Structural Engineering and Mechanics

Techno-Press (테크노프레스)
권호 표지
DOI QR코드

DOI QR Code

Stability and vibration behavior of cellular plates with different cell arrays using a numerical approach

  • Chuan-Xiong Li (College of Civil Construction and Environment, Hubei University of Technology)
  • Received : 2021.05.24
  • Accepted : 2022.08.10
  • Published : 2023.03.25
⟨ Previous Next ⟩

Abstract

In this paper, the shape factors of cellular meta-material plates (MMPs) having diverse cell arrays have been determined as the first attempt to finally examine their stability and vibrational frequencies. The MMPs are actually constructed from cylindrical or cubic cellular cores and two face sheets. Sandwich-like MMPs with circular and square holes in the face sheets have been selected in such a way that the effective material properties depend on the cellular architectures. For verifying the frequency results, finite element (FE) simulations are done in Abaqus software. Several graphical results have been represented to explore the effects of cellular architectures on vibrational frequencies and dynamic responses of the MMPs. Also, the deflection-frequency and stability curves in the case of forced vibrations have been plotted for diverse cell arrays.

Keywords

References

  1. Abdeljaber, O., Avci, O. and Inman, D.J. (2016), "Active vibration control of flexible cantilever plates using piezoelectric materials and artificial neural networks", J. Sound Vib., 363, 33-53. https://doi.org/10.1016/j.jsv.2015.10.029.
  2. Abdelrahman, A.A., Abd-El-Mottaleb, H.E. and Eltaher, M.A. (2020), "On bending analysis of perforated microbeams including the microstructure effects", Struct. Eng. Mech., 76(6), 765. http://doi.org/10.12989/sem.2020.76.6.765.
  3. Al-Furjan, M.S.H., Habibi, M., Shan, L. and Tounsi, A. (2021), "On the vibrations of the imperfect sandwich higher-order disk with a lactic core using generalize differential quadrature method", Compos. Struct., 257, 113150. https://doi.org/10.1016/j.compstruct.2020.113150.
  4. Barati, M.R. and Shahverdi, H. (2017), "An analytical solution for thermal vibration of compositionally graded nanoplates with arbitrary boundary conditions based on physical neutral surface position", Mech. Adv. Mater. Struct., 24(10), 840-853. https://doi.org/10.1080/15376494.2016.1196788.
  5. Barati, M.R. and Shahverdi, H. (2022), "Equivalent material properties of perforated metamaterials based on relative density concept", Steel Compos. Struct., 44(5), 685. https://doi.org/10.12989/scs.2022.44.5.671.
  6. Becker, W. (1998), "The in-plane stiffnesses of a honeycomb core including the thickness effect", Arch. Appl. Mech., 68(5), 334-341. https://doi.org/10.1007/s004190050169.
  7. Bendenia, N., Zidour, M., Bousahla, A.A., Bourada, F., Tounsi, A., Benrahou, K.H. and Tounsi, A. (2020), "Deflections, stresses and free vibration studies of FG-CNT reinforced sandwich plates resting on Pasternak elastic foundation.", Comput. Concrete, 26(3), 213-226. http://doi.org/10.12989/cac.2020.26.3.213.
  8. Bryan, J., Lu, E., Davami, K., Cortes, J., Lin, C., Lilley, D.E. and Bargatin, I. (2016), Two-layer Plate Mechanical Metamaterials, Hilton Head Workshop.
  9. Cai, W. and Shalaev, V.M. (2010), Optical Metamaterials, Vol. 10, Springer, New York.
  10. Del Vescovo, D. and Giorgio, I. (2014), "Dynamic problems for metamaterials: Review of existing models and ideas for further research", Int. J. Eng. Sci., 80, 153-172. https://doi.org/10.1016/j.ijengsci.2014.02.022.
  11. Donaldson, L. (2013), "Metamaterials help thermal flow", Mater. Today, 6(16), 207. https://doi.org/10.1016/j.mattod.2013.06.015.
  12. Findeisen, C., Forest, S., Hohe, J. and Gumbsch, P. (2020), "Discrete and continuum modelling of size effects in architectured unstable metamaterials", Contin. Mech. Thermodyn., 32, 1629-1645. https://doi.org/10.1007/s00161-020-00870-8.
