HSDBT", Earthq. Struct., 17(1), 31-37. https://doi.org/10.12989/eas.2019.17.1.031.
  38. Shariyat, M. and Alipour, M.M. (2015), "Novel layerwise shear correction factors for zigzag theories of circular sandwich plates with functionally graded layers", Lat. Am. J. Solid. Struct., 12(7), 1362-1396. https://doi.org/10.1590/1679-78251477.
  39. Sharma, R., Jadon, V. and Singh, B. (2015), "A review on the finite element methods for heat conduction in functionally graded materials", J. Inst. Eng., 96(1), 73-81. https://doi.org/10.1007/s40032-014-0125-1.
  40. Swaminathan, K., Naveenkumar, D.T., Zenkour, A.M. and Carrera, E. (2015), "Stress, vibration and buckling analyses of FGM plates-A state-of-the-art review", Compos. Struct., 120, 10-31. https://doi.org/10.1016/j.compstruct.2014.09.070.
  41. Tounsi, A., Houari, M.S.A. and Bessaim, A. (2016), "A new 3-unknowns non-polynomial plate theory for buckling and vibration of functionally graded sandwich plate", Struct. Eng. Mech., 60(4), 547-565. https://doi.org/10.12989/sem.2016.60.4.547.
  42. Vel, S.S. and Batra, R. (2004), "Three-dimensional exact solution for the vibration of functionally graded rectangular plates", J. Sound Vib., 272(3-5), 703-730. https://doi.org/10.1016/S0022-460X(03)00412-7.
  43. Woodward, B. and Kashtalyan, M. (2010), "Bending response of sandwich panels with graded core: 3D elasticity analysis", Mech. Adv. Mater. Struct., 17(8), 586-594. https://doi.org/10.1080/15376494.2010.517728.
  44. Zenkour, A.M. (2005), "A comprehensive analysis of functionally graded sandwich plates: Part 1-Deflection and stresses", Int. J. Solid. Struct., 42(18-19), 5224-5242. https://doi.org/10.1016/j.ijsolstr.2005.02.015.
  45. Zenkour, A.M. (2005), "A comprehensive analysis of functionally graded sandwich plates: Part 2-Buckling and free vibration", Int. J. Solid. Struct., 42(18-19), 5243-5258. https://doi.org/10.1016/j.ijsolstr.2005.02.016.