  13. Gibson, L.J. and Ashby, M.F. (1997), Cellular Solids: Structures and Properties, 2nd Edition, Cambridge University Press, Cambridge, UK.
  14. Gibson, L.J., Ashby, M.F., Schajer, G.S. and Robertson, C.I. (1982), "The mechanics of two-dimensional cellular materials", Proc. Roy. Soc. London. A. Math. Phys. Sci., 382(1782), 25-42. https://doi.org/10.1098/rspa.1982.0087.
  15. Hohe, J. and Becker, W. (1999), "Effective elastic properties of triangular grid structures", Compos. Struct., 45(2), 131-145. https://doi.org/10.1016/S0263-8223(99)00016-1.
  16. Huang, H.H., Sun, C.T. and Huang, G.L. (2009), "On the negative effective mass density in acoustic metamaterials", Int. J. Eng. Sci., 47(4), 610-617. https://doi.org/10.1016/j.ijengsci.2008.12.007.
  17. Jiao, P. and Alavi, A.H. (2018), "Buckling analysis of graphene-reinforced mechanical metamaterial beams with periodic webbing patterns", Int. J. Eng. Sci., 131, 1-18. https://doi.org/10.1016/j.ijengsci.2018.06.005.
  18. Khan, M.K., Baig, T. and Mirza, S. (2012), "Experimental investigation of in-plane and out-of-plane crushing of aluminum honeycomb", Mater. Sci. Eng.: A, 539, 135-142. https://doi.org/10.1016/j.msea.2012.01.070.
  19. Kim, B. and Christensen, R.M. (2000), "Basic two-dimensional core types for sandwich structures", Int. J. Mech. Sci., 42(4), 657-676. https://doi.org/10.1016/S0020-7403(99)00028-4.
  20. Leissa, A.W. (1973), "The free vibration of rectangular plates", J. Sound Vib., 31(3), 257-293. https://doi.org/10.1016/S0022-460X(73)80371-2.
  21. Li, H., Li, Z., Safaei, B., Rong, W., Wang, W., Qin, Z. and Xiong, J. (2021a), "Nonlinear vibration analysis of fiber metal laminated plates with multiple viscoelastic layers", Thin Wall. Struct., 168, 108297. https://doi.org/10.1016/j.tws.2021.108297.
  22. Li, H., Li, Z., Xiao, Z., Wang, X., Xiong, J., Zhou, J. and Guan, Z. (2021d), "Development of an integrated model for prediction of impact and vibration response of hybrid fiber metal laminates with a viscoelastic layer", Int. J. Mech. Sci., 197, 106298. https://doi.org/10.1016/j.ijmecsci.2021.106298.
  23. Li, H., Ren, X., Yu, C., Xiong, J., Wang, X. and Zhao, J. (2021c), "Investigation of vibro-acoustic characteristics of FRP plates with porous foam core", Int. J. Mech. Sci., 209, 106697. https://doi.org/10.1016/j.ijmecsci.2021.106697.
  24. Li, H., Wang, W., Wang, Q., Han, Q., Liu, J., Qin, Z. and Wang, X. (2022), "Static and dynamic performances of sandwich plates with magnetorheological elastomer core: Theoretical and experimental studies", J. Sandw. Struct. Mater., 24(3), 1556-1579. https://doi.org/10.1177/10996362211053620.
  25. Li, H., Wang, X., Hu, X., Xiong, J., Han, Q., Wang, X. and Guan, Z. (2021b), "Vibration and damping study of multifunctional grille composite sandwich plates with an IMAS design approach", Compos. Part B: Eng., 223, 109078. https://doi.org/10.1016/j.compositesb.2021.109078.
  26. Li, X. and Gao, H. (2016), "Mechanical metamaterials: Smaller and stronger", Nat. Mater., 15(4), 373-374. https://doi.org/10.1038/nmat4591.
  27. Li, Y., Zi, H., Wu, X. and Zhu, L. (2020), "Flexural wave propagation and vibration isolation characteristics of sandwich plate-type elastic metamaterials", J. Vib. Control, 27(13-14), 1443-1452. https://doi.org/10.1177/1077546320942689.
  28. Ma, G. and Sheng, P. (2016), "Acoustic metamaterials: From local resonances to broad horizons", Sci. Adv., 2(2), e1501595. https://doi.org/10.1126/sciadv.1501595.
  29. Merazka, B., Bouhadra, A., Menasria, A., Selim, M.M., Bousahla, A.A., Bourada, F. and Al-Zahrani, M.M. (2021), "Hygro-thermo-mechanical bending response of FG plates resting on elastic foundations", Steel Compos. Struct., 39(5), 631-643. http://doi.org/10.12989/scs.2021.39.5.631.
  30. Mokhtari, A.A., Lu, Y., Zhou, Q., Amirkhizi, A.V. and Srivastava, A. (2020), "Scattering of in-plane elastic waves at metamaterial interfaces", Int. J. Eng. Sci., 150, 103278. https://doi.org/10.1016/j.ijengsci.2020.103278.
  31. Nouh, M., Aldraihem, O. and Baz, A. (2015), "Wave propagation in metamaterial plates with periodic local resonances", J. Sound Vib., 341, 53-73. https://doi.org/10.1016/j.jsv.2014.12.030.
  32. Pacchioni, G. (2016), "Mechanical metamaterials: The strength awakens", Nat. Rev. Mater., 1(3), 1-1. https://doi.org/10.1038/natrevmats.2016.12.
  33. Ptochos, E. and Labeas, G. (2012), "Elastic modulus and Poisson's ratio determination of micro-lattice cellular structures by analytical, numerical and homogenisation methods", J. Sandw. Struct. Mater., 14(5), 597-626. https://doi.org/10.1177/1099636212444285.
  34. Rabhi, M., Benrahou, K.H., Kaci, A., Houari, M.S.A., Bourada, F., Bousahla, A.A. 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.
  35. Shahverdi, H. and Barati, M.R. (2017), "Vibration analysis of porous functionally graded nanoplates", Int. J. Eng. Sci., 120, 82-99. https://doi.org/10.1016/j.ijengsci.2017.06.008.
  36. Singh, S.J. and Harsha, S.P. (2021), "Free vibration analysis of sandwich plate with honeycomb core and FGM face sheets", Adv. Syst. Eng., 905-917. https://doi.org/10.1007/978-981-15-8025-3_85.
  37. Sobhy, M. (2020), "Differential quadrature method for magneto-hygrothermal bending of functionally graded graphene/Al sandwich-curved beams with honeycomb core via a new higher-order theory", J. Sandw. Struct. Mater., 23(5), 1662-1700. https://doi.org/10.1177/1099636219900668.
  38. Soleimani-Javid, Z., Arshid, E., Khorasani, M., Amir, S. and Tounsi, A. (2021), "Size-dependent flexoelectricity-based vibration characteristics of honeycomb sandwich plates with various boundary conditions", Adv. Nano Res., 10(5), 449-460. http://doi.org/10.12989/anr.2021.10.5.449.
  39. Surjadi, J.U., Gao, L., Du, H., Li, X., Xiong, X., Fang, N.X. and Lu, Y. (2019), "Mechanical metamaterials and their engineering applications", Adv. Eng. Mater., 21(3), 1800864. https://doi.org/10.1002/adem.201800864.
  40. Wadley, H.N. (2006), "Multifunctional periodic cellular metals", Philos. Trans. Roy. Soc. A: Math., Phys. Eng. Sci., 364(1838), 31-68. https://doi.org/10.1098/rsta.2005.1697.
  41. Wang, Y.J., Zhang, Z.J., Xue, X.M. and Zhang, L. (2019), "Free vibration analysis of composite sandwich panels with hierarchical honeycomb sandwich core", Thin Wall. Struct., 145, 106425. https://doi.org/10.1016/j.tws.2019.106425.
  42. Zhang, Q., Yang, X., Li, P., Huang, G., Feng, S., Shen, C. and Lu, T.J. (2015), "Bioinspired engineering of honeycomb structure-Using nature to inspire human innovation", Progr. Mater. Sci., 74, 332-400. https://doi.org/10.1016/j.pmatsci.2015.05.001.
  43. Zhang, Z.J., Han, B., Zhang, Q.C. and Jin, F. (2017). Free vibration analysis of sandwich beams with honeycomb-corrugation hybrid cores", Compos. Struct., 171, 335-344. https://doi.org/10.1016/j.compstruct.2017.03.045.
  44. Zhao, J., Gao, Z., Li, H., Wong, P.K. and Xie, Z. (2022), "Semiactive control for the nonlinear vibration suppression of square-celled sandwich plate with multi-zone MRE filler core", Mech. Syst. Signal Pr., 172, 108953. https://doi.org/10.1016/j.ymssp.2022.108953.
  45. Zhu, R., Huang, H.H., Huang, G.L. and Sun, C.T. (2011), "Microstructure continuum modeling of an elastic metamaterial", Int. J. Eng. Sci., 49(12), 1477-1485. https://doi.org/10.1016/j.ijengsci.2011.04.005.
  46. Zhu, X., Zhang, J., Zhang, W. and Chen, J. (2019), "Vibration frequencies and energies of an auxetic honeycomb sandwich plate", Mech. Adv. Mater. Struct., 26(23), 1951-1957. https://doi.org/10.1080/15376494.2018.1455933.